Machine Kinematics Pune University MCQs

 This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Kinematics of Motion”.

1. The unit of linear acceleration is

a) kg-m

b) m/s

c) m/s 2

d) rad/s 2

Answer: c

Explanation: Linear acceleration is defined as the rate of change of linear velocity of a body with respect to the time.

i.e a = v/t

and unit of velocity is m/s

so, unit of linear acceleration becomes m/s 2 .

2. The angular velocity  of a body rotating at N r.p.m. is

a) π N/60

b) 2 π N/60

c) π N/120

d) π N/180

Answer: b

Explanation: Angular velocity is defined as the rate of change of angular displacement with respect to time. It is usually expressed by a Greek letter ω .

Mathematically, angular velocity,

ω =dθ/dt

If a body is rotating at the rate of N r.p.m. , then its angular velocity,

ω = 2πΝ / 60 rad/s

3. The linear velocity of a body rotating at ω rad/s along a circular path of radius r is given by

a) ω.r

b) ω/r

c) ωs 2 .r

d) ωs 2 /r

Answer: a

Explanation: If the displacement is along a circular path, then the direction of linear velocity at any instant is along the tangent at that point.

therefore, the linear velocity will be

ω.r

4. When a particle moves along a straight path, then the particle has

a) tangential acceleration only

b) centripetal acceleration only

c) both tangential and centripetal acceleration

d) none of the mentioned

Answer: a

Explanation: The acceleration of a particle at any instant moving along a circular path in a direction tangential to that instant, is known as tangential component of acceleration or tangential acceleration.

5. When a particle moves with a uniform velocity along a circular path, then the particle has

a) tangential acceleration only

b) centripetal acceleration only

c) both tangential and centripetal acceleration

d) none of the mentioned

Answer: b

Explanation: The acceleration of a particle at any instant moving along a circular path in a direction normal to the tangent at that instant and directed towards the centre of the circular path is known as normal component of the acceleration or normal acceleration. It is also called radial or centripetal acceleration.

6. When the motion of a body is confined to only one plane, the motion is said to be

a) plane motion

b) rectilinear motion

c) curvilinear Motion

d) none of the mentioned

Answer: a

Explanation: When the motion of a body is confined to only one plane, the motion is said to be plane motion. The plane motion may be either rectilinear or curvilinear.

7. _______________ is the simplest type of motion and is along a straight line path.

a) plane motion

b) rectilinear motion

c) curvilinear Motion

d) none of the mentioned

Answer: b

Explanation: Rectilinear Motion is the simplest type of motion and is along a straight line path. Such a motion is also known as translatory motion.

8. _________________ is the motion along a curved path.

a) plane motion

b) rectilinear motion

c) curvilinear Motion

d) none of the mentioned

Answer: c

Explanation: Curvilinear Motion is the motion along a curved path. Such a motion, when confined to one plane, is called plane curvilinear motion.

9. Displacement of a body is a ___________ quantity.

a) scalar

b) vector

c) scalar and vector

d) none of the mentioned

Answer: b

Explanation: The displacement of a body is a vector quantity, as it has both magnitude and direction. Linear displacement may, therefore, be represented graphically by a straight line.

10. A train covers 60 miles between 2 p.m. and 4 p.m. How fast was it going at 3 p.m.?

a) 60 mph

b) 30 mph

c) 40 mph

d) 50 mph

Answer: b

Explanation: The speed is traveled distance  divided by traveled time :

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Linear Velocity – 1”.

1. The relative velocity of B with respect to A in a rigid link AB is

a) parallel to AB

b) perpendicular to AB

c) along AB

d) at 45 0

Answer: b

Explanation: The relative velocity of any two points on a rigid link is always normal to the line joining the two points.

2. The magnitude of linear velocity of a point B on a link AB relative to point A is

a) ω x AB

b) ω 2

c) ω 2 AB

d)  2

Answer: a

Explanation: None

3. The direction of linear velocity of any point on a link with respect to another point on the same link is

a) parallel to the link joining the points

b) perpendicular to the link joining the points

c) at 45 0 to the link joining the points

d) none of the mentioned

Answer: b

Explanation: The relative velocity of any two points on a rigid link is always normal to the line joining the two points.

4. The two links OA and OB are connected by a pin joint at O. If the link OA turns with angular velocity ω 1 rad/s in the clockwise direction and the link OB turns with angular velocity ω 2 rad/s in the anti-clockwise direction, then the rubbing velocity at the pin joint O is

a) ω 1 .ω 2 .r

b) (ω 1 -ω 2 )r

c) (ω 1 +ω 2 )r

d) (ω 1 -ω 2 )2r

Answer: c

Explanation: Consider two links OA and OB connected by a pin joint at O

Let ω 1 = Angular velocity of the link OA or the angular velocity of the point A with respect to O.

ω 2 = Angular velocity of the link OB or the angular velocity of the point B with respect to O, and

r = Radius of the pin.

According to the definition,

Rubbing velocity at the pin joint O

= (ω 1 – ω 2 ) r, if the links move in the same direction

= (ω 1 + ω 2 ) r, if the links move in the opposite direction

5. In the above question, if both the links OA and OB turns in clockwise direction, then the rubbing velocity at the pin joint O is

a) ω 1 .ω 2 .r

b) (ω 1 -ω 2 )r

c) (ω 1 +ω 2 )r

d) (ω 1 -ω 2 )2r

Answer: b

Explanation: Consider two links OA and OB connected by a pin joint at O

Let ω 1 = Angular velocity of the link OA or the angular velocity of the point A with respect to O.

ω 2 = Angular velocity of the link OB or the angular velocity of the point B with respect to O, and

r = Radius of the pin.

According to the definition,

Rubbing velocity at the pin joint O

= (ω 1 – ω 2 ) r, if the links move in the same direction

= (ω 1 + ω 2 ) r, if the links move in the opposite direction

6. ABCD is a four bar mechanism in which AB = 310mm and CD = 450mm. AB and CD are both perpendicular to the fixed link AD. If the velocity of B at this condition is v. Then the velocity of C is

a) v

v) 2/3 v

c) 3/2 v

d) 9/4 v

Answer: c

Explanation: Velocity at C = CD/AB x velocity at B

= 450/310 x v

= 3/2 v

7. A thin circular disc is rolling with a uniform linear speed, along a straight path on a plane surface. Which of the following statement is correct in this regard?

a) All points of the disc have the same velocity.

b) The centre of the disc has zero acceleration.

c) The centre of the disc has centrifugal acceleration.

d) The point on the disc making contact with the plane surface has zero acceleration.

Answer: b

Explanation: None

8. The component of the accelertion, parallel to the velocity of the particle, at the given instant is called

a) radial component

b) tangential component

c) coriolis component

d) none of the mentioned

Answer: b

Explanation: The centripetal or radial component, is perpendicular to the velocity of the particle at the given instant.

The tangential component, is parallel to the velocity of the particle at the given instant.

9. The component of the accelertion, perpendicular to the velocity of the particle, at the given instant is called

a) radial component

b) tangential component

c) coriolis component

d) none of the mentioned

Answer: a

Explanation: The centripetal or radial component, is perpendicular to the velocity of the particle at the given instant.

The tangential component, is parallel to the velocity of the particle at the given instant.

Answer: c

Explanation: None

This set of Machine Kinematics Interview Questions and Answers focuses on “Linear Velocity – 2”.

1. The unit of linear acceleration is

a) kg-m

b) m/s

c) m/s 2

d) rad/s 2

Answer: c

Explanation: Linear acceleration, a = dv/dt

unit of dv = m/s

and dt = s

therefore, dv/dt = m/s 2

2. The angular velocity  of a body rotating at N r.p.m. is

a) π N/60

b) 2 π N/60

c) π N/120

d) π N/180

Answer: b

Explanation: Angular velocity may be defined as the rate of change of angular displacement with respect to time. It is usually expressed by a Greek letter ω . Mathematically, angular velocity,

ω =dθ/dt

3. The linear velocity of a body rotating at ω rad/s along a circular path of radius r is given by

a) ω.r

b) ω/r

c) ω 2 .r

d) ω 2 /r

Answer: a

Explanation: Linear velocity = ω.r

4. When a particle moves along a straight path, then the particle has

a) tangential acceleration only

b) centripetal acceleration only

c) both tangential and centripetal acceleration

d) none of the mentioned

Answer: a

Explanation: When a particle moves along a straight path, then the radius of curvature is infinitely great. This means that v 2 /r is zero. In other words, there will be no normal or radial or centripetal acceleration. Therefore, the particle has only tangential acceleration.

5. When a particle moves with a uniform velocity along a circular path, then the particle has

a) tangential acceleration only

b) centripetal acceleration only

c) both tangential and centripetal acceleration

d) none of the mentioned

Answer: b

Explanation: When a particle moves with a uniform velocity, then dv/dt will be zero. In other words, there will be no tangential acceleration; but the particle will have only normal or radial or centripetal acceleration.

6. When the motion of a body is confined to only one plane, the motion is said to be

a) translatory motion

b) plane motion

c) culvilinear motion

d) none of the mentioned

Answer: b

Explanation: When the motion of a body is confined to only one plane, the motion is said to be plane motion. When the motion of a body is along a straight line path, it is called translatory motion. When the motion of a body is along a curved path, it is called culvilinear motion.

7. When the motion of a body is along a straight line path, it is called

a) translatory motion

b) plane motion

c) culvilinear motion

d) none of the mentioned

Answer: b

Explanation: When the motion of a body is confined to only one plane, the motion is said to be plane motion. When the motion of a body is along a straight line path, it is called translatory motion. When the motion of a body is along a curved path, it is called culvilinear motion.

Answer: b

Explanation: When the motion of a body is confined to only one plane, the motion is said to be plane motion. When the motion of a body is along a straight line path, it is called translatory motion. When the motion of a body is along a curved path, it is called culvilinear motion.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Linear Acceleration”.

1. The acceleration of a particle at any instant has two components, radial component and tangential component. These two components will be

a) parallel to each other

b) perpendicular to each other

c) inclined at 45 0

d) opposite to each other

Answer: b

Explanation: Both the components will be perpendicular to each other.

2. The centre of gravity of a coupler link in a four bar mechanism will experience

a) no acceleration

b) only linear acceleration

c) only angular acceleration

d) both linear and angular acceleration

Answer: d

Explanation: None

3. When a point moves along a straight line, its acceleration will have

a) radial component only

b) tangential component only

c) coriolis component only

d) radial and tangential components both

Answer: b

Explanation: The tangential component, is parallel to the velocity of the particle at the given instant.

The centripetal or radial component, is perpendicular to the velocity of the particle at the given instant.

4. When a point at the end of a link moves with constant angular velocity, its acceleration will have

a) radial component only

b) tangential component only

c) coriolis component only

d) radial and tangential components both

Answer: a

Explanation: The centripetal or radial component, is perpendicular to the velocity of the particle at the given instant.

The tangential component, is parallel to the velocity of the particle at the given instant.

5. In a shaper mechanism, the coriolis component of acceleration does not exists.

a) True

b) False

Answer: b

Explanation: In a shaper mechanism, the coriolis component of acceleration exists.

6. The tangential component of acceleration of the slider with respect to the coincident point on the link is called coriolis component of acceleration.

a) True

b) False

Answer: a

Explanation: When a point on one link is sliding along another rotating link, such as in quick return motion mechanism, then the coriolis component of the acceleration must be calculated.

7. The coriolis component of acceleration acts

a) along the sliding surface

b) perpendicular to the sliding surface

c) at 45 0 to the sliding surface

d) parallel to the sliding surface

Answer: b

Explanation: None

8. The coriolis component of acceleration is taken into account for

a) slider crank mechanism

b) four bar chain mechanism

c) quick return motion mechanism

d) all of the mentioned

Answer: c

Explanation: When a point on one link is sliding along another rotating link, such as in quick return motion mechanism, then the coriolis component of the acceleration must be calculated.

9. The coriolis component of acceleration depends upon

a) velocity of slider

b) angular velocity of the link

c) all of the mentioned

d) none of the mentioned

Answer: c

Explanation: None

10. A body in motion will be subjected to coriolis acceleration when that body is

a) in plane rotation with variable velocity

b) in plane translation with variable velocity

c) in plane motion which is a resultant of plane translation and rotation

d) restrained to rotate while sliding over another body

Answer: d

Explanation: When a point on one link is sliding along another rotating link, such as in quick return motion mechanism, then the coriolis component of the acceleration must be calculated.

11. A slider moves at a velocity v on a link revolving at ωrad/s. The coriolis component of acceleration is

a) ωv

b) 2ωv

c) ω 2 v

d) 2ωv 2

Answer: b

Explanation: None

12. The coriolis component of acceleration leads the sliding velocity by

a) 45 0

b) 90 0

c) 135 0

d) 180 0

Answer: b

Explanation: The direction of coriolis component of acceleration is obtained by rotating v, at 90°, about its origin in the same direction as that of ω.

Answer: c

Explanation: The direction of coriolis component of acceleration is obtained by rotating v, at 90°, about its origin in the same direction as that of ω.

This set of Machine Kinematics Questions and Answers for Freshers focuses on “Relation Between Linear Motion and Angular Motion”.

1. Which of the following disciplines provides study of inertia forces arising from the combined effect of the mass and motion of the parts?

a) theory of machines

b) applied mechanics

C) kinematics

d) kinetics

Answer: d

Explanation: The study of inertia forces arising from the combined effect of the mass and motion of the parts is called kinetics.

The study of relative motion between the parts of a machine is called kinematics.

The study of the relative motion between the parts of a machine and the forces acting on the parts is called theory of machines.

2. Which of the following disciplines provides study of relative motion between the parts of a machine?

a) theory of machines

b) applied mechanics

C) kinematics

d) kinetics

Answer: c

Explanation: The study of inertia forces arising from the combined effect of the mass and motion of the parts is called kinetics.

The study of relative motion between the parts of a machine is called kinematics.

The study of the relative motion between the parts of a machine and the forces acting on the parts is called theory of machines.

3. Which of the following disciplines provides study of the relative motion between the parts of a machine and the forces acting on the parts?

a) theory of machines

b) applied mechanics

C) kinematics

d) kinetics

Answer: a

Explanation: The study of inertia forces arising from the combined effect of the mass and motion of the parts is called kinetics.

The study of relative motion between the parts of a machine is called kinematics.

The study of the relative motion between the parts of a machine and the forces acting on the partsis called theory of machines.

4. The type of pair formed by two elements which are so connected that one is constrained to turn or revolve about a fixed axis of another element is known as

a) turning pair

b) rolling pair

c) sliding pair

d) spherical pair

Answer: a

Explanation: When two elements of a pair are connected in such a way that one can only turn or revolve about a fixed axis of another link, the pair is known as turning pair.

5. Which of the following is a lower pair?

a) ball and socket

b) piston and cylinder

c) cam and follower

d) both a and b

Answer: d

Explanation: In both ball and socket and piston cylinder there is surface contact between the two elements. Hence, they form a lower pair.

6. If two moving elements have surface contact in motion, such pair is known as

a) sliding pair

b) rolling pair

c) surface pair

d) lower pair

Answer: d

Explanation: when two elements of a pair have a surface contact when relative motion takes place and the surface of one element slides over the surface of the other, the pair formed is known as lower pair.

7. The example of lower pair is

a) shaft revolving in a bearing

b) straight line motion mechanisms

c) automobile steering gear

d) all of the mentioned

Answer: d

Explanation: In all the mentioned elements there is surface contact between the two elements. Hence, they form a lower pair.

8. Pulley in a belt drive acts as

a) cylindrical pair

b) turning pair

c) rolling pair

d) sliding pair

Answer: c

Explanation: When the two elements of a pair are connected in such a way that one rolls over another fixed link, the pair is known as rolling pair. In belt and pulley, the belt rolls over the pulley.

9. The example of rolling pair is

a) bolt and nut

b) lead screw of a lathe

c) ball and socket joint

d) ball bearing and roller bearing

Answer: d

Explanation: In ball bearing and roller bearing one element rolls over the other element. Hence, they are examples of rolling pair.

10. Any point on a link connecting double slider crank chain will trace a

a) straight line

b) circle

c) ellipse

d) parabola

Answer: c

Explanation: One of the inversions of a double slider crank chain is elliptical trammels. So, from the above given options ellipse is best suited.

11. The purpose of a link is to

a) transmit motion

b) guide other links

c) act as a support

d) all of the mentioned

Answer: d

Explanation: None

12. A universal joint is an example of

a) higher pair

b) lower pair

c) rolling pair

d) sliding pair

Answer: b

Explanation: In universal joint, there is surface contact between the two elements. Hence, they form a lower pair.

Answer: b

Explanation: In single slider crank chain rotary motion is converted into reciprocating motion.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Acceleration of a Particle along a Circular Path”.

1. A wheel accelerates uniformly from rest to 2000 r.p.m. in 20 seconds. What is its angular acceleration?

a) 10.475 rad/s 2

b) 12 rad/s 2

c) 14 rad/s 2

d) 15 rad/s 2

Answer: a

Explanation: Solution. Given : N 0 = 0 or ω = 0 ; N = 2000 r.p.m. or ω = 2π × 2000/60 = 209.5 rad/s ; t = 20s

Angular acceleration

Let α = Angular acceleration in rad/s 2

We know that

ω = ω 0 + α.t

or 209.5 = 0 + α × 20

or α = 209.5 / 20 = 10.475 rad/s 2

2. A wheel accelerates uniformly from rest to 2000 r.p.m. in 20 seconds. How many revolutions does the wheel make in attaining the speed of 2000 r.p.m.?

a) 400

b) 300

c) 333.4

d) 200

Answer: c

Explanation: Solution. Given : N 0 = 0 or ω = 0 ; N = 2000 r.p.m. or ω = 2π × 2000/60 = 209.5 rad/s ; t = 20s

We know that the angular distance moved by the wheel during 2000 r.p.m. ,

θ = (ω 0 + ω )t/2

= 20/2

= 2095 rad

Since the angular distance moved by the wheel during one revolution is 2π radians, therefore number of revolutions made by the wheel,

n = θ /2π = 2095/2π = 333.4

3. The acceleration of a particle at any instant moving along a circular path in a direction tangential to that instant, is known

a) tangential component

b) normal component

c) parallel component

d) none of the mentioned

Answer: a

Explanation: The acceleration of a particle at any instant moving along a circular path in a direction tangential to that instant, is known tangential component.

The acceleration of a particle at any instant moving along a circular path in a direction normal to the tangent at that instant and directed towards the centre of the circular path, is known as normal component.

4. The acceleration of a particle at any instant moving along a circular path in a direction normal to the tangent at that instant and directed towards the centre of the circular path, is known as

a) tangential component

b) normal component

c) parallel component

d) none of the mentioned

Answer: b

Explanation: The acceleration of a particle at any instant moving along a circular path in a direction tangential to that instant, is known tangential component.

The acceleration of a particle at any instant moving along a circular path in a direction normal to the tangent at that instant and directed towards the centre of the circular path, is known as normal component.

5. When a particle moves along a straight path, then the radius of curvature is

a) infinitely small

b) zero

c) infinitely great

d) none of the mentioned

Answer: c

Explanation: When a particle moves along a straight path, then the radius of curvature is infinitely great. This means that v 2 /r is zero.

6. When a particle moves with a uniform velocity, then dv/dt will be

a) infinitely small

b) zero

c) infinitely great

d) none of the mentioned

Answer: b

Explanation: When a particle moves with a uniform velocity, then dv/dt will be zero. In other words, there will be no tangential acceleration; but the particle will have only normal or radial or centripetal acceleration.

7. A horizontal bar 1.5 metres long and of small cross-section rotates about vertical axis through one end. It accelerates uniformly from 1200 r.p.m. to 1500 r.p.m. in an interval of 5 seconds. What is the linear velocity at the beginning of the interval ?

a) 188.6 m/s

b) 235.5 m/s

c) 300 m/s

d) 400 m/s

Answer: a

Explanation: Given : r = 1.5 m ; N 0 = 1200 r.p.m. or ω 0 = 2 π × 1200/60 = 125.7 rad/s ;

N = 1500 r.p.m. or ω = 2 π × 1500/60 = 157 rad/s ; t = 5 s

Linear velocity at the beginning

We know that linear velocity at the beginning,

v 0 = r . ω 0 = 1.5 × 125.7 = 188.6 m/s

Answer: b

Explanation: Given : r = 1.5 m ; N 0 = 1200 r.p.m. or ω 0 = 2 π × 1200/60 = 125.7 rad/s ;

N = 1500 r.p.m. or ω = 2 π × 1500/60 = 157 rad/s ; t = 5 s

Linear velocity at the end of 5 seconds

We also know that linear velocity after 5 seconds,

v 5 = r . ω = 1.5 × 157 = 235.5 m/s

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Numericals On Kinematics Of Motion”.

1. A car starts from rest and accelerates uniformly to a speed of 72 km. p.h. over a distance of 500 m. Calculate the acceleration.

a) 0.3 m/s 2

b) 0.4 m/s 2

c) 0.5 m/s 2

d) 0.6 m/s 2

Answer: b

Explanation: Given : u = 0 ; v = 72 km. p.h. = 20 m/s ; s = 500 m

First of all, let us consider the motion of the car from rest.

Acceleration of the car

Let a = Acceleration of the car.

We know that

v 2 = u 2 + 2as

or, 20 2 = 0 + 2a x 500 = 1000a

or, a = 20 2 /1000 = 0.4 m/s 2

2. A car starts from rest and accelerates uniformly to a speed of 72 km. p.h. over a distance of 500 m. Calculate the time taken to attain the speed.

a) 50 s

b) 60 s

c) 70 s

d) 80 s

Answer: a

Explanation: Given : u = 0 ; v = 72 km. p.h. = 20 m/s ; s = 500 m

First of all, let us consider the motion of the car from rest.

Acceleration of the car

Let a = Acceleration of the car.

We know that

v 2 = u 2 + 2as

or, 20 2 = 0 + 2a x 500 = 1000a

or, a = 20 2 /1000 = 0.4 m/s 2

Let t = Time taken by the car to attain the speed.

We know that v = u + a.t

∴ 20 = 0 + 0.4 × t or t = 20/0.4 = 50 s

3. A car starts from rest and accelerates uniformly to a speed of 72 km. p.h. over a distance of 500 m. If a further acceleration raises the speed to 90 km. p.h. in 10 seconds, find this acceleration and the further distance moved.

a) 0.3 m/s 2

b) 0.4 m/s 2

c) 0.5 m/s 2

d) 0.6 m/s 2

Answer: c

Explanation: Given : u = 0 ; v = 72 km. p.h. = 20 m/s ; s = 500 m

First of all, let us consider the motion of the car from rest.

Acceleration of the car

Let a = Acceleration of the car.

We know that

v 2 = u 2 + 2as

or, 20 2 = 0 + 2a x 500 = 1000a

or, a = 20 2 /1000 = 0.4 m/s 2

Let t = Time taken by the car to attain the speed.

We know that v = u + a.t

∴ 20 = 0 + 0.4 × t or t = 20/0.4 = 50 s

Now consider the motion of the car from 72 km.p.h. to 90 km.p.h. in 10 seconds.

Given : Initial velocity, u = 72 km.p.h. = 20 m/s ;

Final velocity, v = 96 km.p.h. = 25 m/s ; t = 10 s

Let a = Acceleration of the car.

We know that v = u + a.t

25 = 20 + a × 10 or a = /10 = 0.5 m 2

4. A car starts from rest and accelerates uniformly to a speed of 72 km. p.h. over a distance of 500 m. A further acceleration raises the speed to 90 km. p.h. in 10 seconds.The brakes are now applied to bring the car to rest under uniform retardation in 5 seconds. Find the distance travelled during braking.

a) 200 m

b) 300 m

c) 225 m

d) 335 m

Answer: c

Explanation: Given : u = 0 ; v = 72 km. p.h. = 20 m/s ; s = 500 m

First of all, let us consider the motion of the car from rest.

Acceleration of the car

Let a = Acceleration of the car.

We know that

v 2 = u 2 + 2as

or, 20 2 = 0 + 2a x 500 = 1000a

or, a = 20 2 /1000 = 0.4 m/s 2

Let t = Time taken by the car to attain the speed.

We know that v = u + a.t

∴ 20 = 0 + 0.4 × t or t = 20/0.4 = 50 s

Now consider the motion of the car from 72 km.p.h. to 90 km.p.h. in 10 seconds.

Given : Initial velocity, u = 72 km.p.h. = 20 m/s ;

Final velocity, v = 96 km.p.h. = 25 m/s ; t = 10 s

Let a = Acceleration of the car.

We know that v = u + a.t

25 = 20 + a × 10 or a = /10 = 0.5 m 2

We know that distance moved by the car,

s = ut + 1/2 at 2

= 20 x 10 + 1/2 0.5 2 = 225 m

5. A wheel accelerates uniformly from rest to 2000 r.p.m. in 20 seconds. What is its angular acceleration?

a) 10.475 rad/s 2

b) 11.475 rad/s 2

c) 12.475 rad/s 2

d) 13.475 rad/s 2

Answer: a

Explanation: Given : N 0 = 0 or ω = 0 ; N = 2000 r.p.m. or ω = 2π × 2000/60 = 209.5 rad/s ; t = 20s

Angular acceleration

Let α = Angular acceleration in rad/s 2 .

We know that

ω = ω 0 + α.t

or 209.5 = 0 + α × 20

∴ α = 209.5 / 20 = 10.475 rad/s 2

6. A wheel accelerates uniformly from rest to 2000 r.p.m. in 20 seconds.How many revolutions does the wheel make in attaining the speed of 2000 r.p.m.?

a) 333.4

b) 444.4

c) 555.4

d) 666.4

a) 10.475 rad/s 2

b) 11.475 rad/s 2

c) 12.475 rad/s 2

d) 13.475 rad/s 2

Answer: a

Explanation: Given : N 0 = 0 or ω = 0 ; N = 2000 r.p.m. or ω = 2π × 2000/60 = 209.5 rad/s ; t = 20s

Angular acceleration

Let α = Angular acceleration in rad/s 2 .

We know that

ω = ω 0 + α.t

or 209.5 = 0 + α × 20

∴ α = 209.5 / 20 = 10.475 rad/s 2

We know that the angular distance moved by the wheel during 2000 r.p.m. ,

θ = (ω 0 + ω)t/2 = 20/2 = 2095 rad

Since the angular distance moved by the wheel during one revolution is 2π radians, therefore

number of revolutions made by the wheel,

n = θ /2π = 2095/2π = 333.4

7. A horizontal bar 1.5 metres long and of small cross-section rotates about vertical axis through one end. It accelerates uniformly from 1200 r.p.m. to 1500 r.p.m. in an interval of 5 seconds. What is the linear velocity at the beginning?

a) 288.6 m/s

b) 388.6 m/s

c) 488.6 m/s

d) 188.6 m/s

Answer: d

Explanation: Given : r = 1.5 m ; N 0 = 1200 r.p.m. or ω 0 = 2 π × 1200/60 = 125.7 rad/s ;

N = 1500 r.p.m. or ω = 2 π × 1500/60 = 157 rad/s ; t = 5 s

Linear velocity at the beginning

We know that linear velocity at the beginning,

v 0 = r . ω 0 = 1.5 × 125.7 = 188.6 m/s

8. A horizontal bar 1.5 metres long and of small cross-section rotates about vertical axis through one end. It accelerates uniformly from 1200 r.p.m. to 1500 r.p.m. in an interval of 5 seconds. What is the linear velocity at the end of the interval ?

a) 235.5 m/s

b) 335.5 m/s

c) 435.5 m/s

d) 535.5 m/s

Answer: a

Explanation: Given : r = 1.5 m ; N 0 = 1200 r.p.m. or ω 0 = 2 π × 1200/60 = 125.7 rad/s ;

N = 1500 r.p.m. or ω = 2 π × 1500/60 = 157 rad/s ; t = 5 s

Linear velocity at the beginning

We know that linear velocity at the beginning,

v 0 = r . ω 0 = 1.5 × 125.7 = 188.6 m/s

Linear velocity at the end of 5 seconds

We also know that linear velocity after 5 seconds,

v 5 = r . ω = 1.5 × 157 = 235.5 m/s

9. A horizontal bar 1.5 metres long and of small cross-section rotates about vertical axis through one end. It accelerates uniformly from 1200 r.p.m. to 1500 r.p.m. in an interval of 5 seconds. What is the normal component of the acceleration of the mid-point of the bar after 5 seconds after the acceleration begins ?

a) 2.7 m/s 2

b) 3.7 m/s 2

c) 4.7 m/s 2

d) 5.7 m/s 2

Answer: c

Explanation: Given : r = 1.5 m ; N 0 = 1200 r.p.m. or ω 0 = 2 π × 1200/60 = 125.7 rad/s ;

N = 1500 r.p.m. or ω = 2 π × 1500/60 = 157 rad/s ; t = 5 s

Linear velocity at the beginning

We know that linear velocity at the beginning,

v 0 = r . ω 0 = 1.5 × 125.7 = 188.6 m/s

Linear velocity at the end of 5 seconds

We also know that linear velocity after 5 seconds,

v 5 = r . ω = 1.5 × 157 = 235.5 m/s

Let α = Constant angular acceleration.

We know that ω = ω 0 + α.t

157 = 125.7 + α × 5 or α =  /5 = 6.26 rad/s 2

Radius corresponding to the middle point,

r = 1.5 /2 = 0.75 m

∴ Tangential acceleration = α. r = 6.26 × 0.75 = 4.7 m/s 2

10. A horizontal bar 1.5 metres long and of small cross-section rotates about vertical axis through one end. It accelerates uniformly from 1200 r.p.m. to 1500 r.p.m. in an interval of 5 seconds. What is the tangential component of the acceleration of the mid-point of the bar after 5 seconds after the acceleration begins ?

a) 18287 m/s 2

b) 18387 m/s 2

c) 18487 m/s 2

d) 18587 m/s 2

Answer: c

Explanation: Given : r = 1.5 m ; N 0 = 1200 r.p.m. or ω 0 = 2 π × 1200/60 = 125.7 rad/s ;

N = 1500 r.p.m. or ω = 2 π × 1500/60 = 157 rad/s ; t = 5 s

Linear velocity at the beginning

We know that linear velocity at the beginning,

v 0 = r . ω 0 = 1.5 × 125.7 = 188.6 m/s

Linear velocity at the end of 5 seconds

We also know that linear velocity after 5 seconds,

v 5 = r . ω = 1.5 × 157 = 235.5 m/s

Let α = Constant angular acceleration.

We know that ω = ω 0 + α.t

157 = 125.7 + α × 5 or α =  /5 = 6.26 rad/s 2

Radius corresponding to the middle point,

r = 1.5 /2 = 0.75 m

∴ Tangential acceleration = α. r = 6.26 × 0.75 = 4.7 m/s 2

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Kinetics of Motion”.

1. The force which acts along the radius of a circle and directed ____________ the centre of the circle is known as centripetal force.

a) away from

b) towards

c) at the

d) none of the mentioned

Answer: b

Explanation: Centripetal force acts radially inwards and is essential for circular motion.

2. The unit of mass moment of inertia in S.I. units is

a) m 4

b) kgf-m-s 2

c) kg-m 2

d) N-m

Answer: c

Explanation: Moment of inertia is the distance, from a give reference, where the whole mass of body is assumed to be concentrated to give the same value of I. The unit of mass moment of inertia in S.I. units is kg-m 2 .

3. Joule is a unit of

a) force

b) work

c) power

d) none of the mentioned

Answer: b

Explanation: In S.I. system of units, the practical unit of work is N-m. It is the work done by a force of 1 newton, when it displaces a body through 1 metre. The work of 1 N-m is known as joule  such that 1 N-m = 1 J.

4. The energy possessed by a body, for doing work by virtue of its position, is called

a) potential energy

b) kinetic energy

c) electrical energy

d) chemical energy

Answer: a

Explanation: Potential energy is the energy possessed by a body for doing work, by virtue of its position.

Kinetic energy is the energy possessed by a body, for doing work, by virtue of its mass and velocity of motion.

5. When a body of mass moment of inertia I  is rotated about that axis with an angular velocity, then the kinetic energy of rotation is

a) 0.5 I.ω

b) I.ω

c) 0.5 I.ω 2

d) I.ω 2

Answer: c

Explanation: When a body of mass moment of inertia I  is rotated about that axis, with an angular velocity ω, then it possesses some kinetic energy. In this case,

Kinetic energy of rotation = 1/ 2I.ω 2

When a body has both linear and angular motions e.g. in the locomotive driving wheels and wheels of a moving car, then the total kinetic energy of the body is equal to the sum of kinetic energies of translation and rotation.

∴ Total kinetic energy = 1/ 2mv 2 +1/ 2I.ω 2

6. The wheels of a moving car possess

a) potential energy only

b) kinetic energy of translation only

c) kinetic energy of rotation only

d) kinetic energy of translation and rotation both.

Answer: d

Explanation: in the locomotive driving wheels and wheels of a moving car, then the total kinetic energy of the body is equal to the sum of kinetic energies of translation and rotation.

7. The bodies which rebound after impact are called

a) inelastic bodies

b) elastic bodies

c) solid bodies

d) none of the mentioned

Answer: b

Explanation: The bodies, which rebound after impact are called elastic bodies and the bodies which does not rebound at all after its impact are called inelastic bodies.

8. The coefficient of restitution for inelastic bodies is

a) zero

b) between zero and one

c) one

d) more than one

Answer: a

Explanation: The process of regaining the original shape is called restitution. Inelastic bodies can not regain their original shapes. Therefore their coefficient of restitution is zero.

9. Which of the following statement is correct ?

a) The kinetic energy of a body during impact remains constant.

b) The kinetic energy of a body before impact is equal to the kinetic energy of a body after impact.

c) The kinetic energy of a body before impact is less than the kinetic energy of a body after impact.

d) The kinetic energy of a body before impact is more than the kinetic energy of a body after impact.

Answer: d

Explanation: Total kinetic energy of the system before impact,

E 1 = 1/2 m 1 (u 1 ) 2 + 1/2 m 2 (u 2 ) 2

When the two bodies move with the same velocity v after impact, then

Kinetic energy of the system after impact,

E 2 = 1/2( m 1 + m 2 ) v 2

∴ Loss of kinetic energy during impact,

E L = E 1 – E 2

Answer: b

Explanation: If the body will move in opposite direction a negative sign would be there.

We know that Common velocity = V 1 – 2

Here both the velocities are same.

Therefore Common velocity = V – 

= V + V = 2V

This set of Machine Kinematics Interview Questions and Answers for freshers focuses on “Numericals On Kinetics Of Motion and Loss of Kinetic Energy”.

1. A road roller has a total mass of 12 tonnes. The front roller has a mass of 2 tonnes, a radius of gyration of 0.4 m and a diameter of 1.2 m. The rear axle, together with its wheels, has a mass of 2.5 tonnes, a radius of gyration of 0.6 m and a diameter of 1.5 m. Calculate kinetic energy of rotation of the wheels and axles at a speed of 9 km/h.

a) 7670 N-m

b) 8670 N-m

c) 9670 N-m

d) 6670 N-m

Answer: a

Explanation: Given : m = 12 t = 12 000 kg ;

m 1 = 2 t = 2000 kg ; k 1 = 0.4 m ; d 1 = 1.2 m or r 1 = 0.6 m ; m 2 = 2.5 t = 2500 kg ; k 2 = 0.6 m ; d 2 = 1.5 m or r 2 = 0.75 m ; v = 9 km/h = 2.5 m/s; s = 6 m

Kinetic energy of rotation of the wheels and axles

We know that mass moment of inertia of the front roller,

I 1 = m 1 (k 1 ) 2 = 2000  2 = 320 kg-m 2

and mass moment of inertia of the rear axle together with its wheels,

I 2 = m 2 (k 2 ) 2 = 2500  2 = 900 kg -m 2

Angular speed of the front roller,

ω 1 = v/r 1 = 2.5/0.6 = 4.16 rad/s

and angular speed of rear wheels,

ω 2 = v/r 2 = 2.5/0.75 = 3.3 rad/s

We know that kinetic energy of rotation of the front roller,

E 1 =1/2 I 1 (ω 1 ) 2 = 1/2 × 320 2 2770 N-m

and kinetic energy of rotation of the rear axle together with its wheels,

E 2 =1/2 I 2 (ω 2 ) 2 = 1/2 × 900 2 4900 N-m

∴ Total kinetic energy of rotation of the wheels,

E = E 1 + E 2 = 2770 + 4900 = 7670 N-m

2. A road roller has a total mass of 12 tonnes. The front roller has a mass of 2 tonnes, a radius of gyration of 0.4 m and a diameter of 1.2 m. The rear axle, together with its wheels, has a mass of 2.5 tonnes, a radius of gyration of 0.6 m and a diameter of 1.5 m. Calculate total kinetic energy of road roller.

a) 25170 N-m

b) 35170 N-m

c) 45170 N-m

d) 55170 N-m

Answer: d

Explanation: Given : m = 12 t = 12 000 kg ;

m 1 = 2 t = 2000 kg ; k 1 = 0.4 m ; d 1 = 1.2 m or r 1 = 0.6 m ; m 2 = 2.5 t = 2500 kg ; k 2 = 0.6 m ; d 2 = 1.5 m or r 2 = 0.75 m ; v = 9 km/h = 2.5 m/s; s = 6 m

Kinetic energy of rotation of the wheels and axles

We know that mass moment of inertia of the front roller,

I 1 = m 1 (k 1 ) 2 = 2000  2 = 320 kg-m 2

and mass moment of inertia of the rear axle together with its wheels,

I 2 = m 2 (k 2 ) 2 = 2500  2 = 900 kg -m 2

Angular speed of the front roller,

ω 1 = v/r 1 = 2.5/0.6 = 4.16 rad/s

and angular speed of rear wheels,

ω 2 = v/r 2 = 2.5/0.75 = 3.3 rad/s

We know that kinetic energy of rotation of the front roller,

E 1 =1/2 I 1 (ω 1 ) 2 = 1/2 × 320 2 2770 N-m

and kinetic energy of rotation of the rear axle together with its wheels,

E 2 =1/2 I 2 (ω 2 ) 2 = 1/2 × 900 2 4900 N-m

∴ Total kinetic energy of rotation of the wheels,

E = E 1 + E 2 = 2770 + 4900 = 7670 N-m

We know that the kinetic energy of motion  of the road roller,

E 3 = 1/2 mv 2 = 1/2 x 1200  2 = 37500 N-m

This energy includes the kinetic energy of translation of the wheels also, because the total mass  has been considered.

∴ Total kinetic energy of road roller,

E 4 = Kinetic energy of translation + Kinetic energy of rotation

= E 3 + E = 37 500 + 7670 = 45 170 N-m

3. A road roller has a total mass of 12 tonnes. The front roller has a mass of 2 tonnes, a radius of gyration of 0.4 m and a diameter of 1.2 m. The rear axle, together with its wheels, has a mass of 2.5 tonnes, a radius of gyration of 0.6 m and a diameter of 1.5 m. Calculate braking force required to bring the roller to rest from 9 km/h in 6 m on the level.

a) 5528.3 N

b) 6528.3 N

c) 7528.3 N

d) 8528.3 N

Answer: c

Explanation: Given : m = 12 t = 12 000 kg ;

m 1 = 2 t = 2000 kg ; k 1 = 0.4 m ; d 1 = 1.2 m or r 1 = 0.6 m ; m 2 = 2.5 t = 2500 kg ; k 2 = 0.6 m ; d 2 = 1.5 m or r 2 = 0.75 m ; v = 9 km/h = 2.5 m/s; s = 6 m

Kinetic energy of rotation of the wheels and axles

We know that mass moment of inertia of the front roller,

I 1 = m 1 (k 1 ) 2 = 2000  2 = 320 kg-m 2

and mass moment of inertia of the rear axle together with its wheels,

I 2 = m 2 (k 2 ) 2 = 2500  2 = 900 kg -m 2

Angular speed of the front roller,

ω 1 = v/r 1 = 2.5/0.6 = 4.16 rad/s

and angular speed of rear wheels,

ω 2 = v/r 2 = 2.5/0.75 = 3.3 rad/s

We know that kinetic energy of rotation of the front roller,

E 1 =1/2 I 1 (ω 1 ) 2 = 1/2 × 320 2 2770 N-m

and kinetic energy of rotation of the rear axle together with its wheels,

E 2 =1/2 I 2 (ω 2 ) 2 = 1/2 × 900 2 4900 N-m

∴ Total kinetic energy of rotation of the wheels,

E = E 1 + E 2 = 2770 + 4900 = 7670 N-m

We know that the kinetic energy of motion  of the road roller,

E 3 = 1/2 mv 2 = 1/2 x 1200  2 = 37500 N-m

This energy includes the kinetic energy of translation of the wheels also, because the total mass  has been considered.

∴ Total kinetic energy of road roller,

E 4 = Kinetic energy of translation + Kinetic energy of rotation

= E 3 + E = 37 500 + 7670 = 45 170 N-m

Let F = Braking force required to bring the roller to rest, in newtons.

We know that the distance travelled by the road roller,

s = 6 m … 

∴ Work done by the braking force

= F × s = 6 F N-m

This work done must be equal to the total kinetic energy of road roller to bring the roller to

rest, i.e.

6 F = 45 170 or F = 45 170/6 = 7528.3 N

4. A haulage rope winds on a drum of radius 500 mm, the free end being attached to a truck. The truck has a mass of 500 kg and is initially at rest. The drum is equivalent to a mass of 1250 kg with radius of gyration 450 mm. The rim speed of the drum is 0.75 m/s before the rope tightens. By considering the change in linear momentum of the truck and in the angular momentum of the drum, find the speed of the truck when the motion becomes steady.

a) 0.502 m/s

b) 0.602 m/s

c) 0.702 m/s

d) 0.802 m/s

Answer: a

Explanation: Given : r = 500 mm = 0.5 m ; m 1 = 500 kg ; m 2 = 1250 kg ; k = 450 mm = 0.45 m ; u = 0.75 m/s

We know that mass moment of inertia of drum,

I 2 = m 2 .k 2 = 1250  2 = 253 kg-m 2

Let v = Speed of the truck in m/s, and

F = Impulse in rope in N-s.

We know that the impulse is equal to the change of linear momentum of the truck. Therefore

F = m 1 .v = 500 v N-s

and moment of impulse = Change in angular momentum of drum

i.e. F x r = I 1 (ω 2 − ω 1 ) = I 2 

500v x 0.5 = 253

or, 250v = 380 − 506v

∴ 250 v + 506 v = 380

or v = 380/756 = 0.502 m/s

5. An electric motor drives a machine through a speed reducing gear of ratio 9:1. The motor armature, with its shaft and gear wheel, has moment of inertia 0.6 kg-m 2 . The rotating part of the driven machine has moment of inertia 45 kg-m 2 . The driven machine has resisting torque of 100 N-m and the efficiency of reduction gear is 95%. Find the power which the motor must develop to drive the machine at a uniform speed of 160 r.p.m.

a) 1764 W

b) 2764 W

c) 3764 W

d) 4764 W

Answer: a

Explanation: Given : G = 9; I A = 0.6 kg-m 2 ; I B = 45 kg-m 2 ;

T B = 100 N-m; η = 95% = 0.95;

N = 160 r.p.m. ; N 1 = 0 ; N 2 = 60 r.p.m. T A = 30 N-m

We know that the power which the motor must develop,

P = 2πN T B /60× η

= 2π × 160 × 100/60 x 0.95

= 1764 W

6. The flywheel of a steam engine has a radius of gyration of 1 m and mass 2500 kg. The starting torque of the steam engine is 1500 N-m and may be assumed constant. Determine : Angular acceleration of the flywheel.

a) 0.6 rad/s 2

b) 0.8 rad/s 2

c) 0.10 rad/s 2

d) none of the mentioned

Answer: b

Explanation: Given : k = 1 m ; m = 2500 kg ; T = 1500 N-m

Angular acceleration of the flywheel

Let α = Angular acceleration of the flywheel.

We know that mass moment of inertia of the flywheel,

I=m.k 2 = 2500×12 = 2500 kg-m 2

We also know that torque ,

1500 = I .α = 2500 × α

or α = 1500 / 2500 = 0.6 rad/s 2

7. The flywheel of a steam engine has a radius of gyration of 1 m and mass 2500 kg. The starting torque of the steam engine is 1500 N-m and may be assumed constant. Determine : Kinetic energy of the flywheel after 10 seconds from the start.

a) 50 kJ

b) 60 kJ

c) 45 kJ

d) none of the mentioned

Answer: c

Explanation: Given : k = 1 m ; m = 2500 kg ; T = 1500 N-m

Angular acceleration of the flywheel

Let α = Angular acceleration of the flywheel.

We know that mass moment of inertia of the flywheel,

I=m.k 2 = 2500×12 = 2500 kg-m 2

We also know that torque ,

1500 = I .α = 2500 × α

or α = 1500 / 2500 = 0.6 rad/s 2

Kinetic energy of the flywheel after 10 seconds from start

First of all, let us find the angular speed of the flywheel (ω 2 ) after t = 10 seconds from the start (i.e. ω 1 = 0 ).

We know that ω 2 = ω 1 + α.t = 0 + 0.6 × 10 = 6 rad/s

∴ Kinetic energy of the flywheel,

E = 1/2 I(ω 2 ) 2

= 1/2 x 2500 x 6 2

= 45 000J

= 45 kJ

8. Which of the following objects have momentum?

a) An electron is orbiting the nucleus of an atom.

b) A UPS truck is stopped in front of the school building.

c) The high school building rests in the middle of town.

d) None of the mentioned

Answer: a

Explanation: Momentum can be thought of as mass in motion. An object has momentum if it has its mass in motion. It matters not whether the object is of large mass or small mass, moving with constant speed or accelerating; if the object is MOVING, then it has momentum.

9. A truck driving along a highway road has a large quantity of momentum. If it moves at the same speed but has twice as much mass, its momentum is ________________

a) zero

b) quadrupled

c) doubled

d) unchanged

Answer: c

Explanation: Momentum is directly related to the mass of the object. So for the same speed, a doubling of mass leads to a doubling of momentum.

Answer: c

Explanation: Since being dropped from the same height, the balls will be moving with the same pre-collision velocity . Upon collision with the ground, the velocity will have to be reduced to zero – that is, the ball will cease moving downwards. This decrease in velocity constitutes the first portion of the velocity change. If the ball bounces, then there is an additional velocity change sending the ball back upwards opposite the original direction. Thus, for the same collision time, bouncing involves a greater velocity change, a greater momentum change, and therefore a greater impulse.

This set of Advanced Machine Kinematics Questions and Answers focuses on “Loss of Kinetic Energy During Elastic Impact”.

1. A sphere of mass 25 Kg is moving at a speed of 1.5 m/s undergoes collision with another sphere of mass 50 Kg moving at 3m/s in the same direction, find the loss of kinetic energy when the collision is inelastic.

a) 18.75 N-m

b) 19.75 N-m

c) 17.75 N-m

d) 16.75 N-m

Answer: a

Explanation: Loss of kinetic energy during inelastic collision is given by

m 1 m 2 /(2(m 1 + m 2 ) (u 1 2 – u 2 2 )

substituting the values we get

El = 18.75 N-m.

2. The coefficient of restitution is 0 for a completely inelastic collision.

a) True

b) False

Answer: a

Explanation: For a completely inelastic collision the bodies stick to each other after collision, hence there is no relative velocity after collision therefore the coefficient of restitution is 0.

3. A sphere of mass 25 Kg is moving at a speed of 1.5 m/s undergoes collision with another sphere of mass 50 Kg moving at 3m/s in the same direction, find the loss of kinetic energy when the collision is inelastic with e = 0.6.

a) 18.75 N-m

b) 12.00 N-m

c) 13.75 N-m

d) 12.75 N-m

Answer: b

Explanation: Loss of kinetic energy during inelastic collision with coefficient of restitution is given by

m 1 m 2 /(2(m 1 + m 2 ) (u 1 2 – u 2 2 )(1-e 2 ))

substituting the values we get

El = 12 N-m.

4. A sphere of mass 25 Kg is moving at a speed of 1.5 m/s undergoes collision with another sphere of mass 50 Kg moving at 3m/s in the same direction, find the common velocity in m/s after collision when the collision is completely inelastic.

a) 2.5

b) 9.75

c) 7.25

d) 6.75

Answer: a

Explanation: Common velocity during inelastic collision is given by

m 1 u 1 + m 2 u 2 /(m 1 + m 2 ) = v

substituting the values we get

V = 2.5 m/s

5. A sphere of mass 25 Kg is moving at a speed of 1.5 m/s undergoes collision with another sphere of mass 50 Kg moving at 3m/s in the same direction, find the velocity of 50 Kg mass in m/s after collision when the collision is elastic.

a) 2.5

b) 2.00

c) 7.25

d) 6.75

Answer: b

Explanation: Velocity during elastic collision is given by

m 1 u 1 + m 2 u 2 /(m 1 + m 2 ) = v

substituting the values we get

V = 2.5 m/s

v 1 = 2V – u 1

v 1 = 2m/s

6. Coefficient of restitution of elastic bodies is ______

a) One

b) More than one

c) Between 0 and one

d) Zero

Answer: a

Explanation: In case of elastic bodies the relative velocity after collision is equal to the relative velocity before collision, hence the coefficient of restitution is 1.

7. Kinetic energy before collision is always equal to the kinetic energy after collision.

a) True

b) False

Answer: b

Explanation: Kinetic energy before collision is equal to the kinetic energy after collision only in case of elastic collisions, in other cases energy is lost during deformation.

8. Which of the following cases has the greatest loss in Kinetic energy?

a) e=0

b) e=1/2

c) e=1/4

d) e=1

Answer: a

Explanation: e=0 signifies that the collision was completely inelastic, in case of completely inelastic collisions the Kinetic energy loss after collision is maximum.

9. A sphere of mass 25 Kg is moving at a speed of 1.5 m/s undergoes collision with another sphere of mass 50 Kg moving at 3m/s in the same direction, find the velocity of 25 Kg mass in m/s after collision when the collision is elastic.

a) 2.5

b) 2.00

c) 3.5

d) 6.75

Answer: c

Explanation: Velocity during elastic collision is given by

m 1 u 1 + m 2 u 2 /(m 1 + m 2 ) = v

substituting the values we get

V = 2.5 m/s

v 2 = 2V – u 2

v 2 = 3.5 m/s

10. A sphere of mass 25 Kg is moving at a speed of 1.5 m/s undergoes collision with another sphere of mass 50 Kg moving at 3m/s in the same direction, find the velocity of 25 Kg mass in m/s after collision when the collision is inelastic with e = 0.6.

a) 2.5

b) 2.00

c) 3.5

d) 3.1

Answer: d

Explanation: Velocity during elastic collision is given by

m 1 u 1 + m 2 u 2 /(m 1 + m 2 ) = v

substituting the values we get

V = 2.5 m/s

v 2 = 2V – eu 2

v 2 = 3.1 m/s.

11. A sphere of mass 25 Kg is moving at a speed of 1.5 m/s undergoes collision with another sphere of mass 50 Kg moving at 3m/s in the same direction, find the velocity of 50 Kg mass in m/s after collision when the collision is inelastic with e = 0.6.

a) 2.2

b) 2.00

c) 3.5

d) 3.1

Answer: a

Explanation: Velocity during elastic collision is given by

m 1 u 1 + m 2 u 2 /(m 1 + m 2 ) = v

substituting the values we get

V = 2.5 m/s

v 1 = 2V – eu 1

v 1 = 2.2 m/s.

12. Which of the following cases momentum is conserved?

a) Perfectly elastic collision

b) Inelastic collision with 0<e<1

c) Perfectly inelastic collision

d) Momentum is always conserved

Answer: d

Explanation: When the net external force acting on the body is 0, the linear momentum is always conserved no matter the type of collision.

13. Which of the following cases Kinetic energy is conserved?

a) Perfectly elastic collision

b) Inelastic collision with 0<e<1

c) Perfectly inelastic collision

d) Momentum is always conserved

Answer: a

Explanation: When the net external force acting on the body is 0, the linear momentum is always conserved no matter the type of collision, however in only completely elastic collisions the kinetic energy of the system remains conserved.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Simple Harmonic Motion”.

1. The periodic time (t p ) is given by

a) ω / 2 π

b) 2 π / ω

c) 2 π × ω

d) π/ω

Answer: b

Explanation: Periodic time is the time taken for one complete revolution of the particle.

∴ Periodic time, t p = 2 π/ω seconds.

2. The velocity of a particle moving with simple harmonic motion is . . . . at the mean position.

a) zero

b) minimum

c) maximum

d) none of the mentioned

Answer: c

Explanation: At mean the value of x = 0. Therefore, it is maximum at mean position.

V max = ω.r.

3. The velocity of a particle  moving with simple harmonic motion, at any instant is given by

a) ω √r 2 − x 2

b) ω √x 2 − r 2

c) ω 2 √r 2 − x 2

d) ω 2 √x 2 − r 2

Answer: a

Explanation: Velocity of any particle v N = vsinθ = ω.rsinθ = ω √r 2 − x 2 .

4. The maximum acceleration of a particle moving with simple harmonic motion is

a) ω

b) ω.r

c) ω 2 .r

d) ω 2 /r

Answer: c

Explanation: Acceleration, a N = ω 2 .rcosθ = ω 2 .r.

5. The frequency of oscillation for the simple pendulum is

a) 1/2π √L/g

b) 1/2π √g/L

c) 2π √L/g

d) 2π√g/L

Answer: b

Explanation: The motion of the bob from one extremity to the other is known as beat or swing. Thus one beat = 1/2 oscillation.

∴ Periodic time for one beat = π √g/L

∴ Frequency = 1/2π √g/L.

6. When a rigid body is suspended vertically and it oscillates with a small amplitude under the action of the force of gravity, the body is known as

a) simple pendulum

b) torsional pendulum

c) compound pendulum

d) second’s pendulum

Answer: c

Explanation: When a rigid body is suspended vertically, and it oscillates with a small amplitude under the action of the force of gravity, the body is known as compound pendulum. Thus the periodic time of a compound pendulum is minimum when the distance between the point of suspension and the centre of gravity is equal to the radius of gyration of the body about its centre of gravity.

7. The frequency of oscillation of a compound pendulum is

a) 1/2π √g.h/k 2 G +h 2

b) 1/2π √k 2 G +h 2 /g.h

c) 2π√g.h/k 2 G +h 2

d) 2π√k 2 G +h 2 /g.h

Answer: a

Explanation: We know that the periodic time,

t p = 2π√Displacement/Accleration = 2π√θ/α

and frequency of oscillation,n = 1/t p = 1/2π √g.h/k 2 G +h 2

where k G = Radius of gyration about the centroidal axis, and

h = Distance between the point of suspension and centre of gravity of the body.

8. The equivalent length of a simple pendulum which gives the same frequency as the compound pendulum is

a) h/ k 2 G +h 2

b) k 2 G +h 2 /h

c) h 2 /k 2 G +h 2

d) k 2 G +h 2 /h 2

Answer: b

Explanation: By comparing the frequencies of simple pendulum to compound pendulum we get the equivalent length of simple pendulum as k 2 G +h 2 /h.

9. The centre of percussion is below the centre of gravity of the body and is at a distance equal to

a) h / k G

b) h.k G

c) h 2 /k G

d) k 2 G /h

Answer: d

Explanation: The centre of oscillation is sometimes termed as centre of percussion. It is defined as that point at which a blow may be struck on a suspended body so that the reaction at the support is zero. The centre of percussion is below the centre of gravity and at a distance k 2 G /h. The distance between the centre of suspension and the centre of percussion is equal to the equivalent length of a simple pendulum.

Answer: b

Explanation: None.

This set of Machine Kinematics Questions and Answers for Experienced people focuses on “Velocity and Acceleration of a Particle Moving with Simple Harmonic Motion”.

1. A body is said to vibrate with simple harmonic motion if its acceleration is proportional to the distance from the mean position.

a) True

b) False

Answer: a

Explanation: A body is said to move with simple harmonic motion, if it satisfies the following two conditions:

a) Its acceleration is always directed towards the center, known as point of reference or mean position.

b) Its acceleration is proportional to the distance from that point.

2. The maximum displacement of a body, from its mean position is called amplitude.

a) True

b) False

Answer: a

Explanation: The time taken for one complete revolution of the particle is called periodic time.

The maximum displacement of a body from its mean position is called amplitude.

3. Frequency of vibrations is usually expressed in

a) number of cycles per hour

b) number of cycles per minute

c) number of cycles per second

d) none of the mentioned

Answer: c

Explanation: The number of cycles per second is called frequency. It is the reciprocal of periodic time.

4. The amplitude of vibrations is always ______________ the radius of the circle.

a) equal to

b) less than

c) greater than

d) none of the mentioned

Answer: a

Explanation: None.

5. The time taken by a particle for one complete oscillation is known as periodic time.

a) True

b) False

Answer: a

Explanation: The time taken for one complete revolution of the particle is called periodic time.

The maximum displacement of a body from its mean position is called amplitude.

6. The periodic time is given by

a) ω/2п

b) 2п/ω

c) ω x 2п

d) п/ω

Answer: b

Explanation: Periodic time, t p = 2п/ω seconds

where ω = Angular velocity of the particle in rad/s.

7. When a body moves with simple harmonic motion, the product of its periodic time and frequency is equal to

a) zero

b) one

c) п/2

d) п

Answer: b

Explanation: The number of cycles per second is called frequency. It is the reciprocal of periodic time. Hence, when it is multiplied it is equal to one.

8. The acceleration of the particle moving with simple harmonic motion is ____________ at the mean position.

a) zero

b) minimum

c) maximum

d) none of the mentioned

Answer: a

Explanation: The acceleration of a body is zero at the mean position and maximum when x = r.

9. The maximum velocity of a particle moving with simple harmonic motion is

a) ω

b) ωr

c) ω 2 r

d) ω/r

Answer: b

Explanation:The velocity of a moving body with simple harmonic motion at any instant is given by

v = ω√r 2 – x 2

The velocity is maximum at the mean position i.e. when x = 0.

Hence, v = ωr.

10. When a particle moves round the circumference of a circle of radius r with ω rad/s, then its maximum acceleration is ω 2 r.

a) True

b) False

Answer: a

Explanation: The acceleration of a body moving with simple harmonic motion at any instant is given by

a = ω 2 r.

11. If a simple pendulum oscillates with an amplitude 50 mm and time period 2s, then its maximum velocity is

a) 0.1 m/s

b) 0.15 m/s

c) 0.8 m/s

d) 0.16 m/s

Answer: b

Explanation: Maximum velocity v max = ωA where ‘ω’ is the angular frequency and ‘A’ is the amplitude. Therefore v max = A = ×50×10-3 = 0.157 m/s.

12. A particle executes linear simple harmonic motion with an amplitude of 2 cm. When the particle is at 1 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is

a) 1/ 2π√3

b) 2π√3

c) 2π/√3

d) √3/2π

Answer: b

Explanation: The magnitudes of the velocity and acceleration of the particle when its displacement is ‘y’ are ω√ and ω2y respectively. Equating them, ω√ = ω2y, from which ω = [√]/y = √ = √3. Period T = 2π/ω = 2π/√3.

13. Suppose you place a sphere of mass ‘m’ and radius ‘r’ inside a smooth, heavy hemispherical bowl of radius of 37r placed on a horizontal table. If the sphere is given a small displacement, what is its period of oscillation?

a) 2π√

b) 2π√

c) 12π√

d) 2π√

Answer: c

Explanation: The arrangement depicted in this question is similar to that of a simple pendulum. Instead of the usual string, you have a concave surface to confine the bob  to its path along the arc of a circle. The usual expression for the period, T = 2π√ holds here also, where the length L = 36r since the length of the pendulum is measured from the centre of gravity of the bob. The point of ‘suspension’ is evidently at the centre of the hemispherical bowl. The correct option is 12π√.

14. The instantaneous displacement of a simple harmonic oscillator is given by y = A cos. Its speed will be maximum at the time

a) 2π/ω

b) ω/2π

c) ω/π

d) π/4ω

Answer: d

Explanation: The velocity is the time derivative of displacement: v = dy/dt = -Aω. Its maximum magnitude equal to Aω is obtained when ωt = π/4, from which t = π/4ω.

Answer: d

Explanation: T = 2π√ where ‘k’ is the force constant, the solution becomes quite easy. From this, k = 4π2m/T2 = 4π2 ×5×10-3/2 = 0.5. Since ‘k’ is the force for unit displacement, the maximum force is k times the maximum displacement . Therefore maximum force = kA = 0.5×0.3 = 0.15N.

This set of Tricky Machine Kinematics Questions and Answers focuses on “Differential Equation of Simple Harmonic Motion”.

1. By how much angle in degrees does the velocity leads the displacement in a body undergoing SIMPLE HARMONIC MOTION?

a) 90

b) 45

c) 180

d) 0

Answer: a

Explanation: For a body undergoing Simple Harmonic Motion, the velocity leads the displacement by an angle of 90 degrees as shown by the differential equation of the motion.

2. For a body undergoing SIMPLE HARMONIC MOTION, the acceleration is always in the direction of the displacement.

a) True

b) False

Answer: b

Explanation: For a body undergoing SIMPLE HARMONIC MOTION, the acceleration is always in the opposite direction of the displacement. This is indicated by a negative sign in the equation.

3. The maximum displacement of the body under Simple Harmonic Motion from its mean position is known as_______

a) Amplitude

b) Frequency

c) Time period

d) Range

Answer: a

Explanation: The maximum displacement of a body undergoing Simple Harmonic Motion is known as Amplitude, it is generally denoted by ‘A’.

4. The piston of an engine moves with SIMPLE HARMONIC MOTION. The crank rotates at a speed of 120 r.p.m. with a stroke of 2 metres. Find the velocity of the piston in m/s, when it is at a distance of 0.75 metre from the centre.

a) 8.31

b) 7.33

c) 8.41

d) 9.02

Answer: a

Explanation: When a body is undergoing SIMPLE HARMONIC MOTION, its velocity is given by the equation

\(v = \omega \sqrt{}\)

substituting the values we get

v = 8.31 m/s.

5. The piston of an engine moves with SIMPLE HARMONIC MOTION. The crank rotates at a speed of 120 r.p.m. with a stroke of 2 metres. Find the velocity of the piston in m/s 2 , when it is at a distance of 0.75 metre from the centre.

a) 118.46

b) 117.33

c) 128.41

d) 119.02

Answer: a

Explanation: When a body is undergoing SIMPLE HARMONIC MOTION, its acceleration is given by the equation

a=ω 2 x

substituting the values we get

a = 118.46 m/s 2

6. A point moves with SIMPLE HARMONIC MOTION. When this point is 0.75 m away from the mid path, it has a velocity of 11 m/s and when 2 m from the centre of its path its velocity is 3 m/s. Find its angular velocity in rad/s.

a) 5.7

b) 7.5

c) 6.7

d) 7.6

Answer: a

Explanation: When a body is undergoing SIMPLE HARMONIC MOTION, its velocity is given by the equation

v = \ = 0.75 m, then its velocity  = 11 m/s

when point  = 2 m, then its velocity  = 3 m/s

When point is 0.75 m away from the mid path  is,

v = \

Similarly, When point is 2 m away from the centre  is,

v = \

Solving Eq & Eq we get,

\(\frac{11}{3} \frac{\omega \sqrt{r^2 – ^2}}{\omega \sqrt{r^2 – 2^2}} = \frac{\sqrt{r^2 – ^2}}{\sqrt{r^2 – 2^2}} \)

Squaring on both sides, we get

\(\frac{121}{9} = \frac{r^2 – 0.5625}{r^2 – 4}\)

121r 2 – 484 = 9r 2 – 5.0625

121r 2 – 9r 2 = 484 – 5.0625

112r 2 = 478.9375

r 2 = \(\frac{478.9375}{112}\)

r 2 = 4.27622

r = 2.07m

Substituting the value of r in Eq we get,

11 = \( \omega \sqrt{^2 – ^2}\)

11 = \( \omega \sqrt{4.2849 – 0.5625}\)

11 = \( \omega \sqrt{3.7224}\)

11 = 1.9293 ω

ω = \(\frac{11}{1.9293}\) = 5.7 rad/s.

7. A point moves with SIMPLE HARMONIC MOTION. When this point is 0.75 m away from the mid path, it has a velocity of 11 m/s and when 2 m from the centre of its path its velocity is 3 m/s. Find its time period in s.

a) 1.1

b) 1.2

c) 1.3

d) 1.4

Answer: a

Explanation: When a body is undergoing SIMPLE HARMONIC MOTION, its velocity is given by the equation

v = \ = 0.75 m, then its velocity  = 11 m/s

when point  = 2 m, then its velocity  = 3 m/s

When point is 0.75 m away from the mid path  is,

v = \

Similarly, When point is 2 m away from the centre  is,

v = \

Solving Eq & Eq we get,

\(\frac{11}{3} \frac{\omega \sqrt{r^2 – ^2}}{\omega \sqrt{r^2 – 2^2}} = \frac{\sqrt{r^2 – ^2}}{\sqrt{r^2 – 2^2}} \)

Squaring on both sides, we get

\(\frac{121}{9} = \frac{r^2 – 0.5625}{r^2 – 4}\)

121r 2 – 484 = 9r 2 – 5.0625

121r 2 – 9r 2 = 484 – 5.0625

112r 2 = 478.9375

r 2 = \(\frac{478.9375}{112}\)

r 2 = 4.27622

r = 2.07m

Substituting the value of r in Eq we get,

11 = \( \omega \sqrt{^2 – ^2}\)

11 = \( \omega \sqrt{4.2849 – 0.5625}\)

11 = \( \omega \sqrt{3.7224}\)

11 = 1.9293 ω

ω = \(\frac{11}{1.9293}\) = 5.7 rad/s.

We know periodic time is,

T p = \(\frac{2 \pi}{\omega} = \frac{2 \pi}{5.7} = \frac{2 \times 3.14}{5.7} = \frac{6.28}{5.7}\) = 1.1 s.

8. A point moves with SIMPLE HARMONIC MOTION. When this point is 0.75 m away from the mid path, it has a velocity of 11 m/s and when 2 m from the centre of its path its velocity is 3 m/s. Find its maximum acceleration in m/s 2 .

a) 61.1

b) 67.2

c) 51.3

d) 41.4

Answer: b

Explanation: When a body is undergoing SIMPLE HARMONIC MOTION, its velocity is given by the equation

v = \ = 0.75 m, then its velocity  = 11 m/s

when point  = 2 m, then its velocity  = 3 m/s

When point is 0.75 m away from the mid path  is,

v = \

Similarly, When point is 2 m away from the centre  is,

v = \

Solving Eq & Eq we get,

\(\frac{11}{3} \frac{\omega \sqrt{r^2 – ^2}}{\omega \sqrt{r^2 – 2^2}} = \frac{\sqrt{r^2 – ^2}}{\sqrt{r^2 – 2^2}} \)

Squaring on both sides, we get

\(\frac{121}{9} = \frac{r^2 – 0.5625}{r^2 – 4}\)

121r 2 – 484 = 9r 2 – 5.0625

121r 2 – 9r 2 = 484 – 5.0625

112r 2 = 478.9375

r 2 = \(\frac{478.9375}{112}\)

r 2 = 4.27622

r = 2.07m

Substituting the value of r in Eq we get,

11 = \( \omega \sqrt{^2 – ^2}\)

11 = \( \omega \sqrt{4.2849 – 0.5625}\)

11 = \( \omega \sqrt{3.7224}\)

11 = 1.9293 ω

ω = \(\frac{11}{1.9293}\) = 5.7 rad/s.

Maximum acceleration is

A max = ω 2 r =  2 × 2.07 = 32.49 × 2.07

= 67.25 m/s 2 .

9. If V is the maximum velocity of a body undergoing SIMPLE HARMONIC MOTION, then what is the average velocity of motion from one extreme to other extreme is?

a) 2V/π

b) 4V/π

c) V/2π

d) 2V/3π

Answer: a

Explanation: V = 2πA/T

V av = 2A/T÷2 = 4A/T

A/T = V/2π

Vav = 2V/π

10. If V is the maximum velocity of a body undergoing SIMPLE HARMONIC MOTION, then what is the average velocity of motion?

a) 2V/π

b) 4V/π

c) V/2π

d) 2V/3π

Answer: a

Explanation: V = Aω

<v> = 4A/T

= 2aω/π

= 2V/π

11. Which of the following is the correct differential equation of the SIMPLE HARMONIC MOTION?

a) d 2 x/dt 2 + ω 2 x = 0

b) d 2 x/dt 2 – ω 2 x = 0

c) d 2 x/dt + ω 2 x = 0

d) d 2 x/dt – ω 2 x = 0

Answer: a

Explanation: For body undergoing Simple Harmonic Motion, it’s motion can be represented as projected uniform circular motion with radius equal to the amplitude of motion.

Therefore x =Acosωt

dx/dt = -Aωsinωt

d 2 x/dt 2 = -aω 2 cosωt

therefore

d 2 x/dt 2 + ω 2 x = 0

12. For a body undergoing Simple Harmonic Motion, the acceleration is maximum at the extreme.

a) True

b) False

Answer: a

Explanation: For a body undergoing SIMPLE HARMONIC MOTION, the acceleration is always in the opposite direction of the displacement. This is indicated by a negative sign in the equation and at an extreme position, the acceleration attains a maximum value.

13. Which of the following is the solution of the differential equation of the SIMPLE HARMONIC MOTION?

a) x = Acosωt + B sinωt

b) x = cosωt

c) x = sinωt

d) x = Atanωt + B sinωt

Answer: a

Explanation: We know that dx/dt = -Aωsinωt

d 2 x/dt 2 = -aω 2 cosωt

therefore

d 2 x/dt 2 + ω 2 x = 0

is the standard differential equation of Simple Harmonic Motion

It’s solution is/are:

x = Acosωt + B sinωt

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Simple Pendulum”.

1. The acceleration of the particle moving with simple harmonic motion is inversely proportional to the displacement of the particle from the mean position.

a) True

b) False

Answer: b

Explanation: The acceleration of the particle moving with simple harmonic motion is directly proportional to the displacement of the particle from the mean position.

2. In order to double the period of a simple pendulum, the length of the string should be

a) halved

b) doubled

c) quadrupled

d) none of the mentioned

Answer: c

Explanation: Periodic time, t p = 2п√L/g

So, if period is doubled, then length should be quadrupled

3. The equivalent length of simple pendulum depends upon the distance between the point of the suspension and the center of gravity.

a) True

b) False

Answer: a

Explanation: None

4. Which of the following statement is correct?

a) The periodic time of a particle moving with simple harmonic motion is the time taken by a particle for one complete oscillation.

b) The periodic time of a particle moving with simple harmonic motion is directly proportional to its angular velocity.

c) The velocity of a particle moving with simple harmonic motion is zero at the mean position.

d) The acceleration of the particle moving with simple harmonic motion is maximum at the mean position.

Answer: a

Explanation: The time taken for one complete revolution of the particle is called periodic time.

5. The periodic time of a compound pendulum is …….. when the distance between the point of suspension and the center of gravity is equal to the radius of gyration of the body about its center of gravity.

a) zero

b) minimum

c) maximum

d) none of the mentioned

Answer: b

Explanation: When a rigid body is suspended vertically and it oscillates with a small amplitude under the action of the force of gravity, the body is known as compound pendulum.

6. In a simple harmonic motion, the velocity vector with respect to displacement vector

a) is in phase

b) leads by 90 0

c) leads by 180 0

d) lags by 90 0

Answer: d

Explanation: None

7. The distance between the center of suspension and center of percussion is equal to the equivalent length of a simple pendulum.

a) True

b) False

Answer: a

Explanation: The periodic time and frequency of oscillation of a simple pendulum depends only upon its length and acceleration due to gravity.

8. The center of suspension and center of percussion are not interchangeable.

a) True

b) False

Answer: b

Explanation: The distance between the center of suspension and center of percussion is equal to the equivalent length of a simple pendulum.

9. When the body is suspended at the point of suspension, its periodic time and frequency will be _____________ as compared to the body suspended at the point of percussion.

a) same

b) two times

c) four times

d) eight times

Answer: a

Explanation: The distance between the center of suspension and center of percussion is equal to the equivalent length of a simple pendulum.

Answer: b

Explanation: None

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Closely-coiled Helical Spring and Compound Pendulum”.

1. In a squared and ground helical spring the effective number of turns is increased by

a) 1

b) 2

c) 1.5

d) 0

Answer: b

Explanation: In a compression spring the ends can be plain, plain and ground, squared, squared and ground. The number of inactive turns in each case are 1.5,1,1 and 2 respectively.

2. Frequency of the fluctuating load on a helical compression spring should be

a) less than natural frequency of vibration

b) twenty times the natural frequency of vibration

c) slightly greater than the natural frequency

d) twenty times the natural frequency of vibration

Answer: d

Explanation: If the frequency of application of load matches the natural frequency of vibration, very high stresses are induced in the spring material causing fatigue failure. It can be avoided by keeping the natural frequency at least 20 times greater.

3. Two concentric springs with stiffness equal to 100 N/mm and 80 N/mm respectively, when subjected to a load of 900 N will deflect by

a) 9 mm

b) 11.25 mm

c) 5 mm

d) 31.5 mm

Answer: c

Explanation: In this case, total stiffness K t is given by,

1/K t = K 1 + K 2

= 100+ 80 = 180N/mm

Therefore, deflection = Force/stiffness

= 900N/180N/mm

= 5 mm.

4. Stiffness of the spring can be increased by

a) increasing the number of turns

b) increasing the free length

c) decreasing the number of turns

d) decreasing the spring wire diameter

Answer: c

Explanation: Stiffness of the spring can be decreased by increasing the number of turns and increased by decreasing the number of turns.

5. The stress induced in an extra full length leaf in case of a prestresed leaf spring is

a) 1.5 times that in graduated leaves

b) equal to that in graduated leaves

c) dependent on the ratio of the number of extra full length and graduated leaves

d) none of the mentioned

Answer: b

Explanation: The leaves which are cut from original triangular leaf, are termed as graduated leaves. In actual practice some extra leaves with the same length as that of top leaf are added to increase the stiffness of the spring.

6. Initial gap between two turns of a close coiled helical tension spring should be

a) 0.5 mm

b) based on the maximum deflection

c) 1 mm

d) 0

Answer: d

Explanation: There is no gap between two turns of a close coiled helical tension spring.

7. Due to addition of extra full length leaves the deflection of a semi-elliptic spring

a) increases

b) decreases

c) does not change

d) is doubled

Answer: b

Explanation: In actual practice some extra leaves with the same length as that of top leaf are added to increase the stiffness of the spring.

8. A connecting rod of mass 5.5 kg is placed on a horizontal platform whose mass is 1.5 kg. It is suspended by three equal wires, each 1.25 m long, from a rigid support. The wires are equally spaced round the circumference of a circle of 125 mm radius. When the c.g. of the connecting rod coincides with the axis of the circle, the platform makes 10 angular oscillations in 30 seconds. Determine the mass moment of inertia about an axis through its c.g.

a) 0.198 kg-m 2

b) 1.198 kg-m 2

c) 2.198 kg-m 2

d) 3.198 kg-m 2

Answer: a

Explanation: Given : m 1 = 5.5 kg ; m 2 = 1.5 kg ; l = 1.25 m ; r = 125 mm = 0.125 m

Since the platform makes 10 angular oscillations in 30 s, therefore frequency of oscillation,

n = 10/30 = 1/3 Hz

Let k G = Radius of gyration about an axis through the c.g.

We know that frequency of oscillation 

1/3 = r/2πk G √g/l = 0.125/2πk G √9.81/1.25 = 0.056/k G

k G = 0.056 x 3 = 0.168 m

and mass moment of inertia about an axis through its c.g.,

I = mk 2 G = (m 1 + m 2 )k 2 G

=   2 kg-m 2

= 0.198 kg-m 2 .

9. In order to find the radius of gyration of a car, it is suspended with its axis vertical from three parallel wires 2.5 metres long. The wires are attached to the rim at points spaced 120° apart and at equal distances 250 mm from the axis. It is found that the wheel makes 50 torsional oscillations of small amplitude about its axis in 170 seconds. Find the radius of gyration of the wheel.

a) 168 mm

b) 268 mm

c) 368 mm

d) 468 mm

Answer: b

Explanation: Given : l = 2.5 m ; r = 250 mm = 0.25 m ;

Since the wheel makes 50 torsional oscillations in 170 seconds, therefore frequency of oscillation,

n = 50/170 = 5/17 Hz

Let k G = Radius of gyration of the wheel

We know that frequency of oscillation ,

5/17 = r/2πk G √g/l = 0.25/2πk G √9.81/2.5 = 0.079/k G

k G = 0.079 x 17/5 = 0.268 m = 268 mm.

10. A small connecting rod of mass 1.5 kg is suspended in a horizontal plane by two wires 1.25 m long. The wires are attached to the rod at points 120 mm on either side of the centre of gravity. If the rod makes 20 oscillations in 40 seconds, find the radius of gyration of the rod about a vertical axis through the centre of gravity.

a) 107 mm

b) 207 mm

c) 307 mm

d) 407 mm

Answer: a

Explanation: Given : m = 1.5 kg ; l = 1.25 m ; x = y = 120 mm = 0.12 m

Since the rod makes 20 oscillations in 40 s, therefore frequency of oscillation,

n = 20/40 = 0.5 Hz

Let k G = Radius of gyration of the connecting rod.

We know that frequency of oscillation ,

0.5 = 1/2πk G √gxy/l = 1/2πk G √9.81 x 0.12 x 0.12/1.25 = 0.0535/k

k G = 0.0535/0.5 = 0.107 m = 107 mm.

11. A small connecting rod of mass 1.5 kg is suspended in a horizontal plane by two wires 1.25 m long. The wires are attached to the rod at points 120 mm on either side of the centre of gravity. If the rod makes 20 oscillations in 40 seconds, find the mass moment of inertia of the rod about a vertical axis through the centre of gravity.

a) 0.014 kg-m 2

b) 0.015 kg-m 2

c) 0.016 kg-m 2

d) 0.017 kg-m 2

Answer: d

Explanation: Given : m = 1.5 kg ; l = 1.25 m ; x = y = 120 mm = 0.12 m

Since the rod makes 20 oscillations in 40 s, therefore frequency of oscillation,

n = 20/40 = 0.5 Hz

Let k G = Radius of gyration of the connecting rod.

We know that frequency of oscillation ,

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Compound Pendulum”.

1. Which of the following shape of the body can be considered as compound pendulum?

a) Cylindrical

b) Cubical

c) Cuboidal

d) Any rigid body

Answer: d

Explanation: Any rigid body having mass when suspended vertically and oscillates with small amplitude under the force of gravity undergoes SHM as a compound pendulum.

2. Compound pendulum needs to be spherical in shape.

a) True

b) False

Answer: b

Explanation: Any rigid body when suspended vertically, and it oscillates with a small amplitude under the action of the force of gravity, the body is known as compound pendulum. The rigid body is asssumed to have a mass and hence mass moment of inertia.

3. If the mass of the object is doubled then what will be the effect of time period of the compound pendulum?

a) Doubled

b) Remains same

c) Halved

d) Decreases by √2 times

Answer: d

Explanation: The time period of a compound pendulum is given by:

\(\sqrt{

 

}\), now the dependency of the time period on the mass is inversely proportional to the root of mass, hence it decreases by √2 times.

4. If the mass moment inertia of the object is increased to 4 times then what will be the effect of time period of the compound pendulum?

a) Doubled

b) Remains same

c) Halved

d) Decreases by √2 times

Answer: a

Explanation: The time period of a compound pendulum is given by:

\(\sqrt{

 

}\), now the dependency of the time period on the mass moment of inertia is directly proportional to the root of Moment of Inertia, hence it increases by 2 times.

5. Calculate the time period of an object having mass moment of inertia = 100 Kg-m 2 , mass of 10 Kg and the centre of gravity lies at a point 20 cm below the point of suspension.

a) 14.1

b) 15.2

c) 13.3

d) 12.9

Answer: a

Explanation: From the given data it is clear that the given rigid body constitutes a compound pendulum, now the time period of a compound pendulum is given by:

\(\sqrt{

 

}\)

substituting the values we get

T = 14.1 sec.

6. Calculate the frequency of vibration in Hz of an object having mass moment of inertia = 100 Kg-m 2 , mass of 10 Kg and the centre of gravity lies at a point 20 cm below the point of suspension.

a) 0.14

b) 0.15

c) 0.13

d) 0.07

Answer: d

Explanation: From the given data it is clear that the given rigid body constitutes a compound pendulum, now the time period of a compound pendulum is given by:

\(\sqrt{

 

}\)

substituting the values we get

T = 14.1 sec.

f = 1/T = 0.07 Hz.

7. Calculate the moment of inertia of an object having time period = 14 sec, mass of 10 Kg and the centre of gravity lies at a point 20 cm below the point of suspension.

a) 94.1

b) 95.2

c) 93.3

d) 97.4

Answer: d

Explanation: From the given data it is clear that the given rigid body constitutes a compound pendulum, now the time period of a compound pendulum is given by:

\(\sqrt{

 

}\)

substituting the values we get

I = 97.4 Kg-m 2 .

8. All simple pendulums are compound pendulums.

a) True

b) False

Answer: a

Explanation: Simple pendulum also is a compound pendulum where the mass is a point mass, hence the distance from centre of gravity is the length of the string.

9. If the mass moment inertia of the object is increased to 4 times then what will be the effect of time period of the simple pendulum?

a) Doubled

b) Remains same

c) Halved

d) Decreases by √2 times

Answer: b

Explanation: The time period of a simple pendulum is given by:

√, now the dependency of the time period on the mass moment of inertia is non existent, hence it remains unchanged.

10. Calculate the moment of inertia of an object having time period = 14 sec, mass moment of inertia= 100 Kg-m 2 and the centre of gravity lies at a point 20 cm below the point of suspension.

a) 9.1

b) 9.2

c) 9.3

d) 10.2

Answer: d

Explanation: From the given data it is clear that the given rigid body constitutes a compound pendulum, now the time period of a compound pendulum is given by:

\(\sqrt{

 

}\)

substituting the values we get

m = 10.2 Kg.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Centre of Percussion”.

1. The piston of a steam engine moves with simple harmonic motion. The crank rotates at 120 r.p.m. with a stroke of 2 metres. Find the velocity of the piston, when it is at a distance of 0.75 metre from the centre.

a) 8 m/s

b) 8.31 m/s

c) 9 m/s

d) none of the mentioned

Answer: b

Explanation: Given : N = 120 r.p.m. or ω = 2π × 120/60 = 4π rad/s ; 2r = 2 m or r = 1 m;

x = 0.75 m

Velocity of the piston

We know that velocity of the piston,

v = ω√r 2 – x 2 = 4π√1 –  2 = 8.31 m/s.

2. The piston of a steam engine moves with simple harmonic motion. The crank rotates at 120 r.p.m. with a stroke of 2 metres. Find the acceleration of the piston, when it is at a distance of 0.75 metre from the centre.

a) 118.46 m/s 2

b) 90 m/s 2

c) 100 m/s 2

d) none of the mentioned

Answer: a

Explanation: Given : N = 120 r.p.m. or ω = 2π × 120/60 = 4π rad/s ; 2r = 2 m or r = 1 m;

x = 0.75 m

Velocity of the piston

We know that velocity of the piston,

v = ω√r 2 – x 2 = 4π√1 –  2 = 8.31 m/s

We also know that acceleration of the piston,

a = ω 2 .x =  2 0.75 = 118.46 m/s 2 .

3. Law of isochronism

a) states the time period (t p ) of a simple pendulum does not depend upon the mass of the body suspended at the free end of the string.

b) states the time period (t p ) of a simple pendulum does not depend upon its amplitude of vibration and remains the same, provided the angular amplitude  does not exceed 4°.

c) states the time period (t p ) of a simple pendulum is directly proportional to √L , where L is the length of the string.

d) none of the mentioned

Answer: b

Explanation: It states the time period (t p ) of a simple pendulum does not depend upon its amplitude of vibration and remains the same, provided the angular amplitude  does not exceed 4°.

4. Law of mass

a) states the time period (t p ) of a simple pendulum does not depend upon the mass of the body suspended at the free end of the string.

b) states the time period (t p ) of a simple pendulum does not depend upon its amplitude of vibration and remains the same, provided the angular amplitude  does not exceed 4°.

c) states the time period (t p ) of a simple pendulum is directly proportional to √L , where L is the length of the string.

d) none of the mentioned

Answer: a

Explanation: It states the time period (t p ) of a simple pendulum does not depend upon the mass of the body suspended at the free end of the string.

5. Law of length

a) states the time period (t p ) of a simple pendulum does not depend upon the mass of the body suspended at the free end of the string.

b) states the time period (t p ) of a simple pendulum does not depend upon its amplitude of vibration and remains the same, provided the angular amplitude  does not exceed 4°.

c) states the time period (t p ) of a simple pendulum is directly proportional to √L , where L is the length of the string.

d) none of the mentioned

Answer: c

Explanation: It states the time period (t p ) of a simple pendulum is directly proportional to √L , where L is the length of the string.

6. Law of gravity

a) states the time period (t p ) of a simple pendulum does not depend upon the mass of the body suspended at the free end of the string.

b) states the time period (t p ) of a simple pendulum does not depend upon its amplitude of vibration and remains the same, provided the angular amplitude  does not exceed 4°.

c) states the time period (t p ) of a simple pendulum is directly proportional to √L , where L is the length of the string.

d) states the time period (t p ) of a simple pendulum is inversely proportional to √g , where g is the acceleration due to gravity.

Answer: d

Explanation: It states the time period (t p ) of a simple pendulum is inversely proportional to √g , where g is the acceleration due to gravity.

7. A helical spring, of negligible mass, and which is found to extend 0.25 mm under a mass of 1.5 kg, is made to support a mass of 60 kg. The spring and the mass system is displaced vertically through 12.5 mm and released. Determine the frequency of natural vibration of the system.

a) 6 Hz

b) 4.98 Hz

c) 5.98 Hz

d) none of the mentioned

Answer: b

Explanation: Given : m = 60 kg ; r = 12.5 mm = 0.0125 m ; x = 5 mm = 0.005 m

Since a mass of 1.5 kg extends the spring by 0.25 mm, therefore a mass of 60 kg will extend the spring by an amount,

δ = 0.25/1.5 x 60 = 10 mm = 0.01m

We know that frequency of the system,

n = 1/2π√g/δ = 1/2π√9.81/0.01 = 4.98 Hz.

8. A helical spring, of negligible mass, and which is found to extend 0.25 mm under a mass of 1.5 kg, is made to support a mass of 60 kg. The spring and the mass system is displaced vertically through 12.5 mm and released. Find the velocity of the mass, when it is 5 mm below its rest position.

a) 0.36 m/s

b) 0.46 m/s

c) 0.56 m/s

d) none of the mentioned

Answer: a

Explanation: Given : m = 60 kg ; r = 12.5 mm = 0.0125 m ; x = 5 mm = 0.005 m

Since a mass of 1.5 kg extends the spring by 0.25 mm, therefore a mass of 60 kg will extend the spring by an amount,

δ = 0.25/1.5 x 60 = 10 mm = 0.01m

We know that frequency of the system,

n = 1/2π√g/δ = 1/2π√9.81/0.01 = 4.98 Hz

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Bifilar Suspension”.

1. Which of the following apparatus is used to find the moment of inertia of an object?

a) Simple pendulum

b) Bifilar suspension

c) Compound pendulum

d) Spring pendulum

Answer: b

Explanation: Experimentally, the moment of inertia of any rigid body can be calculated with an apparatus called bifilar suspension.

2. The strings used in bifilar suspension are perpendicular.

a) True

b) False

Answer: b

Explanation: The body whose moment of inertia is to be determined is suspended by two long parallel flexible strings.

3. From the following data calculate the radius of gyration of the connecting rod.

mass of connecting rod = 1.5 Kg, length of wires = 1.25m, distance of wires to the rods = 0.12m

Time for 20 oscillations = 40 secs.

a) 107 mm

b) 110 mm

c) 95 mm

d) 100 mm

Answer: a

Explanation: From the given data x=y= 0.12m

T = 40/20 = 2 sec, f = 0.5sec

Substituting the values into the bifilar expression we get

Kg = 107 mm.

4. From the following data calculate the mass moment of inertia of the connecting rod in Kg-m 2 .

mass of connecting rod = 1.5 Kg, length of wires = 1.25m, distance of wires to the rods = 0.12m, Time for 20 oscillations = 40 secs.

a) 0.107

b) 0.017

c) 0.095

d) 0.010

Answer: b

Explanation: From the given data x=y= 0.12m

T = 40/20 = 2 sec, f = 0.5sec

Substituting the values into the bifilar expression we get

k = 107 mm = 0.107m

I = mk 2 = 0.017 Kg-m 2 .

5. A rigid body has a radius of gyration of 20cm, if its moment of inertia is 10 Kg-m 2 , find its mass in kilograms.

a) 250

b) 225

c) 500

d) 125

Answer: a

Explanation: We know that I = mk 2

Now I = 10 Kg-m 2 and k = 0.2m

therefore m = I/k 2

= 10/0.04

6. In a bifilar suspension, if the length of the connecting rod is decreased, which of the following quantities will increase?

a) Time period

b) Frequency

c) Radius of gyration

d) Acceleration

Answer: b

Explanation: In a bifilar suspension, the frequency of vibration depends inversely on the square root of the length, hence decreasing length will result in increasing the frequency.

7. When the body is twisted through a small angle θ about a vertical axis through the centre of gravity, which of the following motion will occur?

a) Angular Simple Harmonic Motion

b) Linear Simple Harmonic Motion

c) Linear accelerated motion

d) Angular accelerated motion

Answer: a

Explanation: When a body is subjected to torsion then it twists by a small angle θ about a vertical axis through the centre of gravity which is generally denoted by G, it will vibrate with simple harmonic motion in a horizontal plane.

8. To determine moment of inertia of a rigid object both bifilar and trifilar suspensions can be used.

a) True

b) False

Answer: a

Explanation: The mass moment of inertia of any rigid object can be determined experimentally using an apparatus called bifilar suspension and trifilar suspension.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Bifilar and Trifilar Suspension”.

1. In S.H.M., acceleration is proportional to

a) velocity

b) displacement

c) rate of change of velocity

d) none of the mentioned

Answer: b

Explanation: The acceleration is proportional to its displacement from its mean position.

2. In S.H.M., the velocity vector w.r.t. displacement vector

a) leads by 90 0

b) lags by 90 0

c) leads by 180 0

d) none of the mentioned

Answer: a

Explanation: None.

3. A body having moment of inertia of 30 kg m 2 is rotating at 210 RPM and mashes with another body at rest having M.I. of 40 kg m 2 . The resultant speed after meshing will be

a) 90 RPM

b) 100 RPM

c) 80 RPM

d) none of the mentioned

Answer: a

Explanation: Since moment is conserved, there fore,

30 x 210 = 40 x Resultant speed

or, Resultant speed = 90 RPM.

4. Inertia force acts

a) perpendicular to the accelerating force

b) along the direction of accelerating force

c) opposite to the direction of accelerating force

d) none of the mentioned

Answer: c

Explanation: None.

5. The frequency of oscillation at moon compared to earth will be

a) 6 times more

b) 6 times less

c) 2.44 times more

d) 2.44 times less

Answer: d

Explanation: Frequency = 1/2π√g/l

since on moon gravitational force g becomes 1/6g

therefore, frequency = 2.44 times less.

6. Polar moment of inertia(I P ) of a circular disc is to be determined by suspending it by a wire and noting the frequency of oscillations

a) I P ∞ f

b) I P ∞ f 2

c) I P ∞ 1/f 2

d) none of the mentioned

Answer: c

Explanation: None.

7. The frequency of oscillation of a bigger diameter cylinder compared to a small cylinder inside a cylinder concave surface will be

a) less

b) more

c) same

d) none of the mentioned

Answer: b

Explanation: The frequency of oscillation of a bigger diameter cylinder compared to a small cylinder inside a cylinder concave surface will be more.

The frequency of oscillation of a cylinder inside a cylinder inside a cylindrical concave surface of bigger radius compared to a small radius will be less.

8. The frequency of oscillation of a cylinder inside a cylinder inside a cylindrical concave surface of bigger radius compared to a small radius will be

a) less

b) more

c) same

d) none of the mentioned

Answer: a

Explanation: The frequency of oscillation of a bigger diameter cylinder compared to a small cylinder inside a cylinder concave surface will be more.

The frequency of oscillation of a cylinder inside a cylinder inside a cylindrical concave surface of bigger radius compared to a small radius will be less.

9. If the radius of gyration of a compound pendulum about an axis through c.g. is more, then its frequency of oscillation will be

a) less

b) more

c) same

d) none of the mentioned

Answer: a

Explanation: The frequency of oscillation of a bigger diameter cylinder compared to a small cylinder inside a cylinder concave surface will be more.

The frequency of oscillation of a cylinder inside a cylinder inside a cylindrical concave surface of bigger radius compared to a small radius will be less.

10. The Bifilar suspension method is used to determine

a) natural frequency of vibration

b) position of balancing weights

c) moment of inertia

d) none of the mentioned

Answer: c

Explanation: None.

11. The natural frequency of a spring-mass system on earth is ω n . The natural frequency of this system on the moon (g moon =g earth /6) is

a) ω n

b) 0.408ω n

c) 0.204ω n

d) 0.167ω n

Answer: a

Explanation: We know natural frequency of a spring mass system is,

ω n = √k/m ………………….

This equation  does not depend on the g and weight 

So, the natural frequency of a spring mass system is unchanged on the moon.

Hence, it will remain ωn , i.e. ω moon =ω n .

12. An automotive engine weighing 240 kg is supported on four springs with linear characteristics. Each of the front two springs have a stiffness of 16MN/m while the stiffness of each rear spring is 32MN/m. The engine speed , at which resonance is likely to occur, is

a) 6040

b) 3020

c) 1424

d) 955

Answer: a

Explanation: Given k 1 = k 2 = 16MN/m, k 3 = k 4 = 32MN/m, m = 240 kg

Here, k 1 & k 2 are the front two springs or k 3 and k 4 are the rear two springs.

These 4 springs are parallel, So equivalent stiffness

k eq = k 1 + k 2 + k 3 + k 4 = 16 + 16 + 32 + 32 = 96MN/m 2

We know at resonance

ω = ω n = √k/m

2πN/60 = √k eq /m N =Engine speed in rpm

N = 60/2π√k eq /m

= 60/2π√96 x 10 6 /240

= 6040 rpm.

13. A vehicle suspension system consists of a spring and a damper. The stiffness of the spring is 3.6 kN/m and the damping constant of the damper is 400 Ns/m. If the mass is 50 kg, then the damping factor  and damped natural frequency (f n ), respectively, are

a) 0.471 and 1.19 Hz

b) 0.471 and 7.48 Hz

c) 0.666 and 1.35 Hz

d) 0.666 and 8.50 Hz

Answer: a

Explanation: Given k = 3.6 kN/m, c = 400 Ns/m, m = 50 kg

We know that, Natural Frequency

ω n = √k/m = 8.485 rad/ sec

And damping factor is given by,

d or ε = c/c c

= 0.471

Damping Natural frequency,

ω d = √1 – ε 2 ω n

2πf d = √1 – ε 2 ω n

f d = 1.19 Hz.

14. For an under damped harmonic oscillator, resonance

a) occurs when excitation frequency is greater than undamped natural frequency

b) occurs when excitation frequency is less than undamped natural frequency

c) occurs when excitation frequency is equal to undamped natural frequency

d) never occurs

Answer: c

Explanation: For an under damped harmonic oscillator resonance occurs when excitation frequency is equal to the undamped natural frequency

ω d = ω n .

Answer: d

Explanation: Given m= 12.5 kg, k= 1000N/m, c= 15 Ns/m

Critical Damping,

c c = 2m√k/m = 2√km

On substituting the values, we get

c c = 223.6 Ns/m.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Simple Mechanisms – 1”.

1. In a reciprocating steam engine, which of the following forms a kinematic link ?

a) cylinder and piston

b) piston rod and connecting rod

c) crank shaft and flywheel

d) flywheel and engine frame

Answer: c

Explanation: in a reciprocating steam engine, piston, piston rod and crosshead constitute one link ; connecting rod with big and small end bearings constitute a second link ; crank, crank shaft and flywheel a third link and the cylinder, engine frame and main bearings a fourth link.

2. The motion of a piston in the cylinder of a steam engine is an example of

a) completely constrained motion

b) incompletely constrained motion

c) successfully constrained motion

d) none of the mentioned

Answer: a

Explanation: The piston and cylinder in a steam engine form a pair and the motion of the piston is limited to a definite direction  relative to the cylinder irrespective of the direction of motion of the crank.

3. The motion transmitted between the teeth of gears in mesh is

a) sliding

b) rolling

c) may be rolling or sliding depending upon the shape of teeth

d) partly sliding and partly rolling

Answer: d

Explanation: When the two elements of a pair have a line or point contact when relative motion takes place and the motion between the two elements is partly turning and partly sliding, and in mesh the gears have a point contact.

4. The cam and follower without a spring forms a

a) lower pair

b) higher pair

c) self closed pair

d) force closed pair

Answer: c

Explanation: When the two elements of a pair are connected together mechanically in such a way that only required kind of relative motion occurs, it is then known as self closed pair. The lower pairs are self closed pair and the motion of cam and follower is relative to each other.

5. A ball and a socket joint forms a

a) turning pair

b) rolling pair

c) sliding pair

d) spherical pair

Answer: d

Explanation: When the two elements of a pair are connected in such a way that one element  turns or swivels about the other fixed element, the pair formed is called a spherical pair, and ball and socket joint are such pairs.

6. The lead screw of a lathe with nut forms a

a) sliding pair

b) rolling pair

c) screw pair

d) turning pair

Answer: c

Explanation: When the two elements of a pair are connected in such a way that one element can turn about the other by screw threads, the pair is known as screw pair. The lead screw of a lathe with nut, and bolt with a nut are examples of a screw pair.

7. When the elements of the pair are kept in contact by the action of external forces, the pair is said to be a

a) lower pair

b) higher pair

c) self closed pair

d) force closed pair

Answer: d

Explanation: When the two elements of a pair are not connected mechanically but are kept in contact by the action of external forces, the pair is said to be a force-closed pair. The cam and follower is an example of force closed pair, as it is kept in contact by the forces exerted by spring and gravity.

8. Which of the following is a turning pair ?

a) Piston and cylinder of a reciprocating steam engine

b) Shaft with collars at both ends fitted in a circular hole

c) Lead screw of a lathe with nut

d) Ball and socket joint

Answer: b

Explanation: When the two elements of a pair are connected in such a way that one can only turn or revolve about a fixed axis of another link, the pair is known as turning pair. A shaft with collars at both ends fitted into a circular hole, the crankshaft in a journal bearing in an engine, lathe spindle supported in head stock, cycle wheels turning over their axles etc. are the examples of a turning pair.

9. A combination of kinematic pairs, joined in such a way that the relative motion between the links is completely constrained, is called a

a) structure

b) mechanism

c) kinematic chain

d) inversion

Answer: c

Explanation: When the kinematic pairs are coupled in such a way that the last link is joined to the first link to transmit definite motion , it is called a kinematic chain. In other words, a kinematic chain may be defined as a combination of kinematic pairs, joined in such a way that each link forms a part of two pairs and the relative motion between the links or elements is completely or successfully constrained.

Answer: c

Explanation: If each link is assumed to form two pairs with two adjacent links, then the relation between the number of pairs  forming a kinematic chain and the number of links  may be expressed in the form of an equation :

l = 2 p – 4

This set of Machine Kinematics Interview Questions and Answers for Experienced people focuses on “Simple Mechanisms – 2”.

1. The relation between the number of links  and the number of binary joints  for a kinematic chain having constrained motion is given by j = 3/2 I -2 If the left hand side of this equation is greater than right hand side, then the chain is

a) locked chain

b) completely constrained chain

c) successfully constrained chain

d) incompletely constrained chain

Answer: a

Explanation: If the left hand side is greater than the right hand side, therefore it is not a kinematic chain and hence no relative motion is possible. Such type of chain is called locked chain and forms a rigid frame or structure which is used in bridges and trusses.

2. In a kinematic chain, a quaternary joint is equivalent to

a) one binary joint

b) two binary joints

c) three binary joints

d) four binary joints

Answer: c

Explanation: When four links are joined at the same connection, the joint is called a quaternary joint. It is equivalent to three binary joints.

3. If n links are connected at the same joint, the joint is equivalent to

a)  binary joints

b)  binary joints

c)  binary joints

d) none of the mentioned

Answer: a

Explanation: In general, when n number of links are joined at the same connection, the joint is equivalent to  binary joints.

4. In a 4 – bar linkage, if the lengths of shortest, longest and the other two links are denoted by s, l, p and q, then it would result in Grashof’s linkage provided that

a) l + p < s + q

b) l + s < p + q

c) l + p = s + q

d) none of the mentioned

Answer: b

Explanation: None

5. A kinematic chain is known as a mechanism when

a) none of the links is fixed

b) one of the links is fixed

c) two of the links are fixed

d) all of the links are fixed

Answer: b

Explanation: When one of the links of a kinematic chain is fixed, the chain is known as mechanism. It may be used for transmitting or transforming motion e.g. engine indicators, typewriter etc.

6. The Grubler’s criterion for determining the degrees of freedom  of a mechanism having plane motion is

a) n =  – j

b) n = 2  – 2j

c) n = 3  – 2j

d) n = 4  – 3j

Answer: c

Explanation: The Grubler’s criterion applies to mechanisms with only single degree of freedom joints where the overall movability of the mechanism is unity.

i.e. n = 3  – 2j

where l = Number of links, and j = Number of binary joints.

7. The mechanism forms a structure, when the number of degrees of freedom  is equal to

a) 0

b) 1

c) 2

d) – 1

Answer: a

Explanation: When n = 0, then the mechanism forms a structure and no relative motion between the links is possible.

When n = 1, then the mechanism can be driven by a single input motion.

When n = 2, then two separate input motions are necessary to produce constrained motion for the mechanism.

When n = – 1 or less, then there are redundant constraints in the chain and it forms a statically indeterminate structure.

8. In a four bar chain or quadric cycle chain

a) each of the four pairs is a turning pair

b) one is a turning pair and three are sliding pairs

c) three are turning pairs and one is sliding pair

d) each of the four pairs is a sliding pair.

Answer: a

Explanation: A very important consideration in designing a mechanism is to ensure that the input crank makes a complete revolution relative to the other links. The mechanism in which no link makes a complete revolution will not be useful. In a four bar chain, one of the links, in particular the shortest link, will make a complete revolution relative to the other three links, if it satisfies the Grashof ’s law. Such a link is known as crank or driver.

9. Which of the following is an inversion of single slider crank chain ?

a) Beam engine

b) Watt’s indicator mechanism

c) Elliptical trammels

d) Whitworth quick return motion mechanism

Answer: d

Explanation: None

Answer: c

Explanation: A kinematic chain which consists of two turning pairs and two sliding pairs is known as double slider crank chain and elliptical trammels are such pairs.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Kinematic Link or Element”.

1. In a reciprocating steam engine, which of the following forms a kinematic link?

a) cylinder and piston

b) piston and connecting rod

c) crankshaft and flywheel

d) flywheel and engine frame

Answer: c

Explanation: Each part of a machine which moves relative to some other part, is known as a kinematic link. The piston and cylinder in a steam engine, form a pair and the motion of the piston is limited to a definite direction relative to the cylinder irrespective of the direction of motion of the crank.

2. A link or element need not to be a rigid body, but it must be a resistant body.

a) True

b) False

Answer: a

Explanation: A body is said to be a resistant body if it is capable of transmitting the required forces with negligible deformation. A link or element need not to be a rigid body, but it must be a resistant body.

3. A railway bridge is an example of a machine.

a) True

b) False

Answer: b

Explanation: When a mechanism is required to transmit power or to do some particular type of work, then it becomes a machine. A railway bridge remains static and there is no motion in it. Hence, it is not a machine.

4. The motion between a pair when limited to a definite direction, irrespective of the direction of force applied, is known as

a) completely constrained motion

b) incompletely constrained motion

c) successfully constrained motion

d) none of the mentioned

Answer: a

Explanation: When the motion between a pair is limited to a definite direction irrespective of the direction of force applied, then the motion is said to be a completely constrained motion.

5. The motion between a pair which takes place in ____________ is known as incompletely constrained motion.

a) one direction only

b) more than one direction

c) opposite direction

d) none of the mentioned

Answer: b

Explanation: When the motion between a pair can take place in more than one direction, then the motion is called an incompletely constrained motion.

6. When the connection between the elements forming a pair is such that the constrained motion is not completed by itself, but by some other means, the motion is said to be a completely constrained motion.

a) True

b) False

Answer: b

Explanation: When the motion between a pair is limited to a definite direction irrespective of the direction of force applied, then the motion is said to be a completely constrained motion.

When the connection between the elements forming a pair is such that the constrained motion is not completed by itself, but by some other means, the motion is said to be a successfully constrained motion.

7. The example of completely constrained motion is

a) motion of a piston in the cylinder of a steam engine

b) motion of a square bar in a square hole

c) motion of a shaft with collars at each end in a circular hole

d) all of the mentioned

Answer: d

Explanation: When the motion between a pair is limited to a definite direction irrespective of the direction of force applied, then the motion is said to be a completely constrained motion. In all the above mechanism, motion is limited, so they all are examples of completely constrained motion.

8. The motion of a shaft in a circular hole is an example of

a) completely constrained motion

b) incompletely constrained motion

c) successfully constrained motion

d) none of the mentioned

Answer: b

Explanation: When the motion between a pair can take place in more than one direction, then the motion is called an incompletely constrained motion. A circular bar or shaft in a circular hole, is an example of an incompletely constrained motion as it may either rotate or slide in a hole.

9. The example of successfully constrained motion is a

a) motion of an I.C. engine valve

b) motion of the shaft between a foot-step bearing

c) piston reciprocating inside an engine cylinder

d) all of the mentioned

Answer: d

Explanation: When the connection between the elements forming a pair is such that the constrained motion is not completed by itself, but by some other means, the motion is said to be a successfully constrained motion. so, the above examples have successfully constrained motion.

Answer: c

Explanation: None

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Types of Links”.

1. When the nature of contact between the element of a pair is such that it can only slide relative to the other, the pair is known as a

a) screw pair

b) spherical pair

c) turning pair

d) sliding pair

Answer: d

Explanation: When the nature of contact between the element of a pair is such that one element can turn abut the other by screw threads, the pair is known as a screw pair. When the nature of contact between the element of a pair is such that it can only slide relative to the other, the pair is known as a sliding pair.

2. When the nature of contact between the element of a pair is such that it can turn or revolve about a fixed axis, the pair is known as a rolling pair.

a) True

b) False

Answer: b

Explanation: When the nature of contact between the element of a pair is such that it can turn or revolve about a fixed axis, the pair is known as a turning pair.

3. When the nature of contact between the element of a pair is such that one element can turn abut the other by screw threads, the pair is known as a

a) screw pair

b) spherical pair

c) turning pair

d) sliding pair

Answer: a

Explanation: When the nature of contact between the element of a pair is such that one element can turn abut the other by screw threads, the pair is known as a screw pair.

4. A sliding pair has a completely constrained motion.

a) True

b) False

Answer: a

Explanation: When the nature of contact between the element of a pair is such that it can only slide relative to the other, the pair is known as a sliding pair and it has a completely constrained motion.

5. Which of the following is an example of sliding pair?

a) Piston and cylinder of a reciprocating steam engine

b) Shaft with collars at both ends fitted into a circular hole

c) Lead screw of a lathe with nut

d) Ball and a socket joint

Answer: a

Explanation: When the nature of contact between the element of a pair is such that it can only slide relative to the other, the pair is known as a sliding pair and can be found in piston and cylinder of a reciprocating steam engine.

6. The ball and socket joint is an example of screw pair.

a) True

b) False

Answer: b

Explanation: The ball and socket joint is an example of spherical pair. When the two elements of a pair are connected in such a way that one element turns or swivels about the other fixed element, the pair formed is called a spherical pair.

7. Which of the following is an open pair?

a) Ball and socket joint

b) Journal bearing

c) Lead screw and nut

d) Cam and follower

Answer: a

Explanation: None

8. The lead screw of a lathe with nut forms a

a) rolling pair

b) sliding pair

c) screw pair

d) turning pair

Answer: c

Explanation: When the nature of contact between the element of a pair is such that one element can turn abut the other by screw threads, the pair is known as a screw pair. The lead screw of a lathe with nut is an example of screw pair.

9. Which of the following is a turning pair?

a) Piston and cylinder of a reciprocating steam engine

b) Shaft with collars at both ends fitted into a circular hole

c) Lead screw of a lathe with nut

d) Ball and a socket joint

Answer: b

Explanation: When the two elements of a pair are constrained in such a way that one can only turn or revolve about a fixed axis of another link, the pair is known as turning pair.

Answer: a

Explanation: When the two elements of a pair have surface contact when relative motion, takes place and the surface of one element slides over the surface of the other, the pair formed is known as lower pair. It will be seen that sliding pairs, turning pairs and screw pairs form lower pairs.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Kinematic Pair”.

1. When the two elements of a pair have _____________ when in motion, it is said to a lower pair.

a) line or point contact

b) surface contact

c) permit relative motion

d) none of the mentioned

Answer: b

Explanation: When the two elements of a pair have surface contact when relative motion, takes place and the surface of one element slides over the surface of the other, the pair formed is known as lower pair. It will be seen that sliding pairs, turning pairs and screw pairs form lower pairs.

2. The two elements of a pair are said to form a higher pair, when they

a) have a surface contact when in motion

b) have a line or point contact when in motion

c) are kept in contact by the action of external forces, when in motion

d) permit relative motion

Answer: b

Explanation: When the two elements of a pair have a line or point contact when relative motion takes place and the motion between the two elements is partly turning and partly sliding, then the pair is known as higher pair.

3. In a force-closed pair, the two elements of a pair are not held together mechanically.

a) True

b) False

Answer: b

Explanation: When the two elements of pair are not connected mechanically but are kept in contact by the action of external forces, the pair is said to be a forced-closed pair.

4. The two elements of a pair are said to form a ___________ when they permit relative motion between them.

a) open pair

b) kinematic pair

c) higher pair

d) lower pair

Answer: b

Explanation: The two links or elements of a machine, when in contact with each other, are said to form a pair. If the relative motion between them is completely or successfully constrained, the pair is known as kinematic pair.

5. In an open pair, the two elements of a pair

a) have a surface contact when in motion

b) have a line or point contact when in motion

c) are kept in contact by the action of external forces, when in motion

d) are not held mechanically

Answer: d

Explanation: When the two elements of a pair are not held mechanically, they are called open pair.

6. The sliding pairs, turning pairs and screw pairs form lower pairs.

a) True

b) False

Answer: a

Explanation: When the two elements of a pair have surface contact when relative motion, takes place and the surface of one element slides over the surface of the other, the pair formed is known as lower pair. It will be seen that sliding pairs, turning pairs and screw pairs form lower pairs.

7. A combination of kinematic pairs, joined in such a way that the relative motion between the links is completely constrained, is called a

a) structure

b) mechanism

c) kinematic chain

d) inversion

Answer: c

Explanation: A kinematic chain is defined as a combination of kinematic pairs, joined in such a way that each link forms a part of two pairs and the relative motion between the links or elements is completely or successfully constrained.

8. The relation between number of pairs forming a kinematic chain and the number of links is

a) l = 2p – 2

b) l = 2p – 3

c) l = 2p – 4

d) l = 2p – 5

Answer: c

Explanation: If each link is assumed to form two pairs with adjacent links, then the relation between the number of pairs forming a kinematic chain and the number of links may be expressed in the form of an equation : l = 2p – 4

9. The relation between number of links and number of joints in a kinematic chain is

a) l = 1/2 

b) l = 2/3 

c) l = 3/4 

d) l = j+4

Answer: b

Explanation: Another relation between the number of links  and the number of joints which constitute a kinematic chain is given by the expression : l = 2/3 

Answer: b

Explanation: None

This set of Machine Kinematics test focuses on “Classification of Kinematic Pairs”.

1. The pair is known as a higher pair, when the relative motion between the elements of a pair is

a) turning only

b) sliding only

c) rolling only

d) partly turning and partly sliding

Answer: d

Explanation: When the two elements of a pair have a line or point contact when relative motion takes place and the motion between the two elements is partly turning and partly sliding, then the pair is known as higher pair.

2. Which of the following is a higher pair?

a) Belt and pulley

b) Turning pair

c) Screw pair

d) Sliding pair

Answer: a

Explanation: Belt and pulley are higher pairs as the motion is partly turning and partly sliding between them.

3. When the connection between the two elements is such that only required kind of relative motion occurs, it is known as self-closed pair.

a) True

b) False

Answer: a

Explanation: When the two elements of a pair are connected together mechanically in such a way that only required kind of relative motion occurs, it is then known as self closed pair.

4. When the elements of a pair are kept in contact by the action of external forces, the pair is said to be a

a) lower pair

b) higher pair

c) self-closed pair

d) force-closed pair

Answer: d

Explanation: When the two elements of pair are not connected mechanically but are kept in contact by the action of external forces, the pair is said to be a forced-closed pair.

5. A pair of friction discs is an example of rolling pair.

a) True

b) False

Answer: b

Explanation: A pair of discs are higher pairs as the motion is partly turning and partly sliding between them.

6. The lower pairs are ___________ pairs.

a) self-closed pair

b) force-closed pair

c) screw pair

d) none of the mentioned

Answer: a

Explanation: When the two elements of a pair are connected together mechanically in such a way that only required kind of relative motion occurs, it is then known as self closed pair. The lower pairs are self closed pairs.

7. The cam and follower is an example of

a) sliding pair

b) rolling pair

c) lower pair

d) higher pair

Answer: d

Explanation: The cam and follower is an example of higher pair as it is kept in contact by the forces exerted by spring and gravity.

8. Which of the following is an example of higher pair?

a) Toothed gearing

b) Belt and rope drive

c) Ball and roller bearing

d) All of the mentioned

Answer: d

Explanation: None

9. An automobile steering gear is an example of

a) sliding pair

b) rolling pair

c) lower pair

d) higher pair

Answer: c

Explanation: None

Answer: a

Explanation: The two links or elements of a machine, when in contact with each other, are said to form a pair. If the relative motion between them is completely or successfully constrained, the pair is known as kinematic pair.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Kinematic Chain”.

1. The relation between the number of links and the number of binary joints for a kinematic chain having constrained motion is given by j = 3/2 . If the left hand side of this equation is greater than the right hand side, then the chain is

a) locked chain

b) completely constrained chain

c) successfully constrained chain

d) incompletely constrained chain

Answer: a

Explanation: If the L.H.s. > R.H.S., then the chain is called a locked chain and forms a frame or structure which is used in bridges and trusses.

2. In a kinematic chain, a quaternary joint is equivalent to

a) one binary joint

b) two binary joints

c) three binary joints

d) four binary joints

Answer: c

Explanation: When four links are joined at the same connection, the joint is called a quaternary joint. It is equivalent to three binary joints.

3. A chain consisting of four links and four joints is called a kinematic chain.

a) True

b) False

Answer: a

Explanation: A kinematic chain is defined as a combination of kinematic pairs, joined in such a way that each link forms a part of two pairs and the relative motion between the links or elements is completely or successfully constrained.

4. In a steam engine, the link constitutes a

a) piston, piston rod and cross-head

b) connecting rod with big and small end brasses, caps and bolts

c) crank pin, crankshaft and flywheel

d) all of the mentioned

Answer: d

Explanation: None

5. A mechanism is a assemblage of

a) two links

b) three links

c) four or more than four links

d) all of the mentioned

Answer: c

Explanation: When one of the links of a kinematic chain is fixed, the chain is known as mechanism. A simple mechanism consists of minimum four links.

6. A mechanism consisting more than four links is called a compound mechanism.

a) True

b) False

Answer: a

Explanation: A mechanism with four links is known as simple mechanism, and the mechanism with more than four links is known as compound mechanism.

7. A mechanism consisting of four links is called a _____________ mechanism.

a) simple

b) compound

c) inversion

d) none of the mentioned

Answer: a

Explanation: A mechanism with four links is known as simple mechanism, and the mechanism with more than four links is known as compound mechanism.

8. A mechanism ______________ for transmitting or transforming motion.

a) can be used

b) can not be used

c) both of the mentioned

d) none of the mentioned

Answer: a

Explanation: A mechanism is used for transmitting or transforming motion e.g. engine indicators, typewriter etc.

9. When a mechanism is required to transmit power or to do some particular type of work, then it becomes a machine.

a) True

b) False

Answer: a

Explanation: When a mechanism is required to transmit power or to do some particular type of work, then it becomes a machine. In such cases, the various links or elements have to be designed to withstand the forces safely.

Answer: b

Explanation: When one of the links of a kinematic chain is fixed, the chain is known as mechanism. It may be used for transmitting or transforming motion.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Mechanism – 1”.

1. A type-writer constitutes a machine.

a) True

b) False

Answer: b

Explanation: When a mechanism is required to transmit power or to do some particular type of work, it then becomes a machine.But in case of a typewriter there is no case of power transmission. Hence it is not a machine.

2. The method of obtaining different mechanisms by fixing in turn different links in a kinematic chain, is known as

a) structure

b) machine

c) inversion

d) compound mechanism

Answer: c

Explanation: We can obtain as many mechanisms as the number of links in kinematic chain by fixing, in turn,different links in a kinematic chain. This method is known as inversion of the mechanism.

3. If the number of links in a mechanism are equal to l, then the number of possible inversions are equal to

a) l – 2

b) l – 1

c) l

d) l + 1

Answer: c

Explanation: Whatever is the number of links in a mechanism, only that much number of inversion can be obtained.

4. Which of the following statement is correct as regard to the difference between a machine and a structure?

a) The parts of a machine move relative to one another, whereas the members of a structure do not move relative to one another.

b) The links of a machine may transmit both power and motion, whereas the members of a structure transmit forces only.

c) A machine transforms the available energy into some useful work, whereas in a structure no energy is transformed into useful work.

d) all of the mentioned

Answer: d

Explanation: None

5. A kinematic chain is known as a mechanism when

a) none of the links is fixed

b) one of the links is fixed

c) two of the links are fixed

d) none of the mentioned

Answer: b

Explanation: When one of the links of a kinematic chain is fixed, the chain is known as mechanism.

6. The inversion of a mechanism is

a) changing of a higher pair to a lower pair

b) turning its upside down

c) obtained by fixing different links in a kinematic chain

d) obtained by reversing the input and output motion

Answer: c

Explanation: We can obtain as many mechanisms as the number of links in kinematic chain by fixing, in turn,different links in a kinematic chain. This method is known as inversion of the mechanism.

7. The Grubler’s criterion for determining the degrees of freedom  of a mechanism having plane motion is

a) n =  – j

b) n = 2 – 2j

c) n = 3 – 2j

d) n = 4 – 3j

Answer: c

Explanation: None

8. The mechanism forms a structure, when the number of degrees of freedom  is equal to

a) 0

b) 1

c) 2

d) -1

Answer: a

Explanation: A structure can be formed only when the number of degrees of freedom is zero.

9. In a four bar chain or quadric cycle chain

a) each of the four pairs is a turning pair

b) one is a turning pair and three are sliding pairs

c) two are turning pairs and two are sliding pairs

d) three are turning pairs and one is a sliding pair

Answer: a

Explanation: Four bar chain or quadric cycle chain consists of four links, each of them forms a turning pair.

Answer: d

Explanation: A double slider crank chain consists of two sliding pairs and two turning pairs. The inversions of a double slider crank chain are as follows:

a) elliptical trammel

b) scotch yoke mechanism

c) oldham’s coupling

This set of Machine Kinematics Quiz focuses on “Mechanism – 2”.

1. In a coupling rod of a locomotive, each of the four pairs is a _____________ pair.

a) sliding

b) turning

c) rolling

d) screw

Answer: b

Explanation: In a locomotive, one rod of the coupling rod can only turn or revolve about a fixed axis of another rod. This takes place only in case of turning pair.

2. Whitworth quick return motion mechanism consists of three turning pairs and one sliding pair.

a) True

b) False

Answer: a

Explanation: Whitworth quick return motion mechanism is a form of single slider crank chain and it consists of one sliding pair and three turning pairs.

3. In a single slider crank chain

a) each of the four pairs is a turning pair

b) one is a turning pair and three are sliding pairs

c) two are turning pairs and two are sliding pairs

d) three are turning pairs and one is a sliding pair

Answer: d

Explanation: Single slider crank chain consists of one sliding pair and three turning pairs.

Four bar chain consists of four links and each of them forms a turning pair.

4. The mechanism consisting of three turning pairs and one sliding pair, is called a

a) single slider crank chain

b) whitworth quick return motion mechanism

c) crank and slotted lever quick return motion mechanism

d) all of the mentioned

Answer: d

Explanation: All the mechanisms mentioned above are forms of single slider crank chain only and hence, they all contain three turning pairs and one sliding pair. The inversion of a single slider crank chain are found in the following mechanism:

a) Pendulum pump or Bull engine

b) Rotary internal combustion engine

c) Oscillating cylinder engine

d) Crank and slotted lever quick return motion mechanism

e) Whitworth quick return motion mechanism

5. Which of the following is an inversion of a single slider crank chain?

a) Pendulum pump

b) Oscillating cylinder engine

c) Rotary internal combustion engine

d) All of the mentioned

Answer: d

Explanation: All the mechanisms mentioned above are forms of single slider crank chain only and hence, they all contain three turning pairs and one sliding pair. The inversion of a single slider crank chain are found in the following mechanism:

a) Pendulum pump or Bull engine

b) Rotary internal combustion engine

c) Oscillating cylinder engine

d) Crank and slotted lever quick return motion mechanism

e) Whitworth quick return motion mechanism.

6. A point on a connecting link of a double slider crank mechanism traces a

a) straight line path

b) hyperbolic path

c) parabolic path

d) elliptical path

Answer: d

Explanation: None.

7. The whitworth quick return motion mechanism is formed in a slider crank chain when the

a) coupler link is fixed

b) longest link is a fixed link

c) slider is a fixed link

d) smallest link is a fixed link

Answer: a

Explanation: None.

8. Scotch yoke mechanism is used to generate

a) sine functions

b) square roots

c) logarithms

d) inversions

Answer: a

Explanation: None.

9. Which of the following is an inversion of a double slider crank chain?

a) Oldham’s coupling

b) Elliptical trammel

c) Scotch yoke mechanism

d) All of the mentioned

Answer: d

Explanation: A double slider crank chain consists of two sliding pairs and two turning pairs. The inversions of a double slider crank chain are as follows:

a) elliptical trammel

b) scotch yoke mechanism

c) oldham’s coupling.

10. Whitworth quick return motion mechanism is an inversion of a double slider crank chain.

a) True

b) False

Answer: b

Explanation: Whitworth quick return motion mechanism is a form of single slider crank chain and it consists of one sliding pair and three turning pairs.

Answer: d

Explanation: None.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Number of Degrees of Freedom for Plane Mechanisms”.

1. The total number of instantaneous centres for a mechanism consisting of n links are

a) n/2

b) n

c) n-1

d) n/2

Answer: d

Explanation: The number of pairs of links or the number of instantaneous centres is the number of combinations of n links taken two at a time. Mathematically, number of instantaneous centres, n/2.

2. According to Kennedy’s theorem, if three bodies move relatively to each other, their instantaneous centres will lie on

a) straight line

b) parabolic curve

c) triangle

d) rectangle

Answer: a

Explanation: The Aronhold Kennedy’s theorem states that if three bodies move relatively to each other,

they have three instantaneous centres and lie on a straight line.

3. Which of the following property of the instantaneous center is correct?

a) A rigid link rotates instantaneously relative to another link at the instantaneous centre for the configuration of the mechanism considered.

b) The two rigid links have no linear velocity relative to each other at the instantaneous centre.

c) The velocity of the instantaneous centre relative to any third link is same whether the instantaneous centre is regarded as a point on the first link or on the second rigid link.

d) all of the mentioned

Answer: d

Explanation: None.

4. The magnitude of velocities of the points on a rigid link is

a) directly proportional to the distance from the points to the instantaneous centre and is parallel to the line joining the point to the instantaneous centre.

b) directly proportional to the distance from the points to the instantaneous centre and is perpendicular to the line joining the point to the instantaneous centre.

c) inversely proportional to the distance from the points to the instantaneous centre and is parallel to the line joining the point to the instantaneous centre.

d) inversely proportional to the distance from the points to the instantaneous centre and is perpendicular to the line joining the point to the instantaneous centre.

Answer: d

Explanation: None.

5. In a mechanism, the fixed instantaneous centres are those centres which

a) remain in the same place for all configurations of the mechanism

b) vary with the configuration of the mechanism

c) moves as the mechanism moves, but joints are of permanent nature

d) none of the mentioned

Answer: a

Explanation: Fixed instantaneous centres remain in the same place for all configurations of the mechanism.

6. The instantaneous centres, which moves as the mechanism moves but joints are of permanent nature, are called permanent instantaneous centres.

a) True

b) False

Answer: a

Explanation: The permanent instantaneous centres move when the mechanism moves, but the joints are of permanent nature.

Fixed instantaneous centres remain in the same place for all configurations of the mechanism.

7. The instantaneous centres which vary with the configuration of mechanism, are called

a) permanent instantaneous centres

b) fixed instantaneous centres

c) neither fixed nor permanent instantaneous centres

d) none of the mentioned

Answer: c

Explanation: Neither fixed nor permanent instantaneous centres vary with the configuration of the mechanism.

8. When two links are connected by a pin joint, their instantaneous centre lies

a) on their point of contact

b) at the centre of curvature

c) at the centre of circle

d) at the pin joint

Answer: d

Explanation: None.

9. The two links are said to have a pure rolling contact, when their instantaneous centre __________ on their point of contact.

a) lies

b) does not lie

Answer: a

Explanation: None

10. When a slider moves on a fixed link having ____________ their instantaneous center lies at infinity.

a) straight surface

b) curved surface

c) oval surface

d) none of the mentioned

Answer: a

Explanation: When a slider moves on a fixed link having curved surface, their instantaneous centre lies at the centre of curvature.

When a slider moves on a fixed link having straight surface their instantaneous center lies at infinity.

11. When a slider moves on a fixed link having curved surface, their instantaneous centre lies

a) on their point of contact

b) at the centre of curvature

c) at the centre of circle

d) at the pin joint

Answer: b

Explanation: When a slider moves on a fixed link having curved surface, their instantaneous centre lies at the centre of curvature.

When a slider moves on a fixed link having straight surface their instantaneous center lies at infinity.

12. A slider moving on a fixed link having constant radius of curvature will have its instantaneous centre at the center of the circle.

a) True

b) False

Answer: a

Explanation: None.

Answer: b

Explanation: None.

This set of Machine Kinematics Mcqs focuses on “Application of Kutzbach Criterion to Plane Mechanisms”.

1. In its simplest form, a cam mechanism consists of following number of links

a) 1

b) 2

c) 3

d) 4

Answer: c

Explanation: Cam consists of 3 links.

2. Which of the following mechanisms produces mathematically an exact straight line motion?

a) Grasshopper mechanism

b) Watt mechanism

c) Peaucellier’s mechanism

d) Tchabichiff mechanism

Answer: c

Explanation: Peaucellier’s mechanism gives straight line motion.

3. In a mechanism, usually one link is fixed. If the fixed link is changed in a kinematic chain, then relative motion of other links

a) will remain same

b) will change

c) will not occur

d) none of the mentioned

Answer: a

Explanation: There will be no change.

4. A kinematic chain requires at least

a) 2 links and 3 turning pairs

b) 3 links and 4 turning pairs

c) 4 links and 4 turning pairs

d) 5 links and 4 turning pairs

Answer: c

Explanation: In a Kinematic chain, the number of links should be equal to the number of turning pairs.

5. In a drag link quick return mechanism, the shortest link is always fixed. The sum of the shortest and longest link is

a) equal to sum of other two

b) greater than sum of other two

c) less than sum of other two

d) none of the mentioned

Answer: c

Explanation: None

6. The following is the inversion of slider crank chain mechanism

a) whitworth quick return mechanism

b) hand pump

c) oscillating cylinder engine

d) all of the mentioned

Answer: d

Explanation: None

7. Kinematic pairs are those which have

a) two elements held together mechanically

b) two elements having relative motion

c) two elements having Coroli’s component

d) none of the mentioned

Answer: b

Explanation: Kinematic pair is ajoint of two elements that permits relative motion.

8. According to criterion of constraint by A.W. Klein

a) J + 1/2 H = 3/2L – 2

b) H + 1/2J = 2/3L – 2

c) J + 1/2H = 3/2L – 1

d) J + 3/2H = 1/2L – 2

Answer: a

Explanation: The criterion for a chain to be constrained is

J + 1/2 H = 3/2L – 2

9. A quarternary joint is equivalent to

a) one binary joint

b) two binary joints

c) three binary joints

d) four binary joints

Answer: c

Explanation: None

10. A typewriter mechanism has 7 number of binary joints, six links and none of higher pairs. The mechanism is

a) kinematically sound

b) not sound

c) soundness would depend upon which link is kept fixed

d) none of the mentioned

Answer: a

Explanation: J + 1/2 H = 3/2L – 2

or, 7 + 0 = 3/2 x 6 -2

or, 7 = 7

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on ” Grubler’s Criterion for Plane Mechanisms”.

1. The approximate straight line mechanism is a

a) 4 bar linkage

b) 6 bar linkage

c) 8 bar linkage

d) 3 bar linkage

Answer: a

Explanation: The straight line mechanism has 4 bar linkage.

2. Open pairs are those which have

a) point or line contact between the two elements when in motion

b) surface contact between the two elements when in motion

c) elements of pairs not held together mechanically

d) two elements that permit relative motion

Answer: c

Explanation: Two elemets which are not held together form open pairs.

Two elements held together mechanically form a closed pair.

3. Peaucellier mechanism has

a) 8 links

b) 6 links

c) 4 links

d) 5 links

Answer: a

Explanation: Peaucellier mechanism has 8 links.

Hart mechanism has 6 links.

4. Hart mechanism has

a) 8 links

b) 6 links

c) 4 links

d) 5 links

Answer: b

Explanation: Hart mechanism has 6 links.

Peaucellier mechanism has 8 links.

5. A chain comprises of 5 links having 5 joints. Is it kinematic chain?

a) Yes

b) No

c) It is a marginal case

d) None of the mentioned

Answer: b

Explanation: Kinematic chain is one which satisfies

L = 2/3 ,

which is not satisfied in this case.

6. In the following equation [ L = 2/3] to determine whether or not the given chain in kinematic, higher pair is treated equivalent to

a) two lower pairs and an additional links

b) two higher pairs and two additional links

c) one lower pairs and two additional links

d) none of the mentioned

Answer: a

Explanation: In the above equation, each higher pair is taken equivalent to two lower pairs and an additional link.

If one of the links of the constrained chain is fixed, it results into mechanism.

7. The main disadvantage of the sliding pair is that it is

a) bulky

b) difficult to manufacture

c) wears rapidly

d) both a and c

Answer: d

Explanation: The sliding pair wears rapidly due to friction and is bulky also.

8. For a kinematic chain to be considered as mechanism

a) two links should be fixed

b) one link should be fixed

c) none of the links should be fixed

d) there is no such criterion

Answer: b

Explanation: If one of the links of the constrained chain is fixed, it results into mechanism.

9. An eccentric sheave pivoted at one point rotates and transmits oscillatory motion to a link whose one end is pivoted and other end is connected to it. This mechanism has

a) 2 links

b) 3 links

c) 4 links

d) 5 links

Answer: c

Explanation: Eccentric sheave is equivalent to 2 links, 1 link is due to oscillatory link, and one is fixed link.

Answer: a

Explanation: None.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Inversion of Mechanism”.

1. The number of degrees of freedom of a planer linkage with 8 links and 9 simple revolute joints is

a) 1

b) 2

c) 3

d) 4

Answer: c

Explanation: No. of links, I = 8

No. of revolute joints, J = 9

No. of higher pair, h = 0

Number of degree of freedom, n = 3 – 2j – h

= 3 – 2×9 – 0 = 3.

2. A palnar mechanism has 8 links and 10 rotary joints. The number of degrees of freedom of the mechanism, using Grubler’s criterion, is

a) 0

b) 1

c) 2

d) 3

Answer: b

Explanation: Whatever may be the number of links and joints Grubler’s criterion applies to mechanism with only single degree freedom. Subject to the condition 3I – 2J – 4 = 0 and it satisfy this condition.

Degree of freedom is given by = 3 – 2j = 3 –  = 1.

3. Match the approaches given below to perform stated kinematics/dynamics analysis of machine.

Analysis Approach

P. Continuous relative rotation 1. D’Alembert’s principle

Q. Velocity and acceleration 2. Grubler’s criterion

R. Mobility 3. Grashof’s law

S. Dynamic-static analysis 4. Kennedy’s theorem

a) P-1,Q-2,R-3,S-4

b) P-3,Q-4,R-2,S-1

c) P-2,Q-3,R-4,S-1

d) P-4,Q-2,R-1,S-3

Answer: b

Explanation:

1. D’Alembert’s principle – Dynamic-static analysis

2. Grubler’s criterion – Mobility

3. Grashof’s law – Continuous relative rotation

4. Kennedy’s theorem – Velocity and acceleration.

4. Which of the following statements is incorrect

a) Grashof’s rule states that for a planar crank-rocker four bar mechanism, the sum of the shortest and longest link lengths cannot be less than the sum of the remaining two link lengths.

b) Inversions of a mechanism are created by fixing different links one at a time.

c) Geneva mechanism is an intermittent motion device.

d) Gruebler’s criterion assumes mobality of a planar mechanism to be one.

Answer: a

Explanation: According to Grashof’s rule for complete relative rotation r/w links L + S < p + q.

5. In a four bar linkage, s denotes the shortest link length, L is the longest link length, P and Q are the lengths of other two links. At least one of the three moving links will rotate by 360° if

a) S + L < P + Q

b) S + L > P + Q

c) S + P < L + Q

d) S + P > L + Q

Answer: a

Explanation: According to Grashof’s law for four bar mechanism, the sum of shortest and longest link lengths should not be greater than the sum of remaining two link length.

i.e. S + L < P + Q.

6. The number of inversions for a slider crank mechanism is

a) 6

b) 5

c) 4

d) 3

Answer: c

Explanation: No. of links of a slider crank mechanism = 4

So there are four inversion of slider crank mechanism.

7. The mechanism used in a shaping machine is

a) A closed 4bar chain having 4 revolute pairs

b) A closed 6bar chain having 6 revolute pairs

c) A closed 4bar chain having 2 revolute and 2 sliding pairs

d) An inversion of single slider crank chain

Answer: d

Explanation: Quick return mechanism.

8. Match the following

Types of mechanism Motion achieved

P. Scott Russel mechanism 1. Intermittent motion

Q. Geneva mechanism 2. Quick return motion

R. Off set slider crank mechanism 3. Simple harmonic motion

S. scotch Yoke mechanism 4. Straight line motion

a) P-2,Q-3,R-1,S-4

b) P-3,Q-2,R-4,S-1

c) P-4,Q-1,R-2,S-3

d) P-4,Q-3,R-1,S-2

Answer: c

Explanation:

1. Intermittent motion – Geneva mechanism

2. Quick return motion – Off set slider crank mechanism

3. Simple harmonic motion – scotch Yoke mechanism

4. Straight line motion – Scott Russel mechanism.

9. In a kinematic chain, a quaternary joint is equivalent to

a) one binary joint

b) two binary joint

c) three binary joint

d) four binary joint

Answer: c

Explanation: When ‘l’ number of links are joined at the same connection, the joint is equivalent to  binary joints.

Answer: d

Explanation: When supported on three points, following six degrees of freedom are arrested.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Types of Kinematic Chains”.

1. Scotch yoke mechanism is used to generate

a) Sine functions

b) Square roots

c) logarithms

d) inversions

Answer: a

Explanation: In Scotch Yoke mechanism, the constant rotation of the crank produces harmonic translation of the yoke. Its four binary links are:

1. Fixed link

2. Crank

3. Sliding Block

4. Yoke.

2. Which of the following are inversions of a double slider crank chain?

1. Whitworth return motion 2. Scotch Yoke

3. Oldham’s Coupling 4. Rotary engine

Select correct answer using the codes given below:

Codes:

a) 1 and 2

b) 1, 3 and 4

c) 2 and 3

d) 2, 3 and 4

Answer: c

Explanation: Double slider crank mechanism

It has four binary links, two revolute pairs, two sliding pairs. Its various types are:

1. Scotch Yoke mechanism

2. Oldhams Coupling

3. Elliptical Trammel.

3. Oldham’s coupling is used to transmit power between two parallel shafts which are slightly offset.

a) True

b) false

Answer: a

Explanation: It is used for transmitting angular velocity between two parallel but eccentric shafts.

4. In Oldham’s coupling the condition for maximum speed ratio is

a) w 1 cosα/W

b) w 1 sinα/W

c) w 1 /W = 1/cosα

d) w 1 /W = 1/sinα

Answer: c

Explanation: w 1 /W = cosα/1 – cos 2 ϴsin 2 α

For maximum speed ratio cos 2 ϴ = 1

Therefore, w 1 /W = 1/cosα.

5. The relative acceleration of two points which are at variable distance apart on a moving link can be determined by using the

a) three centers in line theorem

b) instantaneous centre of rotation method

c) Coriolis component of acceleration method

d) Klein’s construction

Answer: b

Explanation: The relative acceleration of two variable points on a moving link can be determined by using the instantaneous centre of rotation method.

6. What is the number of instantaneous centres of rotation for a 6-link mechanism?

a) 4

b) 6

c) 12

d) 15

Answer: d

Explanation: N = n/2 = 6 x /2 = 15.

7. For one degree of freedom planer mechanism having links, which one of the following is the possible combination?

a) Four binary links and two ternary links

b) Four ternary links and two binary links

c) Three ternary links and three binary links

d) One ternary link and five binary links

Answer: d

Explanation: From Grubler’s criteria 1 = 3 – 2j

or, j = 3/2l – 2 for six link

j = 3/2 x 6 – 2 = 7 1 ternary link = 2 binary link

a) j = 4 + 2 x 2 ≠ 7

b) j = 4 x 2 + 2 ≠ 7

c) j = 3 x 2 + 2 ≠ 7

d) j = 1 x 2 + 5 ≠ 7 the ans is d.

8. Inversion of a kinematic chain relative to some other links is a property of the chain and is not that of the mechanism.

a) True

b) False

Answer: a

Explanation: In a kinematic inversion relative motion does not change but absolute motion change drastically.

9. In a shaping operation, the average cutting speed is 

a) NSR

b) NSR/2

c) NS

d) NS/2

Answer: d

Explanation: Time for forward stroke + T f

Time for return stroke = T r

R = T r /T f

Therefore, time for only one cutting stroke = 1/N x T f /(T f + T r )

Average cutting speed = S/T = SN(T f + T r )/T f = SN.

10. Ina kinematic inversion, the relative motions between links of the mechanism change as different links are made the frame by turns.

a) True

B) False

Answer: b

Explanation: Through the process of inversion the relative motions between the various links is not changed in any manner but their absolute motions may be changed drastically.

Answer: b

Explanation: Elliptical trammels have two sliding pairs and two turning pairs. It is an instrument used for drawing ellipse.

This set of Machine Kinematics Multiple Choice Questions & Answers focuses on “Four Bar Chain or Quadric Cycle Chain”.

1. In a crank and slotted lever quick-return motion, the distance between the fixed centres is 150 mm and the length of the driving crank is 75mm. the ratio of the time taken on the cutting and return strokes is

a) 1.5

b) 2.0

c) 2.2

d) 2.93

Answer: b

Explanation: OA = 150mm

AB = 75 mm

sin  = AB/OA

cosα/2 = 1/2

therefore, α = 120 0

β = 360 0 – 120 0 = 240 0

Quick return ratio = β/α = 240/120 = 2.

2. A helical coil spring of stiffness k is cut to two equal halves and then these are connected in parallel to support a vibrating mass m. The angular frequency of vibration, ω n is

a) √k/m

b) √2k/m

c) √4k/m

d) √k/4m

Answer: c

Explanation: stiffness ∞ 1/length

k eq = 2k + 2k = 4k

ω = √4k/m.

3. Consider the following statements:

In a slider-crank mechanism, the slider is at its dead centre position when the

 slider velocity is zero

 slider velocity is maximum

 slider acceleration is zero

 slider acceleration is maximum

Which of the above statements are correct?

a) 1 and 4

b) 1 and 3

c) 2 and 3

d) 2 and 4

Answer: a

Explanation: At dead centre velocity is zero, because instantaneous acceleration is maximum.

4. Which one of the following mechanisms is an inversion of double slider-crank chain?

a) Elliptic trammels

b) Beam engine

c) Oscillating cylinder engine

d) Coupling rod of a locomotive

Answer: a

Explanation: Elliptic trammels are inversion of double slider crank chain.

5. The number of instantaneous centres of rotation for a 10-link kinematic chain is

a) 36

b) 90

c) 120

d) 45

Answer: d

Explanation: Instantaneous centre = n/2 = 45.

6. A slider moves with uniform velocity on a revolving link of length r with angular velocity ω. The Coriolis acceleration component of a point on the slider relative to a coincident point on the link is equal to

a) ω parallel to the link

b) 2ω perpendicular to the link

c) ω perpendicular to the link

d) 2ω parallel to the link

Answer: b

Explanation: coriolis components of acceleration for slider is perpendicular to the link.

7. In a crank and slotted lever type quick return mechanism, the link moves with an angular velocity of 20 rad/s, while the slider moves with the linear velocity of 1.5 m/s. The magnitude and direction of Coriolis component of acceleration with respect to angular velocity are

a) 30 m/s 2 and direction is such as to rotate slider velocity in the same sense as the angular velocity

b) 30 m/s 2 and direction is such as to rotate slider velocity in the opposite sense as the angular velocity

c) 60 m/s 2 and direction is such as to rotate slider velocity in the same sense as the angular velocity

d) 60 m/s 2 and direction is such as to rotate slider velocity in the opposite sense as the angular velocity.

Answer: c

Explanation: Magnitude of Coriolis acceleration = 2Vω

= 2 x 1.5 x 20

= 60 m/s 2

Rotate the link in direction of rotation and see the direction of linear velocity that will be direction of Coriolis acceleration.

8. Which of the following are associated with Ackerman steering mechanism used in automobiles?

1. Has both sliding and turning pairs

2. Less friction and hence long life

3. Mechanically correct in all positions

4. Mathematically not accurate except in three positions.

5. Has only turning pairs 6. Controls movement of two front wheels

a) 2, 4, 5 and 6

b) 1, 2, 3 and 6

c) 2, 3, 5 and 6

d) 1, 2, 3 and 5

Answer: a

Explanation: Ackerman steering mechanism has no sliding mechanism & not suitable for all the positions.

9. The crankshaft of reciprocating engine having a 20 cm crank and 100 cm connecting rod rotates at 210 r.p.m. When the crank angle is 45 o , the velocity of piston is nearly

a) 1.8m/s

b) 1.9m/s

c) 3.5m/s

d) 19m/s

Answer: c

Explanation: V p = ωr𝛳𝛳

ω = 2пN/60 = 21.98rad/sec

r = 6.2m

n = l/r = 100/20 = 5

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Inversions of Four Bar Chain”.

1. Match list I with list II

List I List II

A. Quick return mechanism 1. Lathe

B. Apron mechanism 2. Milling machine

C. Indexing mechanism 3. Shaper

D. Regulating wheel 4. Centreless grinding

a) A-3,B-2,C-1,D-4

b) A-2,B-3,C-4,D-1

c) A-4,B-2,C-3,D-1

d) A-3,B-1,C-2,D-4

Answer: d

Explanation: Quick return mechanism – Shaper

Apron mechanism – Lathe

Indexing mechanism – Milling machine

Regulating wheel – Centreless grinding

2. A point on a link connecting a double slider crank chain will trace a

a) straight line

b) circle

c) parabola

d) ellipse

Answer: d

Explanation: The point on connecting link traces an elliptical path.

3. A wheel is rolling on a straight level track with a uniform velocity ‘v’. The instantaneous velocity of a point on the wheel lying at the mid-point of a radius

a) varies between 3 v/2 and -v/2

b) varies between v/2 and -v/2

c) varies between 3 v/2 and -v/2

d) does not vary and is equal to v

Answer: b

Explanation: None

4. A four-bar chain has

a) all turning pairs

b) one turning pair and the others are sliding pairs

c) one sliding pair and the others are turning pairs

d) all sliding pairs

Answer: a

Explanation: A four-bar linkage, also called a four-bar, is the simplest movable closed chain linkage. It consists of four bodies, called bars or links, connected in a loop by four joints. Generally, the joints are configured so the links move in parallel planes, and the assembly is called a planar four-bar linkage.

5. The mechanism in a shaping machine is

a) a closed 4-bar chain having 6 revolute pairs

b) a closed 6-bar chain having 6 revolute pairs

c) a closed 4-bar chain having 2 revolute and 2 sliding pairs

d) an inversion of single slider crank chain

Answer: d

Explanation: Shaping machines use quick return mechanism which are either Whitworth quick return mechanism or crank and slotted lever quick return mechanism. These are inversions of single slider crank chain.

6. The number of inversions of a slider crank chain is

a) 6

b) 5

c) 4

d) 3

Answer: c

Explanation: A slider crank chain has 4 links and by fixing each link, one at a time, we get 4 different mechanisms, each of which is an inversion. Hence, a slider crank chain has 4 inversions.

7. Which of the following is an inversion of single slider crank chain?

a) Elliptical Trammel

b) Hand Pump

c) Oldham’s Coupling

d) Scotch Yoke

Answer: b

Explanation: Hand pump is an inversion of single slider crank chain.

8. Which of the following are the inversions of double slider crank chain?

1. Oldhan coupling

2. Whitworth quick return mechanism

3. Beam engine mechanism

4. Elliptical Trammel mechanism

The correct answer codes are

a) 1 and 2

b) 1 and 4

c) 2, 3 and 4

d) 1, 2 and 3

Answer: b

Explanation: Oldham coupling and Elliptical trammel are inversions of double slider crank chain.

Whitworth quick return mechanism is an inversion of single slider crank chain. Beam engine mechanism is an inversion of 4-bar linkage.

9. Which of the following is an inversion of single slider crank chain?

a) Beam engine

b) Watt’s indicator mechanism

c) Elliptical Trammel

d) Oscillating cylinder engine

Answer: d

Explanation: Oscillating cylinder engine is an inversion of single slider crank chain.

Answer: b

Explanation: Oldham’s coupling is used to connect slightly offset parallel shafts.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Single Slider Crank Chain and its Inversions – 1”.

1. The quick return mechanism which is an inversion of 4-bar linkage is

a) Drag link mechanism

b) Whitworth quick return mechanism

c) Crank and slotted lever mechanism

d) None of the mentioned

Answer: a

Explanation: Drag link mechanism is an inversion of 4-bar linkage, which is a crank mechanism with different crank lengths. It is made up of revolute pairs only.

2. Match list I with list II

List I List II

A. Pantograph 1. Scotch yoke mechanism

B. Single slider crank 2. Double lever mechanism

C. Double slider crank chain 3. Tchebicheff’s mechanism

D. Straight line motion mechanism 4. Double crank

5. Hand pump

a) A-4,B-3,C-5,D-1

b) A-2,B-5,C-1,D-3

c) A-2,B-1,C-5,D-3

d) A-4,B-5,C-2,D-1

Answer: b

Explanation: Pantograph is double lever mechanism. handpump is an inversion of single slider crank chain. Scotch yoke mechanism is an inversion of double slider crank chain.Tchebiceff’s mechanism is an approximate straight line motion mechanism.

3. Match list I with list II

List I List II

A. Scott-Russel 1. Intemittent mechanism motion

B. Geneva 2. Quick return mechanism motion

C. Offset slider crank 3. Simple motion harmonic mechanism

D. Scotch Yoke 4. Straight line mechanism motion

a) A-2,B-3,C-1,D-4

b) A-3,B-2,C-4,D-1

c) A-4,B-1,C-2,D-3

d) A-4,B-3,C-1,D-2

Answer: c

Explanation: Scott-Russel – Straight line mechanism motion

Geneva – Intemittent mechanism motion

Offset slider crank – Quick return mechanism motion

Scotch Yoke – Simple motion harmonic mechanism.

4. When a cylinder is located in a Vee-block, the number of degrees of freedom which are arrested is

a) 2

b) 4

c) 7

d) 8

Answer: b

Explanation: Before placement on Vee-block, cylinder has 6 degrees of freedom. After placement on Vee-block, the cylinder has only 2 degrees of freedom. Hence, the degrees of freedom which are arrested is 6 – 2 = 4.

5. Match list I with list II

Type of joint Motion constrained

A. Revolute 1. Three

B. Cylindrical 2. Five

C. Spherical 3. Four

4. Two

5. Zero

a) A-1,B-3,C-2

b) A-5,B-4,C-3

c) A-2,B-3,C-1

d) A-4,B-5,C-3

Answer: c

Explanation: For revolute pair, degree of freedom = 1 and constrained

DOF = 6 – 1 = 5

For cylindrical pair, dof =2 and constrained dof = 6 – 2 = 4

For spherical pair, dof = 3 and constrained dof = 6 – 3 = 3.

6. The number of binary links, number of binary joints and number of ternary joints in Peaucelliar mechanism is

a) 6,6,0

b) 8,2,4

c) 8,4,2

d) 8,8,0

Answer: b

Explanation: The Peaucelliar mechanism has 8 binary links, 2 binary joints nad 4 ternary joints.

7. The number of degree of freedom of a planer linkage with 8 links and 9 simple revolute joints is

a) 1

b) 2

c) 3

d) 4

Answer: c

Explanation: L = 8 = number of links

P = 9 = number of simple revolute joints

F = 3 – 2P

= 3 – 2 x 9

= 21 – 18

= 3.

8. The following list of statements is given:

1) Grashoff’s rule states that for a planar crank-rocker 4-bar mechanism, the sum of the shortest and longest link lengths cannot be less than the sum of the remaining two link lengths.

2) Inversions of a mechanism are created by fixing different links, one at a time.

3) Geneva mechanism is an intermittent motion device.

4) Grubler’s criterion assumes mobility of a planar mechanism to be one.

The number of correct statements in the above list is

a) 1

b) 2

c) 3

d) 4

Answer: c

Explanation: Except statement 1, all other three statements are correct.

9. A mechanism has 8 links, out of which 5 are binary, 2 are ternary and 1 is quaternary. The number of instantaneous centres of rotation will be

a) 28

b) 56

c) 62

d) 66

Answer: d

Explanation: n = 5 + 4 + 3 = 12

Number of instantaneous centres, N = n/2

= 12 x /2

= 66.

10. In a dynamically equivalent system, a uniformly distributed mass is divided into

a) Three point masses

b) Four point masses

c) Two point masses

d) Infinite point masses

Answer: c

Explanation: Dynamically equivalent system of a rigid body is made of two point masses.

11. A crank and slotted lever mechanism used in a shaper has a centre distance of 300 mm between the centre of oscillation of the slotted lever and the centre of rotation of the crank. The radius of the crank is 120 mm. Find the ratio of the time of cutting to the time of return stroke.

a) 1.62

b) 1.72

c) 1.82

d) 1.92

Answer: b

Explanation: Given : AC = 300 mm ; CB = 120 mm

sin∠CAB = sin 

CB/AC = 120/300 = 0.4

∠CAB = 90°−α/ 2

or α / 2 = 90° – 23.6° = 66.4°

α = 2 × 66.4 = 132.8°

We know that

Time of cutting stroke/ Time of return stroke = 1.72.

12. The magnitude of velocities of the points on a rigid link is directly proportional to the distances from the points to the instantaneous centre.

a) True

b) False

Answer: b

Explanation: The magnitude of velocities of the points on a rigid link is inversely proportional to the distances from the points to the instantaneous centre and is perpendicular to the line joining the point to the instantaneous centre.

13. The velocity of the instantaneous centre relative to any third rigid link will be different.

a) True

b) False

Answer: b

Explanation: The velocity of the instantaneous centre relative to any third rigid link will be same whether the instantaneous centre is regarded as a point on the first rigid link or on the second rigid link.

14. When the pin connects one sliding member and the other turning member, the angular velocity of the sliding member is __________

a) 0

b) 1

c) 2

d) 3

Answer: a

Explanation: When the pin connects one sliding member and the other turning member, the angular velocity of the sliding member is zero. In such cases,

Rubbing velocity at the pin joint = ω.r

where ω = Angular velocity of the turning member, and

r = Radius of the pin.

Answer: b

Explanation: None.

This set of Tough Machine Kinematics Questions and Answers focuses on “Single Slider Crank Chain and its Inversions – 2”.

1. A single slider crank chain is a _______

a) 4-link mechanism

b) 3-link mechanism

c) 2-link mechanism

d) 6-link mechanism

Answer: a

Explanation: A single slider crank chain is a four link mechanism, any four link mechanisms has 4 links inclusive of higher and lower pairs.

2. Bull engine is an inversion of single slider crank chain.

a) True

b) False

Answer: a

Explanation: In a bull engine the inversion is obtained by fixing the cylinder, thus it is an inversion of a single slider crank chain.

3. Find the ratio of the time of cutting to the time of return stroke from the following information: A crank and slotted lever mechanism used in a shaper has a centre distance of 0.300 m between the centre of oscillation of the slotted lever and the centre of rotation of the crank. The radius of the crank is 0.120 m.

a) 1.72

b) 1.65

c) 1.81

d) 1.79

Answer: a

Explanation: We know that time of cutting stroke to the time of return stroke is given by

360-α/ α

Using trigonometric ratios we find that α =132.8°

therefore, Ratio = 1.72.

4. Find the inclination of the slotted bar with the vertical in degrees in the extreme position from the following information: In a crank and slotted lever quick return motion mechanism, the distance between the fixed centres is 0.240 m and the length of the driving crank is 0.120 m.

a) 30

b) 45

c) 60

d) 75

Answer: a

Explanation: In a crank and slotted lever mechanism, symmetry can be observed. Using this symmetry and trigonometric ratios we find that

angle = 30 degrees.

5. Find the ratio of the time of cutting to the time of return stroke from the following information: In a crank and slotted lever quick return motion mechanism, the distance between the fixed centres is 0.240 m and the length of the driving crank is 0.120 m.

a) 3

b) 4.5

c) 3.2

d) 2

Answer: d

Explanation: In a crank and slotted lever mechanism, symmetry can be observed. Using this symmetry and trigonometric ratios we find that vertical inclination of slotted bar is

angle = 30 degrees.

now 90- α/2 = 30

α=120 degrees

therefore ratio = 2.

6. Find the length of stroke if the length of the slotted bar is 0.45m and LOS passes through the free end of the lever. Length of driving crank = 0.12m, distance between fixe centres = 0.24m. Crank and slotted lever quick return motion mechanism.

a) 450mm

b) 400mm

c) 500mm

d) 475mm

Answer: a

Explanation: We know that length of stroke is:

2x450xsin

α=120 degrees,

therefore

length = 450mm.

7. Which of the following mechanism is mostly used in shaping and slotting machines?

a) Whitworth quick return motion mechanism

b) Bull engine

c) Crank and slotted lever quick return motion mechanism

d) Gnome engine

Answer: a

Explanation: Whitworth quick return motion mechanism is mostly used in shaping and slotting machines, as in this mechanism a turning pair is fixed and the driving crank rotates at a uniform speed.

8. In Whitworth quick return motion mechanism, the driving crank is under an accelerated motion

a) True

b) False

Answer: b

Explanation: In Whitworth quick return motion mechanism, the driving crank rotates at a uniform speed and is widely used in shaping and slotting machines.

9. Which of the following mechanism is used to convert reciprocating motion into rotary motion?

a) Whitworth quick return motion mechanism

b) Oscillating cylinder engine

c) Crank and slotted lever quick return motion mechanism

d) Gnome engine

Answer: a

Explanation: Oscillating cylinder engine is used to convert reciprocating motion into rotary motion, the piston reciprocates and the cylinder oscillates about the pin.

10. How many cylinders are there in Gnome engine?

a) 4

b) 5

c) 6

d) 7

Answer: d

Explanation: Rotary internal combustion engines were used in aviation. Now-a-days gas turbines are used in its place. It consists of seven cylinders in one plane and all revolves about fixed centre.

This set of Machine Kinematics written test Questions & Answers focuses on “Double Slider Crank Chain & its Inversions”.

1. Which of the following instruments is used to draw ellipses?

a) Elliptical trammels

b) Slotted lever and crank

c) Gnome engine

d) Oldham’s coupling

Answer: a

Explanation: Elliptical trammel is an instrument which is an inversion of a double slider crank chain. It is mainly used to draw ellipses.

2. Elliptical trammels are used to convert reciprocating motion into rotary motion.

a) True

b) False

Answer: b

Explanation: Elliptical trammels are used to draw ellipses; scotch yoke mechanisms are used to convert rotary motion into reciprocating motion.

3. How inversion is obtained in an elliptical trammel?

a) Fixing the slotted plate

b) Fixing the sliders

c) Fixing the turning pairs

d) Fixing the pin

Answer: a

Explanation: An elliptical trammel is an instrument which is an inversion of a double slider crank chain, here the inversion is obtained by fixing the slotted plate. It is used to draw ellipses.

4. In the given figure, 1 and 2 are sliders, 3 is a bar and 4 is a fixed slotted plate, identify the mechanism.

machine-kinematics-written-test-questions-answers-q4

a) Elliptical trammel

b) Scotch yoke mechanism

c) Oldham’s coupling

d) Gnome engine

Answer: a

Explanation: In the given figure, the slotted lever is fixed and there are two sliders, hence it is a double slider crank chain, since the slotted plate is fixed, it is an inversion. This inversion is known as elliptical trammels.

5. In the given figure if P is not the midpoint of the line connecting 1 and 2, what is the locus of P?

machine-kinematics-written-test-questions-answers-q4

a) Ellipse

b) Straight line

c) Parabola

d) Rectangular hyperbola

Answer: a

Explanation: The given figure represents an elliptical trammel, in an elliptical trammel any point on the bar traces a path which is an ellipse, hence the locus of P is ellipse.

6. In the given figure if P is the midpoint of the line connecting 1 and 2, what is the locus of P?

machine-kinematics-written-test-questions-answers-q4

a) Ellipse

b) Circle

c) Parabola

d) Rectangular hyperbola

Answer: b

Explanation: The given figure represents an elliptical trammel, in an elliptical trammel any point on the bar traces a path which is an ellipse, hence the locus of P is ellipse, but in this case P is the midpoint hence, the locus of P will be a circle.

7. Which of the mechanism is used to convert rotary motion into a reciprocating motion?

a) Elliptical trammel

b) Scotch yoke mechanism

c) Oldham’s coupling

d) Gnome engine

Answer: b

Explanation: Scotch yoke mechanism is an example of an inversion of a double slider crank chain, this mechanism is used to convert rotary motion into reciprocating motion.

8. In Scotch yoke mechanism, the crank is fixed in order to obtain the inversion.

a) True

b) False

Answer: b

Explanation: In scotch yoke mechanism there are in total 4 links, one is Crank and one is frame. Inversion can be obtained by fixing either of the remaining two links.

9. Which of the following mechanism is used for connecting two parallel shafts whose axes are at a small distance apart?

a) Elliptical trammel

b) Scotch yoke mechanism

c) Oldham’s coupling

d) Gnome engine

Answer: c

Explanation: Oldham’s coupling is an instrument which is an inversion of double slider crank chain, this is used to connect two parallel shafts whose axes are at a small distance apart.

10. Which of the following link is fixed to obtain inversion in Oldham’s coupling?

a) Driving shaft

b) Flange

c) Supporting frame

d) Driven shaft

Answer: c

Explanation: The shafts are coupled in such a way that if one shaft rotates, the other shaft also rotates at the same speed. This inversion is obtained by fixing the link which corresponds to Supporting frame.

11. How many turning pairs are there in a double slider crank chain?

a) 1

b) 2

c) 3

d) 4

Answer: b

Explanation: Double slider crank chain is a kinematic chain which consists of two turning pairs, as a result it is called double slider crank chain.

12. A double slider crank chain has one pair of each sliding and turning pairs.

a) True

b) False

Answer: b

Explanation: In a double slider crank chain, there are two turning pairs and two sliding pairs. In a single slider crank chain there is one sliding pair and three turning pairs.

13. How many sliding pairs are there in a double slider crank chain?

a) 1

b) 2

c) 3

d) 4

Answer: b

Explanation: Double slider crank chain is a kinematic chain which consists of two sliding pairs, as a result it is called double slider crank chain.

14. In which of the following mechanisms inversion is obtained by fixing the cylinder?

a) Pendulum pump

b) Gnome engine

c) Double slider crank chain

d) Oscillating cylinder

Answer: a

Explanation: Pendulum pump also known as the bull engine is an inversion of single slider crank chain, here inversion is obtained by fixing the cylinder.

15. Which of the following is not an inversion of double slider crank chain?

a) Elliptical trammels

b) Scotch yoke mechanism

c) Oldham’s coupling

d) Gnome engine

Answer: d

Explanation: Gnome engine is an example of inversion of single slider crank chain, whereas Elliptical trammels, Scotch yoke mechanism and Oldham’s coupling are inversions of double slider crank chain.

This set of Machine Kinematics online test focuses on “Velocity of a point Link on a Link By Instanteneous Centre Method”.

1. There are two points P and Q on a planar rigid body. The relative velocity between the two points

a) should always be along PQ

b) can be oriented along any direction

c) should always be perpendicular to PQ

d) should be along QP when the body undergoes pure translation

Answer: c

Explanation: Velocity of any point on a link with respect to another point  on the same link is always perpendicular to the line joining these points on the configuration  diagram.

v QP = Relative velocity between P & Q

= v P − v Q always perpendicular to PQ.

2. For a four-bar linkage in toggle position, the value of mechanical advantage is

a) 0.0

b) 0.5

c) 1.0

d) ∞

Answer: d

Explanation: When the mechanism is toggle,then β = 0 0 and 180 0 .

So M.A = ∞.

3. The number of inversion for a slider crank mechanism is

a) 6

b) 5

c) 4

d) 3

Answer: c

Explanation: For a 4 bar slider crank mechanism, there are the number of links or inversions are 4. These different inversions are obtained by fixing different links once at a time for one inversion. Hence, the number of inversions for a slider crank mechanism is 4.

4. Match the item in columns I and II

Column I Column II

P. Addendum 1. Cam

Q. Instantaneous centre of velocity 2. Beam

R. Section modulus 3. Linkage

S. Prime circle 4. Gear

a) P-4, Q-2, R-3, S-1

b) P-4, Q-3, R-2, S-1

c) P-3, Q-2, R-1, S-4

d) P-3, Q-4, R-1, S-2

Answer: b

Explanation: Column I Column II

P. Addendum 4. Gear

Q. Instantaneous centre of velocity 3. Linkage

R. Section modulus 2. Beam

S. Prime circle 1. Cam

So correct pairs are, P-4, Q-3, R-2, S-1.

5. Match the items in columns I and II

Column I Column II

P. Higher Kinematic Pair 1. Grubler’s Equation

Q. Lower Kinemation Pair 2. Line contact

R. Quick Return Mechanism 3. Euler’s Equation

S. Mobility of a Linkage 4. Planar

5. Shaper

6. Surface contact

a) P-2, Q-6, R-4, S-3

b) P-6, Q-2, R-4, S-1

c) P-6, Q-2, R-5, S-3

d) P-2, Q-6, R-5, S-1

Answer: d

Explanation: In this question pair or mechanism is related to contact & machine related to it.

Column I Column II

P. Higher Kinematic Pair 2. Line Contact

Q. Lower Kinematic Pair 6. Surface Contact

R. Quick Return Mechanism 5. Shaper

S. Mobility of a Linkage 1. Grubler’s Equation

So correct pairs are, P-2, Q-6, R-5, S-1.

6. In a four-bar linkage, S denotes the shortest link length, L is the longest link length, P and Q are the lengths of other two links. At least one of the three moving links will rotate by 360 0 if

a) S + L < P + Q

b) S + L > P + Q

c) S + P < L + Q

d) S + P > L + Q

Answer: a

Explanation: Here P,Q,R, & S are the lengths of the links.

According to Grashof’s law : “For a four bar mechanism, the sum of the shortest and longest link lengths should not be greater than the sum of remaining two link lengths, if there is to be continuous relative motion between the two links

S + L < P + Q.

7. The number of degrees of freedom of a planar linkage with 8 links and 9 simple revolute joints is

a) 1

b) 2

c) 3

d) 4

Answer: c

Explanation: Given l= 8, j= 9

We know that, Degree of freedom,

n =3−2j = 3−2 x 9 = 3.

8. The lengths of the links of a 4-bar linkage with revolute pairs are p,q,r, and s units. given that p<q<r<s. Which of these links should be the fixed one, for obtaining a “double crank” mechanism ?

a) link of length p

b) link of length q

c) link of length r

d) link of length s

Answer: a

Explanation: Given p<q<r<s

“Double crank” mechanism occurs, when the shortest link is fixed. From the given pairs p is the shortest link. So, link of length p should be fixed.

9. When a cylinder is located in a Vee-block, the number of degrees of freedom which are arrested is

a) 2

b) 4

c) 7

d) 8

Answer: b

Explanation: Number of degrees of freedom = 2 & movability includes the six degrees of freedom of the device as a whole, as the ground link were not fixed. So, 4 degrees of freedom are constrained or arrested.

10. The minimum number of links in a single degree-of-freedom planar mechanism with both higher and lower kinematic pairs is

a) 2

b) 3

c) 4

d) 5

Answer: c

Explanation: From the Kutzbach criterion the degree of freedom,

n = 3 − 2j − h

For single degree of Freedom ,

1 = 3 − 2j − h

3l − 2j − 4 − h = 0 …

The simplest possible mechanisms of single degree of freedom is four-bar mechanism. For this mechanism j = 4, h = 0

From equation , we have

3l − 2 x 4 − 4 − 0 = 0

or, l = 4.

11. The total number of instantaneous centres for a mechanism consisting of n links are

a) n/2

b) n

c) n – 1/2

d) n/2

Answer: d

Explanation: The number of instantaneous centres in a constrained kinematic chain is equal to the number of possible combinations of two links. The number of pairs of links or the number of instantaneous centres is the number of combinations of n links taken two at a time. Mathematically, number of instantaneous centres, N = n/2 where n = Number of links.

12. According to Aronhold Kennedy’s theorem, if three bodies move relatively to each other, their instantaneous centres will lie on a

a) straight line

b) parabolic curve

c) ellipse

d) none of the mentioned

Answer: a

Explanation: The Aronhold Kennedy’s theorem states that if three bodies move relatively to each other, they have three instantaneous centres and lie on a straight line.

13. In a mechanism, the fixed instantaneous centres are those centres which

a) remain in the same place for all configurations of the mechanism

b) vary with the configuration of the mechanism

c) moves as the mechanism moves, but joints are of permanent nature

d) none of the mentioned

Answer: a

Explanation: Fixed instantaneous centres remain in the same place for all configurations of the mechanism. The permanent instantaneous centres move when the mechanism moves, but the joints are of permanent nature.

14. The instantaneous centres which vary with the configuration of the mechanism, are called

a) permanent instantaneous centres

b) fixed instantaneous centres

c) neither fixed nor permanent instantaneous centres

d) none of the mentioned

Answer: c

Explanation: Fixed instantaneous centres remain in the same place for all configurations of the mechanism. The permanent instantaneous centres move when the mechanism moves, but the joints are of permanent nature. Neither fixed nor permanent instantaneous centres vary with the configuration of the mechanism.

Answer: b

Explanation: When the slider link moves on fixed link having constant radius of curvature, the instantaneous centre lies at the centre of curvature i.e. the centre of the circle, for all configuration of the links.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Properties of Instantaneous Centre”.

1. Which is the false statement about the properties of instantaneous centre?

a) at the instantaneous centre of rotation, one rigid link rotates instantaneously relative to another for the configuration of mechanism considered

b) the two rigid links have no linear velocities relative to each other at the instantaneous centre

c) the two rigid links which have no linear velocity relative to each other at this centre have the same linear velocity to the third rigid link

d) the double centre can be denoted either by O 21 or O 12 , but proper selection should be made

Answer: d

Explanation: The following properties of the instantaneous centre are important from the subject point of view :

1. A rigid link rotates instantaneously relative to another link at the instantaneous centre for the configuration of the mechanism considered.

2. The two rigid links have no linear velocity relative to each other at the instantaneous centre. At this point , the two rigid links have the same linear velocity relative to the third rigid link. In other words, the velocity of the instantaneous centre relative to any third rigid link will be same whether the instantaneous centre is regarded as a point on the first rigid link or on the second rigid link.

2. Instantaneous center of rotation of a link in a four bar mechanism lies on

a) right side pivot of this link

b) left side pivot of this link

c) a point obtained by intersection on extending adjoining links

d) none of the mentioned

Answer: c

Explanation: None.

3. The total number of instantaneous centers for a mechanism of n links is

a) n/2

b) n

c) n – 1

d) n

Answer: a

Explanation: The number of pairs of links or the number of instantaneous centres is the number of combinations of n links taken two at a time. Mathematically, number of instantaneous centres,

N = n/2.

4. The number of links and instantaneous centers in a reciprocating engine mechanism are

a) 4,4

b) 4,5

c) 5,4

d) 4,6

Answer: d

Explanation: First of all, determine the number of instantaneous centres  by using the relation

N = n/2

In present case, N = 4/2 

= 6.

5. According to Kennedy’s theorem, if three bodies have plane motions, their instantaneous centres lie on

a) a triangle

b) a point

c) two lines

d) a straight line

Answer: d

Explanation: The Aronhold Kennedy’s theorem states that if three bodies move relatively to each other, they have three instantaneous centres and lie on a straight line.

6. In a rigid link OA, velocity of A w.r.t. O will be

a) parallel to OA

b) perpendicular to OA

c) at 45 0 to OA

d) along AO

Answer: b

Explanation: None.

7. Two systems shall be dynamically equivalent when

a) the mass of two are same

b) c.g. of two coincides

c) M.I. of two about an axis through c.g. is equal

d) all of the mentioned

Answer: d

Explanation: None.

8. A link is rotating about O. Velocity of point P on link w.r.t. point Q on link will be perpendicular to

a) OP

b) OQ

c) PQ

d) line in between OP and OQ

Answer: c

Explanation: A link is rotating about O. Velocity of point P on link w.r.t. point Q on link will be perpendicular to PQ.

The velocity of any point in mechanism relative to any other point on the mechanism on velocity polygon is represented by the line joining the corresponding points.

9. The velocity of any point in mechanism relative to any other point on the mechanism on velocity polygon is represented by the line

a) joining the corresponding points

b) perpendicular to line

c) at 45 0 to line

d) none of the mentioned

Answer: a

Explanation: A link is rotating about O. Velocity of point P on link w.r.t. point Q on link will be perpendicular to PQ.

The velocity of any point in mechanism relative to any other point on the mechanism on velocity polygon is represented by the line joining the corresponding points.

10. The absolute acceleration of any point P in a link about center of rotation O is

a) along PO

b) perpendicular to PO

c) at 45 0 to PO

d) none of the mentioned

Answer: d

Explanation: The coriolis component of acceleration is always perpendicular to the link.

Answer: b

Explanation: The angular acceleration of the link AB is obtained by dividing the tangential components of the acceleration of B with respect to A to the length of the link.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Method of Locating Instantaneous Centres in a Mechanism”.

1. The direction of Corioli’s component of acceleration is the direction

a) of relative velocity vector for the two coincident points rotated by 90 0 in the direction of the angular velocity of the rotation of the link

b) along the centripetal acceleration

c) along tangential acceleration

d) along perpendicular to angular velocity

Answer: a

Explanation: The direction of coriolis component of acceleration will not be changed in sign if both ω and v are reversed in direction. It is concluded that the direction of coriolis component of acceleration is obtained by rotating v, at 90°, about its origin in the same direction as that of ω.

2. In a shaper mechanism, the Corioli’s component of acceleration will

a) not exist

b) exist

c) depend on position of crank

d) none of the mentioned

Answer: b

Explanation: None.

3. The magnitude of tangential acceleration is equal to

a) velocity 2 x crank radius

b) velocity 2 / crank radius

c)  2

d) velocity x crank radius 2

Answer: b

Explanation: The magnitude of tangential acceleration is equal to velocity 2 / crank radius.

The magnitude of the Corioli’s component of acceleration of a slider moving at velocity V on a link rotating at angular speed ω is 2Vω.

4. Tangential acceleration direction is

a) along the angular velocity

b) opposite to angular velocity

c) perpendicular to angular velocity

d) all of the mentioned

Answer: d

Explanation: None.

5. The magnitude of the Corioli’s component of acceleration of a slider moving at velocity V on a link rotating at angular speed ω is

a) Vω

b) 2Vω

c) Vω/2

d) 2V/ω

Answer: b

Explanation: The magnitude of tangential acceleration is equal to velocity 2 / crank radius.

The magnitude of the Corioli’s component of acceleration of a slider moving at velocity V on a link rotating at angular speed ω is 2Vω.

6. In a rotary engine the angular velocity of the cylinder center line is 25 rad/sec and the relative velocity of a point on the cylinder center line w.r.t. cylinder is 10 m/sec. Corioli’s acceleration will be

a) 500m/sec 2

b) 250m/sec 2

c) 1000m/sec 2

d) 2000m/sec 2

Answer: a

Explanation: Corioli’s component = 2Vω

= 2 x 10 x 25 = 500500m/sec 2 .

7. Corioli’s component is encountered in

a) quick return mechanism of shaper

b) four bar chain mechanism

c) slider crank mechanism

d) all of the mentioned

Answer: a

Explanation: When a point on one link is sliding along another rotating link, such as in quick return motion mechanism, then the coriolis component of the acceleration must be calculated.

8. Klein’s construction gives a graphical construction for

a) slider-crank mechanism

b) velocity polygon

c) acceleration polygon

d) none of the mentioned

Answer: c

Explanation: Klein’s construction represents acceleration polygon.

9. The velocity of a slider with reference to a fixed point about which a bar is rotating and slider sliding on the bar will be

a) parallel to bar

b) perpendicular to bar

c) both of the mentioned

d) none of the mentioned

Answer: c

Explanation: None.

10. Klien’s construction can be used to determine acceleration of various parts when the crank is at

a) inner dead center

b) outer dead center

c) right angles to the link of the stroke

d) all of the mentioned

Answer: d

Explanation: Klien’s construction can be used to determine acceleration in all the mentioned position.

11. The number of dead centers in a crank driven slider crank mechanism are

a) 0

b) 2

c) 4

d) 6

Answer: b

Explanation: None.

12. Corioli’s component acts

a) perpendicular to sliding surfaces

b) along sliding surfaces

c) both of the mentioned

d) all of the mentioned

Answer: a

Explanation: The coriolis component of acceleration is always perpendicular to the link.

13. The sense of Coriol’s component is such that it

a) leads the sliding velocity vector by 90 0

b) lags the sliding velocity vector by 90 0

c) is along the sliding velocity vector by 90 0

d) leads the sliding velocity vector by 180 0

Answer: a

Explanation: The direction of coriolis component of acceleration is obtained by rotating v, at 90°, about its origin in the same direction as that of ω.

14. Klien’s construction can be used when

a) crank has a uniform angular velocity

b) crank has non-uniform velocity

c) crank has uniform angular acceleration

d) crank has uniform angular velocity and angular acceleration

Answer: a

Explanation: None.

Answer: b

Explanation: Klien’s construction can be used to determine acceleration.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Velocity in Mechanisms – 1”.

1. In the figure given below A and D are fixed points, link AB rotates at a uniform angular velocity of 900 rev/min ccw, find the instantaneous velocity of point E in m/s.

Rab = 100mm, Bc = 450, distance of E from BC = 100mm, Cf = 75mm, CD = 275mm, AD = 250mm, perpendicular DF = 17mm, perpendicular BE = 250mm.

machine-kinematics-questions-answers-velocity-mechanisms-q1

a) 8.3

b) 8.7

c) 9

d) 7.6

Answer: a

Explanation: The following question can be solved graphically as well as analytically,

first we find that

Vb = ωxRab = 9.42 m/s

Vcb = 11.42

Vcd = 13.61 m/s

constructing a velocity graph, we find that

Ve = 8.3m/s.

2. Velocity of a point B in a link can be calculated by using the relation

Vb = Va – Vba.

a) True

b) False

Answer: b

Explanation: The velocity of a point B in a link can be calculated when the velocity of point A is known using the relation

Vb = Va + Vba.

3. In the figure given below A and D are fixed points, link AB rotates at a uniform angular velocity of 900 rev/min ccw, find instantaneous velocity of point F in m/s.

Rab = 100mm, Bc = 450, distance of E from BC = 100mm, Cf= 75mm, CD = 275mm, AD =250mm, perpendicular DF = 17mm, perpendicular BE = 250mm.

machine-kinematics-questions-answers-velocity-mechanisms-q1

a) 8.3

b) 8.7

c) 9.4

d) 7.6

Answer: c

Explanation: The following question can be solved graphically as well as analytically,

first we find that

Vb = ωxRab = 9.42 m/s

Vcb = 11.42

Vcd = 13.61 m/s

constructing a velocity graph, we find that

Vf = 9.4 m/s.

4. In the figure given below A and D are fixed points, link AB rotates at a uniform angular velocity of 900 rev/min ccw, find angular velocity of BC in rad/s.

Rab = 100mm, Bc = 450, distance of E from BC = 100mm, Cf= 75mm, CD = 275mm, AD =250mm, perpendicular DF = 17mm, perpendicular BE = 250mm.

machine-kinematics-questions-answers-velocity-mechanisms-q1

a) 28.3

b) 2 8.7

c) 29.4

d) 25.3

Answer: d

Explanation: The following question can be solved graphically as well as analytically,

first we find that

Vb = ωxRab = 9.42 m/s

Vcb = 11.42

ωcb = Vcb/Rcb

= 25.37 rad/s.

5. In the figure given below A and D are fixed points, link AB rotates at a uniform angular velocity of 900 rev/min ccw, find angular velocity of CDin rad/s.

Rab = 100mm, Bc = 450, distance of E from BC = 100mm, Cf= 75mm, CD = 275mm, AD =250mm, perpendicular DF = 17mm, perpendicular BE = 250mm.

machine-kinematics-questions-answers-velocity-mechanisms-q1

a) 48.37

b) 48.77

c) 49.47

d) 45.37

Answer: c

Explanation: The following question can be solved graphically as well as analytically,

first we find that

Vb = ωxRab = 9.42 m/s

Vcd = 13.61 m/s

ωcd = Vcd/Rcd

= 49.47 rad/s.

6. The locus of the instantaneous centre in space during a definite motion of the body is called the _________

a) Space centrode

b) Body centrode

c) Link centrode

d) Mechanism centrode

Answer: a

Explanation: The instantaneous centre is a point inside the body which may be considered fixed at any instant of time. The locus of the instantaneous centre in space during a definite motion of the body is called the space centrode.

7. The locus of the instantaneous centre relative to the body itself is called the _________

a) Space centrode

b) Body centrode

c) Link centrode

d) Mechanism centrode

Answer: b

Explanation: The instantaneous centre is a point inside the body which may be considered fixed at any instant of time. The locus of the instantaneous centre relative to the body itself is called the body centrode.

8. Locus of all instantaneous centres is known as centrode.

a) True

b) False

Answer: a

Explanation: Thus the instantaneous centre of a moving body can be defined as that centre which goes on changing from one instant to another. The locus of all such instantaneous centres is known as a centrode.

9. A line drawn through an instantaneous centre and perpendicular to the plane of motion is called __________

a) Instantaneous axis

b) Relative axis

c) Instantaneous centrode

d) Relative centrode

Answer: a

Explanation: A line drawn through an instantaneous centre and perpendicular to the plane of motion is called instantaneous axis. The locus of this axis is known as axode.

10. The locus of which axis is known as axode?

a) Instantaneous axis

b) Relative axis

c) Instantaneous centrode

d) Relative centrode

Answer: a

Explanation: A line drawn through an instantaneous centre of the links and perpendicular to the plane of motion is known as instantaneous axis. The locus of this axis is known as axode.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Velocity in Mechanisms – 2”.

1. The coriolis component of acceleration exists whenever a point moves along a path that has

a) linear displacement

b) rotational motion

c) gravitational acceleration

d) tangential acceleration

Answer: b

Explanation: When a point on one link is sliding along another rotating link such as in quick return motion mechanism, then Coriolis component of acceleration must be taken into account. It means for Coriolis component, rotational motion is required.

2. In a pantograph, all the pairs are

a) turning pairs

b) sliding pairs

c) spherical pairs

d) self-closed pairs

Answer: a

Explanation: Pantograph is an instrument used to reproduce to an enlarged or a reduced scale and as exactly as possible the path described by a given point. It consists of bars connected by turning pairs.

3. Which of the following mechanism is made up of turning pairs?

a) Scott Russel’s mechanism

b) Peaucellier’s mechanism

c) Hart’s mechanism

d) All of the mentioned

Answer: b and c

Explanation: Exact straight line motion mechanisms are made up of turning pairs. These mechanisms are as follows:

a) Peaucellier’s mechanism

b) Hart’s mechanism.

4. Scott Russel’s mechanism is made up of sliding pair.

a) True

b) False

Answer: a

Explanation: Exact straight line motion mechanisms consists of one sliding pair. The Scott Russell’s mechanism is of this type.

5. An exact straight line motion mechanism is a

a) Scott-Russell’s mechanism

b) Hart’s mechanism

c) Peaucellier’s mechanism

d) All of the mentioned

Answer: d

Explanation: All the mechanisms mentioned above consists of exact straight line motion. Scott-Russell’s mechanism consists of sliding pair whereas Peaucellier’s mechanism and Hart’s mechanism consists of turning pair.

6. Which of the following mechanism is an approximate straight line motion mechanism?

a) Watt’s mechanism

b) Grasshopper mechanism

c) Robert’s mechanism

d) All of the mentioned

Answer: d

Explanation: The mechanism that are approximate straight line motion are as follows:

a) Watt’s mechanism

b) Scott-Russell’s mechanism

c) Grasshopper mechanism

d) Robert’s mechanism

e) Tehebicheff’s mechanism.

7. The fundamental equation for correct steering is

a) sinɸ + sinα = b/c

b) cosɸ – sinα = c/b

c) cotɸ – cotα = c/b

d) tanɸ + cotα = b/c

Answer: c

Explanation: The condition for correct steering is that all the four wheels must turn about the same instantaneous centre.

The fundamental equation for correct steering is

cotɸ – cotα = c/b

where ɸ and α = Angle through which the axix of the outer wheel and inner wheel turns respectively

c = Distance between the pivots of the front axles

b = Wheel base.

8. The condition for correct steering of a Davis steering is

a) sinα = b/c

b) cosα = c/b

c) tanα = c/2b

d) cotα = c/2b

Answer: c

Explanation: In case of Davis steering gear, the condition for correct steering is

tanα = c/2b

where α = Angle of inclination of the links to the vertical.

9. The driving and driven shafts connected by a Hooke’s joint will have equal speeds, if

a) cosϴ = sinα

b) sinϴ = √tanα

c) tanϴ = √cosα

d) cotϴ = cosα

Answer: c

Explanation: A Hooke’s joint is used to connect two shafts, which are intersecting at a small angle. The speed of the driving and driven shafts will be equal, when

tanϴ = √cosα.

Answer: d

Explanation: The Acerman steering gear mechanism is much simpler than Davis gear. The whole mechanism of Ackerman steering gear is on the back of the front wheels, whereas in Davis steering gear, it is in front of the wheels. The Ackerman steering gear consists of turning pairs, whereas Davis steering gear consists of sliding members.

This set of Machine Kinematics online quiz focuses on “Relative Velocity of Two Bodies Moving in Straight Lines”.

1. A machine raised a load of 360 N through a distance of 200 mm. The effort, a force of 60 N moved 1.8 m during the process. Calculate mechanical advantage.

a) 6

b) 7

c) 8

d) 9

Answer: a

Explanation: Given, load raised, W = 360 N

Effort applied, P = 60 N

Distance moved by the effort, y = 1.8 m

Distance moved by the load, x = 200 mm = 0.2 m

Mechanical advantage, M.A. = W/P = 360/60 = 6.

2. A machine raised a load of 360 N through a distance of 200 mm. The effort, a force of 60 N moved 1.8 m during the process. Calculate velocity ratio.

a) 6

b) 7

c) 8

d) 9

Answer: d

Explanation: Given, load raised, W = 360 N

Effort applied, P = 60 N

Distance moved by the effort, y = 1.8 m

Distance moved by the load, x = 200 mm = 0.2 m

Velocity ratio, V.R. = y/x = 1.8/0.2 = 9.

3. A machine raised a load of 360 N through a distance of 200 mm. The effort, a force of 60 N moved 1.8 m during the process. Calculate efficiency at this load.

a) 44.44%

b) 55.55%

c) 66.66%

d) 77.77%

Answer: c

Explanation: Given, load raised, W = 360 N

Effort applied, P = 60 N

Distance moved by the effort, y = 1.8 m

Distance moved by the load, x = 200 mm = 0.2 m

Mechanical advantage, M.A. = W/P = 360/60 = 6

Velocity ratio, V.R. = y/x = 1.8/0.2 = 9

Efficiency at the load, ȵ = M.A./V.R. x 100 = 6/9 x 100 = 66.66%.

4. A machine raised a load of 360 N through a distance of 200 mm. The effort, a force of 60 N moved 1.8 m during the process. Calculate effect of friction.

a) 10 N

b) 20 N

c) 30 N

d) 40 N

Answer: b

Explanation: Given, load raised, W = 360 N

Effort applied, P = 60 N

Distance moved by the effort, y = 1.8 m

Distance moved by the load, x = 200 mm = 0.2 m

Mechanical advantage, M.A. = W/P = 360/60 = 6

Velocity ratio, V.R. = y/x = 1.8/0.2 = 9

Effort lost in friction, F P = P – W/V.R. = 60 – 360/9 = 20 N.

5. In a lifting machine, the effort required to lift loads of 200N and 300N were 50N and 60N respectively. If the velocity ratio of the machine is 20 determine law of the machine.

a) P = 1/10W +30

b) P = 1/20W +30

c) P = 1/30W +30

d) P = 1/40W +30

Answer: a

Explanation: Let the law of machine be P = mW + C

where P = effort applied, W = load lifted and m and C being constants.

when W = 200 N P = 50 N

when W = 300 N P = 60 N

Putting these values in the law of machine.

50 = 200m + C …………

60 = 300m + C …………

Subtracting  and , we get

1 = 10 m

or, m = 1/10

Putting this value in equation , we get

50 = 200 x 1/10 + C

C = 30

Hence, the machine follows the laws

P = 1/10W +30.

6. In a lifting machine, the effort required to lift loads of 200N and 300N were 50N and 60N respectively. If the velocity ratio of the machine is 20 determine efficiency to load of 200 N.

a) 10 %

b) 15 %

c) 20 %

d) 25 %

Answer: c

Explanation: When W = 200 N, P = 50 N

M.A. = W/P = 200/50 = 4

V.R. = 20

Efficiency at this load ȵ = M.A./V.R. x 100 = 4/20 x 100 = 20 %.

7. In a lifting machine, the effort required to lift loads of 200N and 300N were 50N and 60N respectively. If the velocity ratio of the machine is 20 determine efficiency to load of 300 N.

a) 10 %

b) 15 %

c) 20 %

d) 25 %

Answer: d

Explanation: When W = 300 N, P = 60 N

M.A. = W/P = 300/60 = 5

V.R. = 20

Efficiency at this load ȵ = M.A./V.R. x 100 = 5/20 x 100 = 25 %.

8. In a lifting machine, the effort required to lift loads of 200N and 300N were 50N and 60N respectively. If the velocity ratio of the machine is 20 determine effort loss in friction at 200 N.

a) 30 N

b) 35 N

c) 40 N

d) 45 N

Answer: c

Explanation: When W = 200 N, P = 50 N

Effort lost in friction, F P = P – W/ V.R. = 50 – 200/20 = 40 N.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Motion of a Link”.

1. What is the direction of velocity of a point in a link relative to another point on the same link rotating in a specific direction.

a) Perpendicular to line joining both the links

b) Parallel to line joining both the links

c) Perpendicular to the surface of the link

d) Parallel to the surface of the link

Answer: a

Explanation: Velocity of any point on a link with respect to another point on the same link is always in the direction perpendicular to the line joining these points on the space diagram.

2. The direction of velocity is parallel if the rotation is anticlockwise and perpendicular to the line joining links if the rotation is clockwise.

a) True

b) False

Answer: b

Explanation: Velocity of any point on a link with respect to another point on the same link is always in the direction perpendicular to the line joining these points on the space diagram both during anticlockwise and clockwise rotations.

3. What is the correct representation of velocity of point A with respect to B in a link?

a) Vab

b) Vba

c) Va-b

d) Vb-a

Answer: a

Explanation: When there are two points on a link, the velocity of a point A wrt to other point on the same link is represented by Vab.

4. What is the velocity of point C with respect to A in the given figure?

machine-kinematics-questions-answers-velocity-mechanisms-q1

a) Perpendicular to line joining BC

b) Perpendicular to line joining AC

c) Parallel to line joining BC

d) Parallel to line joining AC

Answer: b

Explanation: In the above figure we can assume an imaginary link between A and C, as per the rule, the velocity of a point with respect to any other point on the same link is perpendicular to the line joining the links.

5. Which type of pair formed by two elements which are so connected that one is constrained to turn or revolve about a fixed axis of another element?

a) Turning pair

b) Rolling pair

c) Sliding pair

d) Higher pair

Answer: a

Explanation: The type of pair formed by two elements which are so connected that one is constrained to turn or revolve about a fixed axis of another element is known as turning pair.

6. Which of the following is a lower pair?

a) Pulleys in belt drive

b) Cam and follower

c) Belt drive

d) Ball and socket joint

Answer: d

Explanation: If two moving elements do not have surface contact in motion, then the pair is known as lower pair, in the given question ball and socket joint is a lower pair.

7. In a lifting machine, the effort required to lift loads of 200N and 300N were 50N and 60N respectively. If the velocity ratio of the machine is 20 determine effort loss in friction at 200 N.

a) 30 N

b) 35 N

c) 40 N

d) 45 N

Answer: d

Explanation: When W = 300 N, P = 60 N

Effort lost in friction, F P = P – W/V.R. = 60 – 300/20 = 45 N.

8. In a lifting machine, the effort required to lift loads of 200N and 300N were 50N and 60N respectively. If the velocity ratio of the machine is 20 determine maximum efficiency which can be expected from this machine.

a) 30 %

b) 40 %

c) 50 %

d) 60 %

Answer: c

Explanation: Maximum possible efficiency of any machine = 1/m x V.R. = 1/1/10 x 20 = 0.5 = 50 %.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on ” Velocity of a Point on a Link by Relative Velocity Method”.

1. The instantaneous centre is a point which is always fixed.

a) True

b) False

Answer: b

Explanation: The instantaneous center is not always fixed.

2. The angular velocity of a rotating body is expressed in terms of

a) revolution per minute

b) radians per second

c) any one of the mentioned

d) none of the mentioned

Answer: c

Explanation: Angular velocity is expressed both as revolution per minute and radians per second.

3. The linear velocity of a rotating body is given by the relation

a) v = rω

b) v = r/ω

c) v = ω/r

d) v = ω 2 /r

Answer: a

Explanation: The linear velocity of a rotating body is given by the relation v = rω

The linear acceleration of a rotating body is given by the relation a = rα.

4. The linear acceleration of a rotating body is given by the relation

a) a = rα

b) a = r/α

c) a = α/r

d) a = α 2 /r

Answer: a

Explanation: The linear velocity of a rotating body is given by the relation v = rω

The linear acceleration of a rotating body is given by the relation a = rα.

5. The relation between linear velocity and angular velocity of a cycle

a) exists under all conditions

b) does not exist under all conditions

c) exists only when it does not slip

d) exists only when it moves on horizontal plane

Answer: a

Explanation: None.

6. The velocity of piston in a reciprocating pump mechanism depends upon

a) angular velocity of the crank

b) radius of the crank

c) length of the connecting rod

d) all of the mentioned

Answer: d

Explanation: None.

7. The linear velocity of a point B on a link rotating at an angular velocity ω relative to another point A on the same link is

a) ω 2 AB

b) ωAB

c) ω 2

d) ω/AB

Answer: b

Explanation: None.

8. The linear velocity of a point relative to another point on the same link is ……….. to the line joining the points.

a) perpendicular

b) parallel

c) at 45 0

d) none of the mentioned

Answer: a

Explanation: The total linear acceleration of a particle can be obtained by combining the two mutually perpendicular accelerations.

9. According to Kennedy’s theorem the instantaneous centres of three bodies having relative motion lie on a

a) curved path

b) straight line

c) point

d) none of the mentioned

Answer: b

Explanation: The Aronhold Kennedy’s theorem states that if three bodies move relatively to each other, they have three instantaneous centres and lie on a straight line.

Answer: c

Explanation: The instantaneous centers of a slider moving in a linear guide lies at infinity.

The instantaneous centers of a slider moving in a curved surface lies at the center of curvature.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Velocities in a Slider Crank Mechanism and Motion of a Link”.

1. The lengths of the links of a 4- bar linkage with revolute pairs only are p,q,r and s units. Given that p < q < r < s and s+p < q+r which of these links should be the fixed one, for obtaining a ‘double crank’ mechanism?

a) ink of length p

b) link of length q

c) link of length r

d) link of length s

Answer: a

Explanation: For Double crank mechanism Shortest link is fixed.

Here shortest link is ‘P’.

2. For a four-bar linkage in toggle position, the value of mechanical advantage is

a) 0.0

b) 0.5

c) 1.0

d) ∞

Answer: d

Explanation: At Toggle position output velocity is zero

And hence, mechanical advantage = input velocity/output velocity = ∞.

3. In a slider-crank mechanism, the crank is rotating with an angular velocity of 20 rad/s in counterclockwise direction. At the instant when the crank is perpendicular to the direction of the piston movement, velocity of the piston is 2 m/s. Radius of the crank is

a) 100 cm

b) 10 cm

c) 1 cm

d) 0.1 cm

Answer: b

Explanation: V p = ωr𝛳𝛳

In this case ϴ = 90 0

V p = ωr

r = V p /ω = 2/20 = 0.1 m or 10 cm.

4. In a single link robotic arm the end-effector slides upward along the link with a velocity of 0.5 m/s while the link rotates about revolute joint with an angular speed of 1 rad/sec. When the end-effector is at a distance of 1 m from the joint, the acceleration experienced by the end-effector will be

a) 1 m/s 2

b) 1.41 m/s 2

c) 1.71 m/ 2

d) 2 m/ 2

Answer: a

Explanation: a = 2ωV = 2 x 1 x 0.5 = 1 m/s 2 .

5. For the same crank length and uniform angular velocity of the crank in an offset slider crank mechanism, if the connecting rod length is increased by 1.5 times, the velocity of piston will

a) remain unchanged

b) increase 1.5 times

c) decrease by 1.5 times

d) increase by 1.5√2 times

Answer: c

Explanation: V 1 = ωr𝛳𝛳

V 2 = ωr𝛳𝛳

from these two equation, V 2 < V 1

V 2 will decrease but correct quantification can not be done with available data.

Among the available options, best answer is .

6. It is planned to construct a four-bar mechanism ABCD with length AB= 60mm, BC = 100mm, CD = 70 mm and fixed link AD = 200 mm. If at least one link is required to have a complete rotation, this mechanism is

a) of crank-rocker type

b) of double-crank type

c) of double rocker type

d) impossible to construct

Answer: c

Explanation: S + L = 60 + 200 = 260 mm

P + Q = 100 + 70 = 170 mm

From grashoff equality when S + L > P + Q

So always double rocker.

7. The number of links in a planer mechanism with revolute joints having 10 instantaneous centres is

a) 3

b) 4

c) 5

d) 6

Answer: c

Explanation: n/2 = 10

n = 20

n = 5.

8. A weston differential pulley block consists of a lower block and upper block. The upper block has two cogged grooves, one of which has a radius of 150 mm and the other a radius of 125 mm. If the efficiency of the machine is 50% calculate the effort required to raise a load of 1.5 kN.

a) 250 N

b) 300 N

c) 350 N

d) 400 N

Answer: a

Explanation: We know that in case of a Weston differential pulley block,

V.R. = 2D/D – d = 2 x 300/300 -250 = 12

Using the relation, Efficiency = M.A./V.R. x 100

or, 50 = M.A./12 x 100

M.A. = 6

Again, M.A. = W/P

6 = 1.5 x 1000/ P

P = 250 N.

9. Following are the specifications of a single purchase crab:

Diameter of load drum, d = 200 mm

Length of lever, l = 1.2 m

No. of teeth on pinion, T 1 = 10

No. of teeth on spur wheel, T 2 = 100

Find the velocity ratio of this machine.

a) 100

b) 110

c) 120

d) 130

Answer: c

Explanation: V.R. = 2l/d x T 2 /T 1

= 2 x 120/20 x 100/10 = 120.

10. On a machine efforts of 100 N and 160 N are required to lift the loads of 3000 N and 9000 N respectively. Find the law of the machine.

a) P = 1/100W + 60

b) P = 1/100W + 70

c) P = 1/100W + 80

d) P = 1/100W + 90

Answer: c

Explanation: Let the law of machine be P = mW + C

where P = effort applied, W = load lifted and m and C being constants.

when P = 100 N W = 3000 N

when P = 160 N W = 9000 N

Putting these values in the law of machine.

100 = 3000m + C …………

160 = 9000m + C …………

Subtracting  and , we get

60 = 6000 m

or, m = 1/100

Putting this value in equation , we get

100 = 3000 x 1/100 + C

C = 70

Hence, the machine follows the laws

P = 1/100W +70.

11. Following are the specifications of a single purchase crab:

Diameter of load drum, d = 200 mm

Length of lever, l = 1.2 m

No. of teeth on pinion, T 1 = 10

No. of teeth on spur wheel, T 2 = 100

On this machine efforts of 100 N and 160 N are required to lift the loads of 3000 N and 9000 N respectively. Find the efficiency at 3000N.

a) 10 %

b) 15 %

c) 20 %

d) 25 %

Answer: d

Explanation: V.R. = 2l/d x T 2 /T 1

= 2 x 120/20 x 100/10 = 120

M.A. = W/P = 3000/100 = 30

Efficiency = M.A./V.R. = 30/120 = 0.25 = 25%.

12. Following are the specifications of a single purchase crab:

Diameter of load drum, d = 200 mm

Length of lever, l = 1.2 m

No. of teeth on pinion, T 1 = 10

No. of teeth on spur wheel, T 2 = 100

On this machine efforts of 100 N and 160 N are required to lift the loads of 3000 N and 9000 N respectively. Find the efficiency at 9000N.

a) 30 %

b) 40 %

c) 46.8 %

d) 56.8 %

Answer: d

Explanation: V.R. = 2l/d x T 2 /T 1

= 2 x 120/20 x 100/10 = 120

M.A. = W/P = 9000/160 = 900/16

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Forces Acting in a Mechanism”.

1. Coriolis component of acceleration is a component of translatory acceleration.

a) True

b) False

Answer: a

Explanation: Its unit is m/s 2 . Therefore translatory acceleration (a t = 2ωV).

2. If the relative motion between two links of a mechanism is pure sliding, then the relative instantaneous center for these two links does not exist.

a) True

b) False

Answer: b

Explanation: It does exists at infinity distance. Kennedy theorem says number of instantaneous center N = n/2

3. A slider sliding at 10 cm/s on a link which is rotating at 60 r.p.m. is subjected to Coriolis acceleration of magnitude

a) 40п 2 cm/s 2

b) 0.4пcm/s 2

c) 40пcm/s 2

d) 4пcm/s 2

Answer: c

Explanation: Coriolis acceleration = 2ωV = 2 x 2пN/60 x V = 2 x 2п x 60/60 x 10 = 40пcm/s 2

4. A body in motion will be subjected to coriolis acceleration when that body is

a) in plane rotation with variable velocity

b) in plane translation with variable velocity

c) in plane motion which is a resultant of plane translation and rotation

d) restrained to rotate while sliding over another body

Answer: d

Explanation: When a point on one link is sliding along another rotating link, such as in quick return motion mechanism, then the coriolis component of the acceleration must be calculated.

5. Mechanism used to produce a diagram to an enlarged or reduced sacle

a) hart’s mechanism

b) pantograph

c) grasshopper mechanism

d) peaucellier’s mechanism

Answer: b

Explanation: Pantograph mechanism is used to produce a diagram to an enlarged or reduced sacle.

Hart’s mechanism is used to produce exact straight line motion mechanism.

6. A straight line mechanism made up of turning pairs

a) hart’s mechanism

b) pantograph

c) grasshopper mechanism

d) none of the mentioned

Answer: a

Explanation: Exact straight line motion mechanisms made up of turning pairs are peaucellier’s mechanism and hart’s mechanism.

7. Approximate straight line motion consisting of one sliding pair

a) hart’s mechanism

b) pantograph

c) grasshopper mechanism

d) peaucellier’s mechanism

Answer: c

Explanation: Hart’s mechanism is used to produce exact straight line motion mechanism.

Grasshopper mechanism gives approximate straight line motion consisting of one sliding pair.

8. Exact straight line motion mechanism

a) hart’s mechanism

b) pantograph

c) grasshopper mechanism

d) none of the mentioned

Answer: a

Explanation: Exact straight line motion mechanisms made up of turning pairs are peaucellier’s mechanism and hart’s mechanism.

9. The sense of Coriolis component 2ωV is the same as that of the relative velocity vector V rotated.

a) 45 0 in the direction of rotation of the link containing the path

b) 45 0 in the direction opposite to the rotation of the link containing the path

c) 90 0 in the direction of rotation of the link containing the path

d) 180 0 in the direction opposite to the rotation of the link containing the path

Answer: c

Explanation: The sense of Coriolis component 2ωV is the same as that of the relative velocity vector V rotated 90 0 in the direction of rotation of the link containing the path.

The direction of coriolis component is along a line rotated 90 0 from the sliding velocity in a direction same as that of the angular velocity of the slotted lever.

Answer: d

Explanation: The sense of Coriolis component 2ωV is the same as that of the relative velocity vector V rotated 90 0 in the direction of rotation of the link containing the path.

The direction of coriolis component is along a line rotated 90 0 from the sliding velocity in a direction same as that of the angular velocity of the slotted lever.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Acceleration in Mechanisms”.

1. The instantaneous centers of a slider moving in a curved surface lies at

a) infinity

b) their point of contact

c) the center of curvature

d) the pin point

Answer: c

Explanation: The instantaneous centers of a slider moving in a linear guide lies at infinity.

The instantaneous centers of a slider moving in a curved surface lies at the center of curvature.

2. The fixed instantaneous center of mechanism

a) varies with the configuration

b) remains at the same place for all configurations

c) all of the mentioned

d) none of the mentioned

Answer: b

Explanation: The fixed instantaneous center of mechanism remains at the same place for all configurations.

The instantaneous centres which vary with the configuration of the mechanism, are called neither fixed nor permanent instantaneous centres.

3. The instantaneous center of rotation of a circular disc rolling on a straight path is

a) at the center of the disc

b) at their point of contact

c) at the center of gravity of the disc

d) at infinity

Answer: b

Explanation: The space centrode of a circular disc rolling on a straight path is a straight line.

4. The locus of instantaneous center of a moving body relative to a fixed body is known as the

a) space centrode

b) body centrode

c) moving centrode

d) none of the mentioned

Answer: a

Explanation: The locus of the instantaneous centre in space during a definite motion of the body is called the space centrode and the locus of the instantaneous centre relative to the body itself is called the body centrode.

5. The space centrode of a circular disc rolling on a straight path is

a) circle

b) parabola

c) a straight line

d) none of the mentioned

Answer: c

Explanation: The instantaneous center of rotation of a circular disc rolling on a straight path is at their point of contact.

6. The component of the acceleration directed towards the center of rotation of a revolving body is known as ____________ component.

a) tangential

b) centripetal

c) coriolis

d) none of the mentioned

Answer: b

Explanation: The centripetal or radial component, which is perpendicular to the velocity of the particle at the given instant.

The tangential component, which is parallel to the velocity of the particle at the given instant.

7. At an instant the link AB of length r has an angular velocity ω and an angular acceleration α. What is the total acceleration of AB?

a) [(ω 2 r) 2 + αr) 2 ] 1/2

b) [ 2 + αr) 2 ] 1/2

c) [(ω 2 r) 2 + αr)] 1/2

d) [(ω 2 r)2 + αr) 2 ] 1/2

Answer: a

Explanation: None.

8. At an instant, if the angular velocity of a link is clockwise then the angular acceleration will be

a) clockwise

b) counterclockwise

c) in any direction

d) none of the mentioned

Answer: c

Explanation: None.

9. Angular acceleration of a link AB is given by

a) centripetal acceleration/length

b) tangential acceleration/length

c) total acceleration/length

d) none of the mentioned

Answer: b

Explanation: None.

Answer: b

Explanation: The coriolis component is always perpendicular to the link and is given by 2ωv.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Acceleration of a Point on a Link”.

1. Match list I with list II

List I List II

A. Law of correct steering 1. f = 3 – 2j

B. Displacement relation of Hook’e joint 2. x = R[ 𝛳 + sin 2 ϴ/2n].

C. Relation between kinematic pairs and links 3. cotɸ – cotɸ = c/b

D. Displacement equation of reciprocating engine piston 4. tanϴ = tanɸ cosα

a) A-1,B-4,C-3,D-2

b) A-1,B-2,C-3,D-4

c) A-3,B-4,C-1,D-2

d) A-3,B-2,C-1,D-4

Answer: c

Explanation: Law of correct steering – cotɸ – cotɸ = c/b

Displacement relation of Hook’e joint – tanϴ = tanɸ cosα

Relation between kinematic pairs and links – f = 3 – 2j

Displacement equation of reciprocating engine piston – x = R[ 𝛳 + sin 2 ϴ/2n].

2. Consider the following statements regarding motions in machines:

1. Tangential acceleration is a function of angular velocity and the radial acceleration is a function of angular acceleration.

2. The resultant acceleration of a point A with respect to a point B on a rotating link is perpendicular to AB.

3. The direction of the relative velocity of a point A with respect to a point B on a rotating link is perpendicular.

Which of these statements is/are correct?

a) 1 alone

b) 2 and 3

c) 1 and 2

d) 3 alone

Answer: d

Explanation: Only statement 1 is correct.

3.The speed of driving shaft of a Hooke’s Joint of angle 19.5 0 is 500 r.p.m. The maximum speed of the driven shaft is nearly

a) 168 r.p.m.

b) 444 r.p.m.

c) 471 r.p.m.

d) 531 r.p.m.

Answer: d

Explanation: N max = N/cosα = 500/cos19.5 0 = 531 r.p.m.

4. In a slider crank mechanism. the maximum acceleration of slider is obtained when the crank is

a) at the inner dead centre position

b) at the outer dead centre position

c) exactly midway position between the two dead centres

d) slightly in advance of the midway position between the two dead centres

Answer: b

Explanation: None.

5. In a shaper machine, the mechanism for tool feed is

a) Geneva mechanism

b) Whitworth mechanism

c) Ratchet and Pawl mechanism

d) Ward Leonard system

Answer: c

Explanation: The crank shaper, in which the tool carrier is driven forward and backward by an oscillating arm operated by a crankpin in the main driving gear, or “bull wheel,” and in which the feed is transmitted to the worktable by ratchet-and-pawl mechanism, is so commonly used as to be termed standard.

6. The instantaneous centre of rotation of a rigid thin disc rolling without slip on a plane rigid surface is located at

a) the centre of the disc

b) an infinite distance perpendicular to the plane surface

c) the point of contact

d) the point on the circumference situated vertically opposite to the contact point

Answer: a

Explanation: The instantaneous centre of rotation of a rigid thin disc without slip is located at the centre of the disc.

7. Match list I with list II

List I List II

A. Sliding pair 1. A road roller rolling over the ground

B. Revolute pair 2. Crank shaft in a journal bearing in an engine

C. Rolling pair 3. Ball and socket joint

D. Spherical pair 4. Piston and cylinder

5. Nut and screw

a) A-5,B-2,C-4,D-3

b) A-4,B-3,C-1,D-2

c) A-5,B-3,C-4,D-2

d) A-4,B-2,C-1,D-3

Answer: d

Explanation: Sliding pair – Piston and cylinder

Revolute pair – Crank shaft in a journal bearing in an engine

Rolling pair – A road roller rolling over the ground

Spherical pair – Ball and socket joint.

8. Slider crank chain is an inversion of the four bar mechanism.

a) True

b) False

Answer: a

Explanation: Slider crank chain often finds applications in most of the reciprocating machinery.

9. f = 3  – 2j. In the Gruebler’s equation for planer mechanisms given, j is the

a) Number of mobile links

b) Number of links

c) Number of lower pairs

d) Length of the longest link

Answer: c

Explanation: None.

Answer: c

Explanation: Except statement 1 all are examples of forced closed kinematic pairs.

This set of Machine Kinematics Objective Questions & Answers focuses on “Acceleration in the Slider Crank Mechanism & Coriolis Component”.

1. A point is moving at the end of the link rotating with constant angular velocity ω, what will be the value of tangential component of acceleration?

a) 0

b) ω 2 R

c) Infinite

d) ω 2 R/2

Answer: a

Explanation: Any point at the end of the link which is moving with a constant angular velocity has no component as tangential acceleration, it only possesses radial component of acceleration.

2. The tangential component of acceleration is maximum when the link rotates with a constant angular velocity.

a) True

b) False

Answer: b

Explanation: The tangential component of acceleration is zero when the link is rotating with a constant angular velocity, hence the given statement is false.

3. A point is moving at the end of the link rotating with constant angular velocity ω, what will be the value of radial component of acceleration?

a) 0

b) ω 2 R

c) Infinite

d) ω 2 R/2

Answer: b

Explanation: Any point at the end of the link which is moving with a constant angular velocity has no component as tangential acceleration, it only possess radial component of acceleration whose value is given by ω 2 R, where R is the distance of the point from the reference point.

4. In a slider crank mechanism, the crank rotates with a constant angular velocity of 300 rpm, Length of crank is 150mm, and the length of the connecting rod is 600mm. Determine linear velocity of the midpoint of the connecting rod in m/s. Crank angle = 45° from IDC.

a) 4.1

b) 4.4

c) 4.8

d) 5.2

Answer: a

Explanation: Let the Intersection point of crank and connecting rod be termed as ‘x’

velocity of x = ωxL

= 4.713 m/s

We draw a corresponding velocity diagram for the same,

where this velocity is perpendicular to the crank, this diagram when drawn to scale turns out to be a triangle.

From the reference point we can measure the velocity of midpoint of connecting rod

V = 4.1 m/s.

5. In a slider crank mechanism, the crank rotates with a constant angular velocity of 300 rpm, Length of crank is 150mm, and the length of the connecting rod is 600mm. Determine acceleration of the midpoint of the connecting rod in m/s 2 . Crank angle = 45° from IDC.

a) 117

b) 144

c) 148

d) 252

Answer: a

Explanation: Let the Intersection point of crank and connecting rod be termed as ‘x’

velocity of x = ωxL

= 4.713 m/s

We draw a corresponding velocity diagram for the same,

where this velocity is perpendicular to the crank, this diagram when drawn to scale turns out to be a triangle.

From the reference point we can measure the velocity of midpoint of connecting rod V = 4.1 m/s

From the acceleration diagram of the same , we find that acceleration of midpoint of the connecting rod comes out to be

117m/s 2 .

6. What will be the shape of the velocity diagram of the slider crank mechanism if there are three links including the slider.

a) Triangle

b) Parallelogram

c) Square

d) Trapezium

Answer: a

Explanation: When there are two links and a slider in a slider crank mechanism, there are in total 3 links. In this case the shape of the velocity polygon is a triangle.

7. If the normal component of the acceleration is doubled, what will be the effect on the radial component?

a) Doubled

b) Halved

c) Remains same

d) Becomes 4 times

Answer: a

Explanation: The component which is normal to the motion is known as the normal component which comes from the angular velocity, this is also known as the radial component. Hence radial and normal components are the same.

8. If the body is not rotating with a constant angular velocity then there are both radial and tangential component of acceleration.

a) True

b) False

Answer: a

Explanation: The radial component always exists as long as the body is rotating with some angular velocity, however the tangential components acts only if the angular velocity is not constant. In this case both the components will act on the given link.

9. In the given figure, the direction of radial velocity vector and angular velocity is given what will be the direction of coriolis force?

machine-kinematics-objective-questions-answers-q9

a) Along the radial velocity vector

b) Opposite to radial velocity vector

c) Perpendicular to radial velocity vector towards right

d) Perpendicular to radial velocity vector towards left

Answer: d

Explanation: The direction of the coriolis component of acceleration is obtained by rotating the radial velocity vector by 90 degrees in the direction of the angular velocity.

10. Coriolis component of acceleration exists when there is relative motion between two points from the ground frame.

a) True

b) False

Answer: a

Explanation: When there is relative motion between two points from the ground frame, Pseudo force exists.

11. Calculate the coriolis component of acceleration in m/s 2 from the following data:

ω = 12 rad/s

v = 2 m/s

R = 1 m

a) 24

b) 12

c) 36

d) 6

Answer: a

Explanation: The coriolis component of acceleration is given by

2ωV

inserting the values we get

a = 24 m/s 2 .

12. Which component of acceleration is parallel to the given link?

a) Radial

b) Tangential

c) Coriolis

d) Pseudo

Answer: a

Explanation: The radial component also known as the normal component is parallel to the link and always exists as long as there is angular velocity.

13. Which of the following mechanism will have coriolis component?

a) Quick return motion mechanisms

b) Slider crank mechanism

c) Four bar chains

d) Gnome engine

Answer: a

Explanation: Quick return motion mechanism have sliders attached to the link, hence out of the given options quick return motion mechanisms will have coriolis component of acceleration.

14. Which component of acceleration is parallel to the velocity of given link?

a) Radial

b) Tangential

c) Coriolis

d) Pseudo

Answer: b

Explanation: The radial component also known as the normal component is parallel to the link and always exists as long as there is angular velocity. However the tangential component acts in a direction parallel to the velocity of the link.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on ” Mechanisms with Lower Pairs”.

1. A pantograph consists of

a) 4 links

b) 6 links

c) 8 links

d) 10 links

Answer: a

Explanation: In a pantograph, all the pairs are turning pairs. It has 4 links.

2. Which of these mechanisms gives an approximately straight line?

a) hart

b) watt

c) peaucellier

d) tchebicheff

Answer: b

Explanation: Watt’s mechanism is a crossed four bar chain mechanism and was used by Watt for his early steam engines to guide the piston rod in a cylinder to have an approximate straight line motion.

3. Which of these mechanism has six links?

a) tchebicheff

b) hart

c) peaucellier

d) watt

Answer: b

Explanation: Hart’s mechanism requires only six links as compared with the eight links required by the Peaucellier mechanism.

4. Which of these mechanisms use two identical mechanisms?

a) hart

b) watt

c) peaucellier

d) none of the mentioned

Answer: d

Explanation: None.

5. The Davis steering gear is not used because

a) it has turning pairs

b) it is costly

c) it has sliding pair

d) it does not fulfil the condition of correct gearing

Answer: b

Explanation: Though the gear is theoretically correct, but due to the presence of more sliding members, the wear will be increased which produces slackness between the sliding surfaces, thus eliminating the original accuracy. Hence Davis steering gear is not in common use.

6. The Davis steering gear fulfils the condition of correct steering at

a) two positions

b) three positions

c) all positions

d) one positions

Answer: c

Explanation: It can be used in all positions.

Ackermann steering gear fulfils the condition of correct steering at only three positions.

7. The Ackermann steering gear fulfils the condition of correct steering at

a) no position

b) one position

c) three positions

d) all positions

Answer: c

Explanation: Ackermann steering gear fulfils the condition of correct steering at only three positions.

8. A Hooke’s joint is used to join two shafts which are

a) aligned

b) intersecting

c) parallel

d) none of the mentioned

Answer: b

Explanation: Hooke’s joint is used to connect two shafts, which are intersecting at a small angle.

9. The maximum velocity of the driven shaft of a Hooke’s joint is

a) ω 1 cosα

b) ω 1 /cosα

c) ω 1 sinα

d) ω 1 /sinα

Answer: b

Explanation: Maximum speed of the driven shaft,

ω 1 = ωcosα/ 1 – sin 2 α = ωcosα/cos 2 α = ω/cosα.

Answer: a

Explanation: Maximum velocity is determined at 0 0 ,180 0 and 360 0 .

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on ” Straight Line Mechanism”.

1. A double universal joint is used to connect two shafts in the same plane. The intermediate shaft is inclined at an angle of 20° to the driving shaft as well as the driven shaft. Find the maximum speed of the intermediate shaft if the driving shaft has a constant speed of 500 r.p.m.

a) 532.1 r.p.m

b) 469.85 r.p.m

c) 566.25 r.p.m

d) 441.5 r.p.m.

Answer: a

Explanation: Given α = 20° ; N A = 500 r.p.m.

Let A, B and C are the driving shaft, intermediate shaft and driven shaft respectively. We know that for the driving shaft  and intermediate shaft ,

Maximum speed of the intermediate shaft,

N B = N A /cosα = 500/cos 20°= 532.1 r.p.m.

2. A double universal joint is used to connect two shafts in the same plane. The intermediate shaft is inclined at an angle of 20° to the driving shaft as well as the driven shaft. Find the minimum speed of the intermediate shaft if the driving shaft has a constant speed of 500 r.p.m.

a) 532.1 r.p.m

b) 469.85 r.p.m.

c) 566.25 r.p.m.

d) 441.5 r.p.m.

Answer: b

Explanation: Given α = 20° ; N A = 500 r.p.m.

Let A, B and C are the driving shaft, intermediate shaft and driven shaft respectively. We know that for the driving shaft  and intermediate shaft ,

minimum speed of the intermediate shaft,

N B = N A cosα = 500 × cos 20° = 469.85 r.p.m.

3. A double universal joint is used to connect two shafts in the same plane. The intermediate shaft is inclined at an angle of 20° to the driving shaft as well as the driven shaft. Find the maximum speed of the driven shaft if the driving shaft has a constant speed of 500 r.p.m.

a) 532.1 r.p.m

b) 469.85 r.p.m.

c) 566.25 r.p.m.

d) 441.5 r.p.m.

Answer: c

Explanation: Given α = 20° ; N A = 500 r.p.m.

Let A, B and C are the driving shaft, intermediate shaft and driven shaft respectively. We know that for the driving shaft  and intermediate shaft ,

Maximum speed of the driven shaft,

N C = N B /cosα = N A /cos 2 α = 566.25 r.p.m.

4. A double universal joint is used to connect two shafts in the same plane. The intermediate shaft is inclined at an angle of 20° to the driving shaft as well as the driven shaft. Find the minimum speed of the driven shaft if the driving shaft has a constant speed of 500 r.p.m.

a) 532.1 r.p.m

b) 469.85 r.p.m.

c) 566.25 r.p.m.

d) 441.5 r.p.m.

Answer: d

Explanation: Given α = 20° ; N A = 500 r.p.m.

Let A, B and C are the driving shaft, intermediate shaft and driven shaft respectively. We know that for the driving shaft  and intermediate shaft ,

minimum speed of the driven shaft,

N C = N B × cos α = N A cos 2 α = 441.5 r.p.m.

5. In a pantograph, all the pairs are

a) turning pairs

b) sliding pairs

c) spherical pairs

d) self-closed pairs

Answer: a

Explanation: In a pantograph, all the pairs are turning pairs. It has 4 links.

6. Which of the following mechanism is made up of turning pairs ?

a) Scott Russel’s mechanism

b) Peaucellier’s mechanism

c) Hart’s mechanism

d) Both  and 

Answer: d

Explanation: None.

7. Which of the following mechanism is used to enlarge or reduce the size of a drawing ?

a) Grasshopper mechanism

b) Watt mechanism

c) Pantograph

d) none of the mentioned

Answer: c

Explanation: A pantograph is an instrument used to reproduce to an enlarged or a reduced scale and as exactly as possible the path described by a given point.

8. The Ackerman steering gear mechanism is preferred to the Davis steering gear mechanism, because

a) whole of the mechanism in the Ackerman steering gear is on the back of the front wheels

b) the Ackerman steering gear consists of turning pairs

c) the Ackerman steering gear is most economical

d) both  and 

Answer: d

Explanation: The Ackerman steering gear mechanism is much simpler than Davis gear. The difference between the Ackerman and Davis steering gears are :

1. The whole mechanism of the Ackerman steering gear is on back of the front wheels; whereas in Davis steering gear, it is in front of the wheels.

2. The Ackerman steering gear consists of turning pairs, whereas Davis steering gear consists of sliding members.

9. The driving and driven shafts connected by a Hooke’s joint will have equal speeds, if

a) cos θ = sin α

b) sinθ = ±√tanα

c) tanθ = ±√cosα

d) cot θ = cos α

Answer: c

Explanation: None.

Answer: a

Explanation: c = 1.2 m ; b = 2.7 m

Let α = Inclination of the track arm to the longitudinal axis.

We know that tan α = c/2b = 1.2/2 x 2.7

or, α = 12.5°.

This set of Machine Kinematics Question Paper focuses on “Exact Straight Line Motion Consisting of One Sliding Pair”.

1. Which of the following is an exact straight line mechanism?

a) Scott Russell’s mechanism

b) Watt’s mechanism

c) Grasshopper mechanism

d) Robert’s mechanism

Answer: a

Explanation: Scott Russell’s mechanism is an exact straight line mechanism, however this mechanism is not so useful for practical purposes as friction and wear of sliding pair is more than that of turning pair.

2. Scott Russell’s mechanism is very important for practical purposes.

a) True

b) False

Answer: b

Explanation: Scott Russell’s mechanism is not so useful for practical purposes as friction and wear of sliding pair is more than that of turning pair.

3. Which of the following mechanisms is an approximate straight line mechanism?

a) Scott Russell’s mechanism

b) Watt’s mechanism

c) Gnome engine

d) Oscillating engine

Answer: b

Explanation: Watt’s mechanism is an approximate straight line mechanism. It is a crossed four bar chain mechanism used in early steam engines.

4. Which of the following mechanism forms an elliptical trammel?

a) Modified Scott Russell’s mechanism

b) Watt’s mechanism

c) Gnome engine

d) Oscillating engine

Answer: a

Explanation: Modified Scott Russell’s mechanism is similar to Scott russell’s mechanism but in this case the path traced by an arbitrary point P on the link is an ellipse.

5. Which of the following mechanisms has the form of trapezium in its mean position?

a) Scott Russell’s mechanism

b) Watt’s mechanism

c) Grasshopper mechanism

d) Robert’s mechanism

Answer: d

Explanation: Robert’s mechanism is a four bar chain mechanism, which, in its mean position, has the form of a trapezium.

6. Which of the following mechanisms was used in early days to give long stroke with a very short crank?

a) Scott Russell’s mechanism

b) Watt’s mechanism

c) Grasshopper mechanism

d) Robert’s mechanism

Answer: c

Explanation: The Grasshopper mechanism was used in early days as an engine mechanism which gave long stroke with a very short crank.

7. In Scott Russell’s mechanism the straight line motion is generated.

a) True

b) False

Answer: b

Explanation: In Scott Russell’s mechanism, straight line motion is not generated but merely copied and this mechanism is not much of practical value due to wear and friction in sliding pair.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Steering Gear Mechanism”.

1. The tilting of the front wheels away from the vertical is called

a) caster

b) camber

c) toe-in

d) toe-out

Answer: b

Explanation: The angle between the vertical line from the centre point of the tyre and the central line of the tyre is known as the camber angle.

2. In the steering gear, a gear sector or toothed roller is meshed with a

a) ball bearing

b) roller bearing

c) worm

d) steering wheel

Answer: c

Explanation: A rotary valve power steering gear for the integral system uses recirculating ball-type worm and wheel steering gear.

3. The only service that a steering linkage normally requires is

a) tie-rod adjustment

b) lubrication

c) ball-joint replacement

d) none of the mentioned

Answer: a

Explanation: In the linkage-type power steering system, the power cylinder is not a part of the steering system. Instead, the power cylinder is fitted into the steering linkage.

4. Caster action on the front wheels of a vehicle will

a) make it easier for the driver to take corners

b) help reduce the load on the king-pins

c) automatically achieve the straight wheel position

d) none of the mentioned

Answer: c

Explanation: Negative caster produces directional stability to the vehicle keeping the wheel position straight.

5. Too much toe-in will be noticed by

a) excessive tyre wear because of taking corners

b) steering wander

c) feathering of tyres

d) light steering

Answer: a

Explanation: The toe-in ensures parallel rolling of the front wheels. It stabalises steering and prevents side slipping and excessive wear of the tyres.

6. Hard steering is a result of

a) very loose steering linkage

b) worn out steering linkage

c) too loose front wheel bearings

d) incorrect lubricant

Answer: d

Explanation: Hard steering is caused because of the following reasons:

a) incorrect lubricant

b) broken or bent steering arms or knuckles

c) too tight spherical ball joints

d) insufficient lubricant

e) low or uneven pressure.

7. Excessive play or looseness in the steering system is caused by

a) worn out front wheel bearings

b) broken or bent steering arms or knuckles

c) too tight spherical ball joints

d) insufficient lubricant

Answer: a

Explanation: Excessive play or looseness in the steering system is the result of

a) very loose steering linkage

b) worn out steering linkage

c) too loose front wheel bearings

d) worn out front wheel bearings

e) loose steering gear flexible coupling

f) worn out steering gear flexible coupling.

8. Erratic steering is caused due to

a) worn out brake lining

b) broken or bent steering arms or knuckles

c) too tight spherical ball joints

d) insufficient lubricant

Answer: a

Explanation: It is caused due to following reasons

a) worn out brake lining

b) brake lining choked with oil

c) brake lining choked with brake fluid.

9. Wheel wobbles occur due to

a) inoperative stabilizer

b) wheel out of balance

c) bent kin-pin

d) bent steering knuckle

Answer: b

Explanation: It is caused due to following reasons

a) wheel out of balance

b) worn joints in assembly

c) loose wheel bearing.

10. Wheel wobbling can be fixed by

a) adjusting and repairing it

b) repairing the stabilizer

c) replacing kin-pin

d) replacing brake lining

Answer: a

Explanation: It can be fixed by the following remedies

a) adjusting and repairing it

b) balancing wheels

c) adjusting bearings.

11. Hard steering can be fixed by

a) replacing the bent or broken parts

b) replacing worn out parts

c) tightening the loose bearings

d) none of the mentioned

Answer: a

Explanation: It can be fixed by the following remedies

a) inflate the tyres to correct pressure

b) replace all tight ball joints

c) replacing the bent or broken parts.

12. Erratic steering can be adjusted by

a) replacing worn out parts

b) replacing the brake lining

c) tightening the loose bearings

d) none of the mentioned

Answer: b

Explanation: It can be fixed by the following remedies

a) replacing the brake lining

b) locating and removing the cause for choke

c) removing the cause for choke due to the brake fluid.

Answer: c

Explanation: It can be fixed by the following remedies

a) replacing worn out parts

b) replacing worn out couplings

c) tightening the loose bearings.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Double Hooke’s Joint”.

1. What is the purpose of double hooke’s joint?

a) Have constant linear velocity ratio of driver and driven shafts

b) Have constant acceleration ratio of driver and driven shafts

c) Have constant angular velocity ratio of driver and driven shafts

d) Have constant angular acceleration ratio of driver and driven shafts

Answer: c

Explanation: The velocity of the driven shaft is not constant, but varies from maximum to minimum values. In order to have a constant velocity ratio of the driving and driven shafts, an intermediate shaft with a Hooke’s joint at each end is used.

2. Double hooke’s joint can be used to keep the angular velocity of the shaft constant.

a) True

b) False

Answer: b

Explanation: Double hooke’s joint is used to keep the velocity ratio of driver shaft and driven shaft, It does not necessarily keeps the velocity constant.

3. Two shafts having an included angle of 150° are connected by a Hooke’s joint. The driving shaft runs at a uniform speed of 1500 r.p.m. The driven shaft carries a flywheel of mass 12 kg and 100 mm radius of gyration. Using the above data, calculate the maximum angular acceleration of the driven shaft in rad/s 2 .

a) 6853

b) 6090

c) 6100

d) 6500

Answer: a

Explanation: α = 180 -150 = 30⁰

cos2θ = 2sin 2 α/1-sin 2 α = 0.66

angular acc = dω/dt

= 6853.0 rad/s 2 .

4. Two shafts having an included angle of 150° are connected by a Hooke’s joint. The driving shaft runs at a uniform speed of 1500 r.p.m. The driven shaft carries a flywheel of mass 12 kg and 100 mm radius of gyration. Using the above data, calculate the maximum torque required in N-m.

a) 822

b) 888

c) 890

d) 867

Answer: a

Explanation: α = 180 -160 = 30⁰

cos2θ = 2sin 2 α/1-sin 2 α = 0.66

angular acc = dω/dt

= 6853 rad/s 2

I = 0.12 Kg-m 2

Therefore max torque = I.ang acc.

= 822 N-m.

5. Two shafts connected by a Hooke’s joint have an angle of 18 degrees between the axes.

Find the angle through which it should be turned to get the velocity ratio maximum.

a) 180

b) 30

c) 45

d) 90

Answer: a

Explanation: Velocity ratio is ω 1 /ω = cosα/(1 – cos 2 θsin 2 α)

now this to be maximum cos 2 θ = 1

therefore θ = 0 or 180 degrees.

6. Two shafts connected by a Hooke’s joint have an angle of 18 degrees between the axes.

Find the angle through which it should be turned to get the velocity ratio equal to 1.

a) 30.6

b) 30.3

c) 44.3

d) 91.2

Answer: c

Explanation: Velocity ratio is ω 1 /ω = cosα/(1 – cos 2 θsin 2 α)

now this to be 1

we get, cosα = 1 – cos 2 θsin 2 α

solving this equation we get

θ = 44.3 or 135.7 degrees.

7. Two shafts with an included angle of 160° are connected by a Hooke’s joint. The driving shaft runs at a uniform speed of 1500 r.p.m. The driven shaft carries a flywheel of mass 12 kg and 100 mm radius of gyration. Find the maximum angular acceleration of the driven shaft.

a) 3090 rad/s 2

b) 4090 rad/s 2

c) 5090 rad/s 2

d) 6090 rad/s 2

Answer: a

Explanation: Given : α = 180° – 160° = 20°; N = 1500 r.p.m.; m = 12 kg ; k = 100 mm = 0.1 m

We know that angular speed of the driving shaft,

ω = 2 π × 1500 / 60 = 157 rad/s

and mass moment of inertia of the driven shaft,

I = m.k 2 = 12 2 = 0.12 kg – m 2

Let dω 1 / dt = Maximum angular acceleration of the driven shaft, and

θ = Angle through which the driving shaft turns.

We know that, for maximum angular acceleration of the driven shaft,

cos 2θ = 2sin 2 α/2 – sin 2 α = 2sin 2 20°/2 – sin 2 20° = 0.124

2θ = 82.9° or θ = 41.45°

and dω 1 / dt = ω 2 cosα sin2θsin 2 α/(1 – cos 2 θsin 2 α) 2

= 3090 rad/s 2 .

8. The angle between the axes of two shafts connected by Hooke’s joint is 18°. Determine the angle turned through by the driving shaft when the velocity ratio is maximum.

a) 90°

b) 180°

c) 270°

d) 360°

Answer: b

Explanation: Given : α = 98°

Let θ = Angle turned through by the driving shaft.

We know that velocity ratio,

ω 1 /ω = cosα/1 – cos 2 θsin 2 α

The velocity ratio will be maximum when cos 2 θ is minimum, i.e. when

cos 2 θ = 1 or when θ = 0° or 180°.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Friction and Double Hooke’s Joint”.

1. The angle of inclination of the plane, at which the body begins to move down the plane, is called

a) angle of friction

b) angle of repose

c) angle of projection

d) none of the mentioned

Answer: a

Explanation: Consider that a body A of weight  is resting on a horizontal plane B. If a horizontal force P is applied to the body, no relative motion will take place until the applied force P is equal to the force of friction F, acting opposite to the direction of motion. The magnitude of this force of friction is F = μ.W = μ.R N , where RN is the normal reaction.

2. In a screw jack, the effort required to lift the load W is given by

a) P = W tan 

b) P = W tan 

c) P = W cos 

d) P = W cos 

Answer: b

Explanation: If one complete turn of a screw thread by imagined to be unwound, from the body of the screw and developed, it will form an inclined plane. P = W tan 

where α = Helix angle, and

φ = Angle of friction.

3. The efficiency of a screw jack is given by

a) tan /tan α

b) tan α / tan 

c) tan / tan α

d) tan α/ tan 

Answer: b

Explanation: Efficiency, η = Ideal effort/ Actual effort

= P 0 / P

= W tanα/ W tan

= tan α / tan .

4. The radius of a friction circle for a shaft of radius r rotating inside a bearing is

a) r sin φ

b) r cos φ

c) r tan φ

d) r cot φ

Answer: a

Explanation: If a circle is drawn with centre O and radius OC = r sin φ, then this circle is called the friction circle of a bearing. The force R exerted by one element of a turning pair on the other element acts along a tangent to the friction circle.

5. The efficiency of a screw jack is maximum, when

a) α = 45º + φ/2

b) α = 45º – φ/2

c) α = 90º + φ

d) α = 90º − φ

Answer: b

Explanation: The efficiency of a screw jack is maximum when sin  is maximum, i.e. when

α = 45º – φ/2.

6. The maximum efficiency of a screw jack is

a) 1 – sinφ/ 1 + sinφ

b) 1 + sinφ/ 1 – sinφ

c) 1 – tanφ/ 1 + tanφ

d) 1 + tanφ/ 1 – tanφ

Answer: a

Explanation: Maximum efficiency, η max = sin º – sinφ/sin º + sinφ

= sin 90º – sin φ/sin 90º + sin φ

= 1 – sinφ/ 1 + sinφ.

7. The frictional torque transmitted in a flat pivot bearing, considering uniform pressure, is

a) 1/2 × μ.W. R

b) 2/3 × μ.W. R

c) 3/4 × μ.W. R

d) μ.W.R

Answer: b

Explanation: Total frictional force = 2/3 × μ.W. R

where μ = Coefficient of friction,

W = Load over the bearing, and

R = Radius of the bearing surface.

8. The frictional torque transmitted in a conical pivot bearing, considering uniform wear, is

a) 1/2 × μ.W. R cosec α

b) 2/3 × μ.W. R cosec α

c) 3/4 × μ.W. R cosec α

d) μ.W.R cosec α

Answer: a

Explanation: Total frictional torqur = 1/2 × μ.W. R cosec α

where R = Radius of the shaft, and

α = Semi-angle of the cone.

9. The frictional torque transmitted by a disc or plate clutch is same as that of

a) flat pivot bearing

b) flat collar bearing

c) conical pivot bearing

d) trapezoidal pivot bearing

Answer: b

Explanation: None.

10. The frictional torque transmitted by a cone clutch is same as that of

a) flat pivot bearing

b) flat collar bearing

c) conical pivot bearing

d) trapezoidal pivot bearing

Answer: d

Explanation: None.

11. In automobiles, Hooke’s joint is used between which of the following?

a) Clutch and gear box

b) Gear box and differential

c) Differential and wheels

d) Flywheel and clutch

Answer: b

Explanation: The main application of the universal or Hooke’s coupling is found in the transmission from the gear box to the differential or back axle of the automobiles. In such a case, we use two Hooke’s coupling, one at each end of the propeller shaft, connecting the gear box at one end and the differential on the other end.

12. Which of the following statements is not correct?

a) Hooke’s joint is used to connect two rotating co-planar, non-intersecting shafts

b) Hooke’s joint is used to connect two rotating co-planar, intersecting shafts

c) Oldham’s coupling is used to connect two parallel rotating shafts

d) Hooke’s joint is used in the steering mechanism for automobiles

Answer: a

Explanation: None.

13. A Hooke’s joint is used to connect two

a) coplanar and non-parallel shafts

b) non-coplanar and non-parallel shafts

c) coplanar and parallel shafts

d) non-coplanar and parallel shafts

Answer: b

Explanation: A Hooke’s joint is used to connect two shafts, which are intersecting at a small angle.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Types of Friction”.

1. _____________ friction is the force of friction experienced by a body when it is at rest.

a) Dynamic

b) Static

c) Sliding

d) Rolling

Answer: b

Explanation: Static friction is the force of friction experienced by a body when it is at rest.

OR Static friction is the value of the limiting friction just before slipping occurs.

2. _____________ friction is the value of the limiting friction just before slipping occurs.

a) Dynamic

b) Static

c) Sliding

d) Rolling

Answer: b

Explanation: Static friction is the force of friction experienced by a body when it is at rest.

OR Static friction is the value of the limiting friction just before slipping occurs.

3. ____________friction is the force of friction experienced by a body when it is in motion.

a) Dynamic

b) Static

c) Sliding

d) Rolling

Answer: a

Explanation: Dynamic friction is the force of friction experienced by a body when it is in motion.

OR Dynamic friction is the value of frictional force after slipping has occurred.

4. _____________ friction is the value of frictional force after slipping has occurred.

a) Dynamic

b) Static

c) Sliding

d) Rolling

Answer: a

Explanation: Dynamic friction is the force of friction experienced by a body when it is in motion.

OR Dynamic friction is the value of frictional force after slipping has occurred.

5. When a body slides over another, the frictional force experienced by the body is known as ____________ friction.

a) sliding

b) rolling

c) static

d) none of the mentioned

Answer: a

Explanation: When a body slides over another, the frictional force experienced by the body is known as sliding friction.

When a body rolls over another, frictional force experienced by the body is known as rolling friction.

6. When a body rolls over another, frictional force experienced by the body is known as _______________ friction.

a) sliding

b) rolling

c) static

d) none of the mentioned

Answer: b

Explanation: When a body slides over another, the frictional force experienced by the body is known as sliding friction.

When a body rolls over another, frictional force experienced by the body is known as rolling friction.

7. Co-efficient of rolling friction is _______________ than co-efficient of sliding friction.

a) greater

b) equal to

c) lesser

d) none of the mentioned

Answer: c

Explanation: For the same pair of surfaces, co-efficient of rolling friction is lesser than co-efficient of sliding friction.

8. Co-efficient of sliding friction for rubber on concrete is

a) 0.030

b) 0.70

c) 0.18

d) 0.004

Answer: b

Explanation: Co-efficient of sliding friction for rubber on concrete is 0.70. When tires made of rubber rolls on concrete, co-efficient of rolling friction becomes 0.030.

9. Co-efficient of sliding friction for steel is

a) 0.030

b) 0.70

c) 0.18

d) 0.004

Answer: c

Explanation: Co-efficient of sliding friction for steel is 0.18. When railway wheels made of steel rolls on rails made of steel, the co-eficient of rolling friction becomes 0.004.

Answer: c

Explanation: Since the value of F in dynamic friction is little lesser than in static friction, the ratio F/N and hence, the co-efficient of dynamic friction will also be a little lesser than static friction.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Friction Between Lubricated Surfaces”.

1. _____________ is the friction, experienced by a body, due to the motion of rotation as in case of foot step bearings.

a) Pivot friction

b) Solid friction

c) Dry friction

d) None of the mentioned

Answer: a

Explanation: Pivot friction is the friction, experienced by a body, due to the motion of rotation as in case of foot step bearings.

2. ______________ is the friction experienced between two dry and unlubricated surfaces in contact.

a) Pivot friction

b) Solid friction

c) Boundary friction

d) None of the mentioned

Answer: b

Explanation: The friction experienced between two dry and unlubricated surfaces in contact is known as dry or solid friction. It is due to the surface roughness.

3. ______________ is the friction, experienced between the rubbing surfaces, when the surfaces have a very thin layer of lubricant.

a) Pivot friction

b) Solid friction

c) Boundary friction

d) None of the mentioned

Answer: c

Explanation: Boundary friction It is the friction, experienced between the rubbing surfaces, when the surfaces have a very thin layer of lubricant. The thickness of this very thin layer is of the molecular dimension.

4. _____________ is the friction, experienced between the rubbing surfaces, when the surfaces have a thick layer of the lubricant.

a) Fluid friction

b) Solid friction

c) Boundary friction

d) None of the mentioned

Answer: a

Explanation: Fluid friction is the friction, experienced between the rubbing surfaces, when the surfaces have a thick layer of the lubricant. In this case, the actual surfaces do not come in contact and thus do not rub against each other.

5. _____________ is a measure of the resistance offered to the sliding one layer of the lubricant over an adjacent layer.

a) Viscocity

b) Density

c) Oiliness

d) None of the mentioned

Answer: a

Explanation: The viscosity is a measure of the resistance offered to the sliding one layer of the lubricant over an adjacent layer.

6. The absolute viscosity of a lubricant may be defined as the force required to cause a plate of unit area to slide with unit velocity relative to a parallel plate.

a) True

b) False

Answer: a

Explanation: The absolute viscosity of a lubricant may be defined as the force required to cause a plate of unit area to slide with unit velocity relative to a parallel plate, when the two plates are separated by a layer of lubricant of unit thickness.

7. The lubricant which gives ______________ force of friction is said to have greater oiliness.

a) greater

b) lesser

c) similar

d) none of the mentioned

Answer: b

Explanation: The lubricant which gives lower force of friction is said to have greater oiliness.

Answer: a

Explanation: When these lubricants are smeared on two different surfaces, it is found that the force of friction with one lubricant is different than that of the other. This difference is due to the property of the lubricant known as oiliness.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Limiting Friction”.

1. What is the direction in which the limiting friction acts?

a) Opposite to the direction in which the body tends to move

b) Opposite to the direction in which the body moves

c) In the direction in which the body tends to move

d) In the direction in which the body moves

Answer: a

Explanation: Limiting friction acts in the opposite direction in which the body tends to move. It has a maximum value beyond which it cannot increase.

2. The force of friction is independent of the roughness of the surface.

a) True

b) False

Answer: b

Explanation: The force of friction is dependent on the roughness of the surface. There is a coefficient of friction on which the frictional force depends.

3. If the area of contact between the two surfaces is increased by two times, what will be the effect of it on the force of friction?

a) Increases by two times

b) Decreases by two times

c) Remains same

d) Depends on the surface

Answer: c

Explanation: If the area of contact between the two surfaces is increased by two times then there will be no effect on the force of friction as it is independent of the area of contact surface.

4. The ratio of frictional force to normal reaction is known as _______

a) Coefficient of friction

b) Coefficient of restitution

c) Coefficient of inertia

d) Coefficient of force

Answer: a

Explanation: The ratio of frictional force to the normal reaction at the surface of contact bears a constant ratio, this ratio is known as the coefficient of friction.

5. Which of the following is true regarding the limiting friction?

a) Its value is equal to the force applied in the opposite direction which tends to move the body

b) Its value is equal to the force applied in the opposite direction which moves the body

c) Its value is equal to μ.N

d) It is equal to the normal reaction

Answer: a

Explanation: For the limiting friction, the maximum value it can attain is μ.N, until then it has the same value as the force applied in the opposite direction which tends to move the body.

6. The angle at which the body just begins to slide down an incline is known as ________

a) Angle of inclination

b) Angle of motion

c) Angle of repose

d) Angle of stability

Answer: c

Explanation: When a body is kept on an incline, upto a certain angle it remains at rest but at a specific angle the body begins to slide down if the angle is increased further, this angle is known as the angle of repose.

7. For a body on an inclined plane, the value of coefficient of friction is equal to _____ 

a) Tanθ

b) Cotθ

c) Sinθ

d) Cosθ

Answer: a

Explanation: For a body on an inclined plane, the coefficient of friction can also be expressed in the form of the inclination as μ = Tanθ.

8. Static frictional force is equal to the coefficient of friction if the normal reaction is unity.

a) True

b) False

Answer: b

Explanation: The above statement talks about static frictional force, this force is always equal to the force which is applied on the body and tends to move away.

9. What is the maximum value of static friction?

a) Limiting friction

b) 0

c) Rolling friction

d) Kinetic friction

Answer: a

Explanation: When the applied force is less than the limiting friction, the body remains at rest, and the friction into play is called static friction which may have any value between zero and limiting friction.

10. A body of mass 1 kg is kept on a rough surface having coefficient of friction = 0.25 being pulled by a force of 2N, what will be the value of friction force in N?

a) 2

b) 2.5

c) 0

d) 4

Answer: a

Explanation: Since the applied force of 2N has a value less than the limiting friction 0.25×9.81

The acting friction will be static having a value of 2N.

11. A body of mass 1 kg is kept on a rough surface having coefficient of friction = 0.25 being pulled by a force of 2N, which frictional force will be acting on the body?

a) Limiting friction

b) Static friction

c) Kinetic friction

d) Rolling friction

Answer: b

Explanation: Since the applied force of 2N has a value less than the limiting friction 0.25×9.81

The acting friction will be static friction and the body will stay at rest.

12. A body of mass 1 kg is kept on a rough surface having coefficient of friction = 0.25 being pulled by a force of 2N, after how long will the body come to rest again?

a) 2s

b) 2.5s

c) 0s

d) 4s

Answer: c

Explanation: Since the applied force of 2N has a value less than the limiting friction 0.25×9.81

The acting friction will be static friction and the body will stay at rest and will not undergo any motion until the applied force exceeds the value of limiting friction.

13. A body, resting on a rough horizontal plane required a pull of 181 N inclined at 30° to the plane just to move it. It was recorded that a push of 220 N inclined at 30° to the plane just moved the body. Estimate the weight of the body in N.

a) 2000N

b) 2500N

c) 1000N

d) 4000N

Answer: c

Explanation: For vertical equilibrium we have reaction R = W – 181sin30

horizontally,

f = 181cos30

Now considering a push of 220N

horizontally

f =220cos30

vertically

R = W + 220sin30

solving the equations we get

W = 1000N.

14. A body, resting on a rough horizontal plane required a pull of 181 N inclined at 30° to the plane just to move it. It was recorded that a push of 220 N inclined at 30°° to the plane just moved the body. Estimate the coefficient of friction.

a) 0.17

b) 0.2

c) 0.5

d) 0.75

Answer: a

Explanation: For vertical equilibrium we have reaction R = W – 181sin30

horizontally,

f = 181cos30

Now considering a push of 220N

horizontally

f = 220cos30

vertically

R = W + 220sin30

solving the equations we get

μ = 0.171.

15. A body of mass 1 kg is kept on a rough surface is being pulled by a force of 2N, what will be the value of coefficient of friction if it just begins to move. Take g = 10m/s 2 .

a) 0.2

b) 0.25

c) 0

d) 0.4

Answer: a

Explanation: The acting friction will be limiting having a value of 2N.

Since the body just begins to move, we have

f = μN = 2N

therefore

μx10 = 2N

μ = 0.2.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Laws of Solid Friction and Limiting Friction”.

1. The force of friction always acts in a direction, ___________ to that in which the body tends to move.

a) same

b) opposite

c) both of the mentioned

d) none of the mentioned

Answer: b

Explanation: The force of friction always acts in a direction, opposite to that in which the body tends to move.

2. The magnitude of the force of friction is ____________ to the force, which tends the body to move.

a) equal

b) different

c) both of the mentioned

d) none of the mentioned

Answer: a

Explanation: The magnitude of the force of friction is exactly equal to the force, which tends the body to move.

3. The magnitude of the limiting friction  bears a constant ratio to the normal reaction (R N ) between the two surfaces.

a) True

b) False

Answer: a

Explanation: The magnitude of the limiting friction  bears a constant ratio to the normal reaction (RR N ) between the two surfaces. Mathematically

F/RR N = constant.

4. The force of friction is _____________ of the area of contact, between the two surfaces.

a) dependent

b) independent

c) both of the mentioned

d) none of the mentioned

Answer: b

Explanation: The force of friction is independent of the area of contact, between the two surfaces.

5. The force of friction does not depends upon the roughness of the surfaces.

a) True

b) False

Answer: b

Explanation: The force of friction depends upon the roughness of the surfaces.

6. The ratio of magnitude of the kinetic friction to the normal reaction between the two surfaces is_____________ than that in case of limiting friction.

a) greater

b) less

c) equal

d) none of the mentioned

Answer: b

Explanation: The magnitude of the kinetic friction bears a constant ratio to the normal reaction between the two surfaces. But this ratio is slightly less than that in case of limiting friction.

7. For moderate speeds, the force of friction

a) increases

b) decreases

c) remains constant

d) none of the mentioned

Answer: c

Explanation: For moderate speeds, the force of friction remains constant. But it decreases slightly with the increase of speed.

8. A body of mass 400 g slides on a rough horizontal surface. If the frictional force is 3.0 N, find the angle made by the contact force on the body with the vertical.

a) 35 0

b) 36 0

c) 37 0

d) 38 0

Answer: c

Explanation: Let the contact force on the block by the surface be F which makes an angle ϴ with the vertical.

The component of F perpendicular to the contact surface is the normal force N and the component of F parallel to the surface is the friction f As the surface is horizontal, N is vertically upward. For vertical equilibrium,

N = mg =  (10 m/s 2 ) = 4.0 N.

The frictional force is f = 3.0 N.

tan ϴ = f/N = 3/4

or, ϴ = tan -1  = 37 0 .

9. A body of mass 400 g slides on a rough horizontal surface. If the frictional force is 3.0 N, find the magnitude of the contact force.

a) 5 N

b) 10 N

c) 15 N

d) 20 N

Answer: a

Explanation: Let the contact force on the block by the surface be F which makes an angle ϴ with the vertical.

The component of F perpendicular to the contact surface is the normal force N and the component of F parallel to the surface is the friction f As the surface is horizontal, N is vertically upward. For vertical equilibrium,

N = mg =  (10 m/s 2 ) = 4.0 N.

The frictional force is f = 3.0 N.

F = √N 2

= √4 2 + 3 2 = 5 N.

10. A heavy box of mass 20 kg is pulled on a horizontal surface by applying a horizontal force. If the coefficient of kinetic friction between the box and the horizontal surface is 0.25, find the force of friction exerted by the horizontal surface on the box.

a) 29 N

b) 39 N

c) 49 N

d) 59 N

Answer: c

Explanation: As the box slides on the horizontal surface, the surface exerts kinetic friction on the box. The magnitude of the kinetic friction is

f = μN

= μmg

= 0.25 x  x (9.8 m/s 2 ) = 49 N.

This force acts in the direction opposite to the pull.

11. A boy  sitting on his horse whips it. The horse speeds up at an average acceleration of 2.0 m/s 2.If the boy does not slide back, what is the force of friction exerted by the horse on the boy ?

a) 20 N

b) 30 N

c) 40 N

d) 60 N

Answer: d

Explanation: The forces acting on the boy are

 the weight Mg.

 the normal contact force N and

 the static friction f s

As the boy does not slide back, its acceleration a is equal to the acceleration of the horse. As friction is the only horizontal force, it must act along the acceleration and its magnitude is given by Newton’s second law

f s = Ma =  (2.0 m/s 2 ) = 60 N.

12. A boy  sitting on his horse whips it. The horse speeds up at an average acceleration of 2.0 m/s 2.If the boy slides back during the acceleration, what can be said about the coefficient of static friction between the horse and the boy.

a) 0.10

b) 0.20

c) 0.30

d) 0.40

Answer: b

Explanation: If the boy slides back, the horse could not exert a

friction of 60 N on the boy. The maximum force of static

friction that the horse may exert on the boy is

f s = μ s = μ s Mg

μ s  (10m/s 2 ) = μ s 300 N

where μ s is the coefficient of static friction. Thus,

μ s  <60 N

or, μ s <60/300 = 0.20.

13. A wooden block is kept on a polished wooden plank and the inclination of the plank is gradually increased. It is found that the block starts slipping when the plank makes an angle of 18° with the horizontal. However, once started the block can continue with uniform speed if the inclination is reduced to 15°. Find the coefficient of static friction between the block and the plank.

a) tan 18 0

b) tan 15 0

c) tan 33 0

d) tan 3 0

Answer: a

Explanation: The coefficient of static friction is

μ s = tan 18 0 .

Answer: b

Explanation: The coefficient of kinetic friction is

μ k = tan 15 0 .

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Laws of Fluid Friction”.

1. A multiple disc clutch has five plates having four pairs of active friction surfaces. If the intensity of pressure is not to exceed 0.127 N/mm 2 , find the power transmitted at 500 r.p.m. The outer and inner radii of friction surfaces are 125 mm and 75 mm respectively. Assume uniform wear and take coefficient of friction = 0.3.

a) 17.8 kW

b) 18.8 kW

c) 19.8 kW

d) 20.8 kW

Answer: b

Explanation: n 1 + n 2 = 5 ; n = 4 ; p = 0.127 N/mm 2 ; N = 500 r.p.m. or ω = 2π × 500/60 = 52.4 rad/s ; r 1 = 125 mm ; r 2 = 75 mm ; μ = 0.3

Since the intensity of pressure is maximum at the inner radius r 2 , therefore

p.r 2 = C or C = 0.127 × 75 = 9.525 N/mm

We know that axial force required to engage the clutch,

W = 2 π C (r 1 – r 2 ) = 2 π × 9.525  = 2990 N

and mean radius of the friction surfaces,

R = r 1 + r 2 /2 = 125 + 75/2 = 100 mm = 0.1 m

We know that torque transmitted,

T = n.μ.W.R = 4 × 0.3 × 2990 × 0.1 = 358.8 N-m

∴ Power transmitted,

P = T.ω = 358.8 × 52.4 = 18 800 W = 18.8 kW.

2. A single plate clutch, with both sides effective, has outer and inner diameters 300 mm and 200 mm respectively. The maximum intensity of pressure at any point in the contact surface is not to exceed 0.1 N/mm 2 . If the coefficient of friction is 0.3, determine the power transmitted by a clutch at a speed 2500 r.p.m.

a) 61.693 kW

b) 71.693 kW

c) 81.693 kW

d) 91.693 kW

Answer: a

Explanation: Given : d 1 = 300 mm or r 1 = 150 mm ; d 2 = 200 mm or r 2 = 100 mm ; p = 0.1 N/mm 2 ; μ = 0.3 ; N = 2500 r.p.m. or ω = 2π × 2500/60 = 261.8 rad/s

Since the intensity of pressure  is maximum at the inner radius (r 2 ), therefore for uniform wear,

p.r 2 = C or C = 0.1 × 100 = 10 N/mm

We know that the axial thrust,

W = 2 π C (r 1 – r 2 ) = 2 π × 10  = 3142 N

and mean radius of the friction surfaces for uniform wear,

R = r 1 + r 2 /2 = 150 + 100/2 = 125 mm = 0.125m

We know that torque transmitted,

T = n.μ.W.R = 2 × 0.3 × 3142 × 0.125 = 235.65 N-m …

∴ Power transmitted by a clutch,

P = T.ω = 235.65 × 261.8 = 61 693 W = 61.693 kW.

3. A 60 mm diameter shaft running in a bearing carries a load of 2000 N. If the coefficient of friction between the shaft and bearing is 0.03, find the power transmitted when it runs at 1440 r.p.m.

a) 171.4 W

b) 271.4 W

c) 371.4 W

d) 471.4 W

Answer: b

Explanation: Given : d = 60 mm or r = 30 mm = 0.03 m ; W = 2000 N ; μ = 0.03 ; N = 1440 r.p.m.

or ω = 2π × 1440/60 = 150.8 rad/s

We know that torque transmitted,

T = μ.W.r = 0.03 × 2000 × 0.03 = 1.8 N-m

∴ Power transmitted, P = T.ω = 1.8 × 150.8 = 271.4 W.

4. The force of friction is inversely proportional to the normal load between the surfaces.

a) True

b) False

Answer: b

Explanation: The force of friction is directly proportional to the normal load between the surfaces.

5. The force of friction is dependent of the area of the contact surface for a given normal load.

a) True

b) False

Answer: b

Explanation: The force of friction is independent of the area of the contact surface for a given normal load.

6. The force of friction depends upon the material of which the contact surfaces are made.

a) True

b) False

Answer: a

Explanation: Following are the laws of solid friction :

1. The force of friction is directly proportional to the normal load between the surfaces.

2. The force of friction is independent of the area of the contact surface for a given normal load.

3. The force of friction depends upon the material of which the contact surfaces are made.

4. The force of friction is independent of the velocity of sliding of one body relative to the other body.

7. The force of friction is dependent of the velocity of sliding of one body relative to the other body.

a) True

b) False

Answer: b

Explanation: The force of friction is independent of the velocity of sliding of one body relative to the other body.

8. The force of friction is almost dependent of the load.

a) True

b) False

Answer: b

Explanation: The force of friction is almost independent of the load.

9. The force of friction is dependent of the substances of the bearing surfaces.

a) True

b) False

Answer: b

Explanation: The force of friction is independent of the substances of the bearing surfaces.

Answer: a

Explanation: The force of friction is different for different lubricants.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Coefficient of Friction”.

1. A block whose mass is 650 gm is fastened to aspring constant K equals 65 N/m whose other end is fixed. The block is pulled a distance x = 11 cm from its equilibrium position at x = 0 on a smooth surface, and released from rest at t = 0. The maximum speed ‘S’ of the oscillating block is

a) 11 cm /sec

b) 11 m/sec

c) 11 mm/sec

d) 1.1 m/sec

Answer: d

Explanation: Maximum speed of the spring will be at x = 0, when total spring energy will be converted into kinematic energy of mass.

1/2 kx 2 = 1/2 mv 2

1/2 x 65 x 2 = 1/2 x V 2

V = 1.1 m/sec.

2. Which of the following statements regarding laws governing the friction between dry surfaces are correct?

a) The friction force is directly proportional to the normal force.

b) The friction force is dependent on the materials of the contact surfaces.

c) The friction force is independent of the area of contact.

d) all of the mentioned

Answer: d

Explanation: Following are the laws of solid friction :

1. The force of friction is directly proportional to the normal load between the surfaces.

2. The force of friction is independent of the area of the contact surface for a given normal load.

3. The force of friction depends upon the material of which the contact surfaces are made.

4. The force of friction is independent of the velocity of sliding of one body relative to the other body.

3. If two bodies one light and other heavy have equal kinetic energies, which one has a greater momentum

a) heavy body

b) light body

c) both have equal momentum

d) it depends on the actual velocities

Answer: a

Explanation: 1/2m 1 V 1 2 = 1/2m 2 V 2 2

v 2 /V 1 = √m 1 /m 2

For momentum ratio, M 1 /M 2 = √m 1 /m 2 .

4. A heavy block of mass m is slowly placed on a conveyer belt moving with speed v. If coefficient of friction between block and the belt is μ, the block will slide on the belt through distance

a) v/μg

b) v 2 /√μg

c)  2

d) v 2 /2μg

Answer: d

Explanation: Retardation due to friction force = μg

V 2 = 2.μg s

s = v 2 /2μg.

5. A car moving with uniform acceleration cover 450 m in a 5 second interval, and covers 700 m in the next 5 second interval. The acceleration of the car is

a) 7 m/s 2

b) 50 m/s 2

c) 25 m/s 2

d) 10 m/s 2

Answer: d

Explanation: s = ut + 1/2at 2

at t = 5 sec, s = 450

450 = u + 1/2a

at t = 10 sec, s = 450 + 700 = 1150

1150 = u = 1/2a

a = 10 m/sec 2 .

6. A particle starts with a velocity 2 m/sec and moves on a straight-line track with retardation 0.1 m/s 2 . The time at which the particle is 15 m from the startin g point would be

a) 10 s

b) 20 s

c) 50 s

d) 40 s

Answer: a

Explanation: u = 2m/sec a = 0.1 m/sec

s = ut – 1/2at 2

15 = 2t – 1/2t 2

t = 30, t = 10.

7. Two particles with masses in the ratio 1 : 4 are moving with equal kinetic energies. The magnitude of their linear momentums will conform to the ratio

a) 1 : 8

b) 1 : 2

c) √2 : 1

d) √2

Answer: b

Explanation: 1/2m 1 V 1 2 = 1/2m 2 V 2 2

m 1 /m 2 = (V 2 /V 1 ) 2 = 1/4

V 2 /V 1 = 1/2

L 1 /L 2 = m 1 V 1 /m 2 V 2 = 1/2.

8. A stone is projected horizontally from a cliff at 10 m/sec and lands on the ground below at 20 m from the base of the cliff. Find the height of the cliff.

a) 18 m

b) 20 m

c) 22 m

d) 24 m

Answer: b

Explanation: h = 1/2at 2

h = 1/2 x 10 x 4 = 20m.

9. A car moving with speed u can be stopped in minimum distance x when brakes are applied. If the speed becomes n times, the minimum distance over which the car can be stopped would take the value

a) x/n

b) nx

c) x/n 2

d) n 2 x

Answer: d

Explanation: x = u 2 /2g

x’ =  2 /2g

x’ = n 2 x.

Answer: d

Explanation: v 1 /v 2 = √g 1 /g 2 √R 2 /R 1

v 1 /v 2 = √s/√k = √s/k.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Limiting Angle of Friction”.

1. When the rubbing surfaces are separated from each other by a very thin film of lubricant it is known as

a) kinetic friction

b) dry friction

c) boundary lubrication

d) none of the mentioned

Answer: c

Explanation: When the rubbing surfaces are separated from each other by a very thin film of lubricant it is known as boundary lubrication.

When the two solid surfaces sliding over each other are free from contaminating fluid or film, the resistance encountered is called dry friction.

2. Sliver sulphate, tungsten disulphide, graphite, molybdenum disulphide, lead oxide are examples of

a) boundary lubrication

b) viscous lubrication

c) solid lubrication

d) none of the mentioned

Answer: c

Explanation: Sliver sulphate, tungsten disulphide, graphite, molybdenum disulphide, lead oxide are examples of solid lubrication.

Step bearing is used to resist the end thrust of the shafts.

3. __________ is used to resist the end thrust of the shafts.

a) friction circle

b) step bearings

c) injector

d) none of the mentioned

Answer: b

Explanation: Step bearing is used to resist the end thrust of the shafts.

4. When the two solid surfaces sliding over each other are free from contaminating fluid or film, the resistance encountered is called

a) kinetic friction

b) dry friction

c) boundary lubrication

d) none of the mentioned

Answer: b

Explanation: When the two solid surfaces sliding over each other are free from contaminating fluid or film, the resistance encountered is called dry friction.

When the rubbing surfaces are separated from each other by a very thin film of lubricant it is known as boundary lubrication.

5. For design of ordinary machinery, value of journal friction can be taken as

a) 0.008 to 0.02

b) 0.07 to 0.15

c) 0.05 to 0.80

d) none of the mentioned

Answer: a

Explanation: For very low velocities of rotation, high loads, and with good lubrication can be taken as 0.07 to 0.15.

For design of ordinary machinery, value of journal friction can be taken as 0.008 to 0.02.

6. For very low velocities of rotation, high loads, and with good lubrication can be taken as

a) 0.008 to 0.02

b) 0.07 to 0.15

c) 0.05 to 0.80

d) none of the mentioned

Answer: b

Explanation: For very low velocities of rotation, high loads, and with good lubrication can be taken as 0.07 to 0.15.

For design of ordinary machinery, value of journal friction can be taken as 0.008 to 0.02.

7. When the lubrication is arranged so that rubbing surfaces are separated by a fluid film, and the load on the surfaces is carried entirely by the hydrostatic or hydrodynamic pressure in the film, it is known as

a) boundary lubrication

b) viscous lubrication

c) solid lubrication

d) none of the mentioned

Answer: b

Explanation: When the lubrication is arranged so that rubbing surfaces are separated by a fluid film, and the load on the surfaces is carried entirely by the hydrostatic or hydrodynamic pressure in the film, it is known as viscous lubrication.

When the rubbing surfaces are separated from each other by a very thin film of lubricant it is known as boundary lubrication.

8. When the load on the rubbing surfaces is carried partly by a fluid viscous film and partly by areas of boundary lubrication, it is known as

a) incomplete lubrication

b) viscous lubrication

c) solid lubrication

d) none of the mentioned

Answer: a

Explanation: When the lubrication is arranged so that rubbing surfaces are separated by a fluid film, and the load on the surfaces is carried entirely by the hydrostatic or hydrodynamic pressure in the film, it is known as viscous lubrication.

When the rubbing surfaces are separated from each other by a very thin film of lubricant it is known as boundary lubrication.

When the load on the rubbing surfaces is carried partly by a fluid viscous film and partly by areas of boundary lubrication, it is known as incomplete lubrication.

9. When effect of friction is negligible, the force is transmitted by the link from driver to the driven link through the centre line of the pins connecting the link. With friction, the line of action shifts and is tangent to _____________

a) kinetic friction

b) dry friction

c) friction circle

d) none of the mentioned

Answer: c

Explanation: When effect of friction is negligible, the force is transmitted by the link from driver to the driven link through the centre line of the pins connecting the link. With friction, the line of action shifts and is tangent to friction circle.

When the load on the rubbing surfaces is carried partly by a fluid viscous film and partly by areas of boundary lubrication, it is known as incomplete lubrication.

Answer: a

Explanation: If one surface slides over the other, being pressed together by a normal force N, a frictional force F resisting the motion must be overcome. The ratio F/N is called kinetic friction.

When the two solid surfaces sliding over each other are free from contaminating fluid or flim, the resistance encountered is called dry friction.

This set of Basic Machine Kinematics Questions and Answers focuses on “Friction of a Body Lying on a Rough Inclined Plane”.

1. If the threads are cut on the outer surface of a solid rod, these are known as

a) internal threads

b) external threads

c) helix

d) none of the mentioned

Answer: b

Explanation: The fastenings have screw threads, which are made by cutting a continuous helical groove on a cylindrical surface. If the threads are cut on the outer surface of a solid rod, these are known as external threads. But if the threads are cut on the internal surface of a hollow rod, these are known as internal threads.

2. If the threads are cut on the internal surface of a hollow rod, these are known as

a) internal threads

b) external threads

c) helix

d) none of the mentioned

Answer: a

Explanation: The fastenings have screw threads, which are made by cutting a continuous helical groove on a cylindrical surface. If the threads are cut on the outer surface of a solid rod, these are known as external threads. But if the threads are cut on the internal surface of a hollow rod, these are known as internal threads.

3. The curve traced by a particle, while describing a circular path at a uniform speed and advancing in the axial direction at a uniform rate is known as

a) internal threads

b) external threads

c) helix

d) none of the mentioned

Answer: c

Explanation: Helix is the curve traced by a particle, while describing a circular path at a uniform speed and advancing in the axial direction at a uniform rate. In other words, it is the curve traced by a particle while moving along a screw thread.

4. The distance from a point of a screw to a corresponding point on the next thread, measured parallel to the axis of the screw is the

a) helix

b) pitch

c) lead

d) none of the mentioned

Answer: b

Explanation: Pitch is the distance from a point of a screw to a corresponding point on the next thread, measured parallel to the axis of the screw.

Lead is the distance, a screw thread advances axially in one turn.

5. The distance, a screw thread advances axially in one turn is known as the

a) helix

b) pitch

c) lead

d) none of the mentioned

Answer: c

Explanation: Lead is the distance, a screw thread advances axially in one turn.

6. The distance between the top and bottom surfaces of a thread is known as

a) depth of thread

b) pitch

c) lead

d) none of the mentioned

Answer: a

Explanation: Depth of thread is the distance between the top and bottom surfaces of a thread .

7. The lead of a screw is equal to its pitch, it is known as

a) depth of thread

b) single threaded screw

c) lead

d) none of the mentioned

Answer: b

Explanation: If the lead of a screw is equal to its pitch, it is known as single threaded screw.

8. If more than one thread is cut in one lead distance of a screw, it is known as

a) depth of thread

b) single threaded screw

c) multi threaded screw

d) none of the mentioned

Answer: c

Explanation: If more than one thread is cut in one lead distance of a screw, it is known as multi-threaded screw e.g. in a double threaded screw, two threads are cut in one lead length. In such cases, all the threads run independently along the length of the rod.

9. The nominal diameter of a screw thread is also known as

a) root diameter

b) minor diameter

c) outside diameter

d) none of the mentioned

Answer: c

Explanation: The core diameter of a screw thread is also known as inner diameter or root diameter or minor diameter.

The nominal diameter of a screw thread is also known as outside diameter or major diameter.

Answer: b

Explanation: The core diameter of a screw thread is also known as inner diameter or root diameter or minor diameter.

The nominal diameter of a screw thread is also known as outside diameter or major diameter.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Efficiency of Self Locking Screws”.

1. Which of the following screw thread is adopted for power transmission in either direction?

a) Acme threads

b) Square threads

c) Buttress threads

d) Multiple threads

Answer: b

Explanation: A square thread, is adapted for the transmission of power in either direction. This thread results in maximum efficiency and minimum radial or bursting pressure on the nut.

2. Multiple threads are used to secure

a) low efficiency

b) high efficiency

c) high load lifting capacity

d) high mechanical advantage

Answer: b

Explanation: The power screws with multiple threads such as double, triple etc. are employed when it is desired to secure a large lead with fine threads or high efficiency. Such type of threads are usually found in high speed actuators.

3. Screws used for power transmission should have

a) low efficiency

b) high efficiency

c) very fine threads

d) strong teeth

Answer: b

Explanation: None.

4. If α denotes the lead angle and φ, the angle of friction, then the efficiency of the screw is written as

a) tan/tanα

b) tanα/tan 

c) tan/tanα

d) tanα/tan 

Answer: d

Explanation: Efficiency, η = Ideal effort/Actual effort = tanα/tan .

5. A screw jack has square threads and the lead angle of the thread is α. The screw jack will be self locking when the coefficient of friction  is

a) μ > tan α

b) μ = sin α

c) μ = cot α

d) μ = cosec α

Answer: a

Explanation: A screw will be self locking if the friction angle is greater than helix angle or coefficient of friction is greater than tangent of helix angle i.e. μ or tan φ > tan α.

6. To ensure self locking in a screw jack, it is essential that the helix angle is

a) larger than friction angle

b) smaller than friction angle

c) equal to friction angle

d) such as to give maximum efficiency in lifting

Answer: b

Explanation: A screw will be self locking if the friction angle is greater than helix angle or coefficient of friction is greater than tangent of helix angle i.e. μ or tan φ > tan α.

7. A screw is said to be self locking screw, if its efficiency is

a) less than 50%

b) more than 50%

c) equal to 50%

d) none of the mentioned

Answer: a

Explanation: Efficiency of self locking screws is less than 1/2 or 50%. If the efficiency is more than 50%, then the screw is said to be overhauling.

8. A screw is said to be over hauling screw, if its efficiency is

a) less than 50%

b) more than 50%

c) equal to 50%

d) none of the mentioned

Answer: b

Explanation: Efficiency of self locking screws is less than 1/2 or 50%. If the efficiency is more than 50%, then the screw is said to be overhauling.

9. While designing a screw in a screw jack against buckling failure, the end conditions for the screw are taken as

a) both ends fixed

b) both ends hinged

c) one end fixed and other end hinged

d) one end fixed and other end free.

Answer: d

Explanation: For buckling failure, The screw is considered to be a strut with lower end fixed and load end free. For one end fixed and the other end free, C = 0.25.

Answer: d

Explanation: For the prevention of the rotation of load being lift, the load cup of a screw jack is made separate from the head of the spindle.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Friction of a V-thread”.

1. Which of the following screw thread is used for jacks, vices and clamps?

a) square thread

b) trapezoidal threads

c) buttress threads

d) acme threads

Answer: a

Explanation: The square threads are employed in screw jacks, presses and clamping devices.

2. Which of the following screw thread is used for transmitting force in one direction?

a) square thread

b) trapezoidal threads

c) buttress threads

d) v threads

Answer: c

Explanation: A buttress thread, is used when large forces act along the screw axis in one direction only. This thread combines the higher efficiency of square thread and the ease of cutting and the adaptability to a split nut of acme thread.

3. Which of the following screw thread is adaptable to split type nut?

a) square thread

b) trapezoidal threads

c) buttress threads

d) v threads

Answer: b

Explanation: An acme or trapezoidal thread, is a modification of square thread. The slight slope given to its sides lowers the efficiency slightly than square thread and it also introduce some bursting pressure on the nut, but increases its area in shear. It is used where a split nut is required and where provision is made to take up wear as in the lead screw of a lathe.

4. Which of the following screw thread is stronger than other threads?

a) square thread

b) trapezoidal threads

c) buttress threads

d) V threads

Answer: c

Explanation: Buttress thread is stronger than other threads because of greater thickness at the base of the thread. The buttress thread has limited use for power transmission. It is employed as the thread for light jack screws and vices.

5. Which of the following screw thread is used for lead screw of lathe?

a) square thread

b) trapezoidal threads

c) buttress threads

d) V threads

Answer: b

Explanation: The square threads are employed in screw jacks, presses and clamping devices.

For lead screw of lathe, trapezoidal threads are used.

6. For self locking screw

a) φ > α

b) α > φ

c) μ < tanα

d) μ = cosecα

Answer: a

Explanation: If φ < α, then torque required to lower the load will be negative. In other words, the load will start moving downward without the application of any torque. Such a condition is known as over hauling of screws. If however, φ > α, the torque required to lower the load will be positive, indicating that an effort is applied to lower the load. Such a screw is known as self locking screw.

7. For over hauling screw

a) φ > α

b) α > φ

c) φ > α

d) none of the mentioned

Answer: b

Explanation: If φ > α, then torque required to lower the load will be negative. In other words, the load will start moving downward without the application of any torque. Such a condition is known as over hauling of screws. If however, φ > α, the torque required to lower the load will be positive, indicating that an effort is applied to lower the load. Such a screw is known as self locking screw.

8. A cup is provided in screw jack

a) to reduce the friction

b) to prevent rotation of load

c) to increase load capacity

d) to increase efficiency

Answer: b

Explanation: For the prevention of the rotation of load being lift, the load cup of a screw jack is made separate from the head of the spindle.

9. The maximum efficiency of square threaded power depends upon

a) lead angle of screw

b) friction angle

c) pitch of screw

d) nominal diameter of screw

Answer: b

Explanation: The efficiency of a square threaded screw depends upon the helix angle α and the friction angle φ.

Answer: d

Explanation: None.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Friction in Journal Bearing- Friction Circle”.

1. The minimum force required to slide a body of weight W on a rough horizontal plane is

a) W sinϴ

b) W cosϴ

c) W tanϴ

d) W cosecϴ

Answer: a

Explanation: The minimum force required to slide a body of weight W on a rough horizontal plane is W sinϴ. A body of weight W is required to move up the rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by P = W .

2. A body will begin to move down an inclined plane, if the angle of inclination of the plane is ____________ the angle of friction.

a) equal to

b) less than

c) greater than

d) none of the mentioned

Answer: c

Explanation: None.

3. A body of weight W is required to move up the rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by

a) P = W tanα

b) P = W tan ɸ

c) P = W 

d) P = W 

Answer: c

Explanation: The minimum force required to slide a body of weight W on a rough horizontal plane is W sinϴ. A body of weight W is required to move up the rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by P = W .

4. The coefficient of friction is the ratio of the limiting friction to the normal reaction between the two bodies.

a) True

b) False

Answer: a

Explanation: The coefficient of friction is defined as the ratio of the limiting friction to the normal reaction(R N ) between the two bodies. Mathematically,

μ = F/R N .

5. In a screw jack, the effort required to lift the load W is given by

a) P = W tan ɸ

b) P = W tan ɸ

c) P = W tan ɸ

d) P = W cos ɸ

Answer: b

Explanation: The effort required at the circumference of the screw to lift the load W is given by

P = W tan ɸ

The effort required at the circumference of the screw to lower the load W is given by

P = W tan ɸ.

6. In a screw jack, the effort required to lower the load W is given by

a) P = W tan ɸ

b) P = W tan ɸ

c) P = W tan ɸ

d) P = W cos ɸ

Answer: c

Explanation: The effort required at the circumference of the screw to lower the load W is given by

P = W tan ɸ

The effort required at the circumference of the screw to lift the load W is given by

P = W tan ɸ.

7. The frictional torque for square thread at the mean radius r while raising load W is given by

a) T = W.rtanɸ

b) T = W.rtanɸ

c) T = W.rtanα

d) T = W.rtanɸ

Answer: b

Explanation: None.

8. Efficiency of a screw jack is given by

a) tanɸ/tanα

b) tanα/ tanɸ

c) tanɸ/tanα

d) tanα/tanɸ

Answer: b

Explanation: None.

9. The load cup of a screw jack is made separate from the head of the spindle to

a) enhance the load carrying capacity of the jack

b) reduce the effort needed for lifting the working load

c) reduce the value of frictional torque required to be countered for lifting the load

d) prevent the rotation of load being lifted

Answer: d

Explanation: In screw jack, the load to be raised or lowered, is placed on the head of the square threaded rod which is rotated by the application of an effort at the end of the lever for lifting or lowering the load.

Answer: b

Explanation: None.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Friction of Pivot and Collar Bearing”.

1. The power from the engine to the rear axle of an automobile is transmitted by means of

a) worm and worm wheel

b) spur gears

c) bevel gears

d) hooke’s joint

Answer: d

Explanation: A Hooke’s joint is used to connect two shafts, which are intersecting at a small angle. In automobiles, the power is transmitted through this only.

2. A force acting in the opposite direction to the motion of the body is called force of friction.

a) True

b) False

Answer: a

Explanation: The force of friction always acts in a direction, opposite to that in which the body tends to move.

3. The maximum frictional force, which comes into play, when a body just begins to slide over the surface of the other body, is known as

a) static friction

b) dynamic friction

c) limiting friction

d) coefficient of friction

Answer: c

Explanation: The friction, experienced by a body, when at rest, is known as static friction.

The friction, experienced by a body, when in motion, is known as dynamic friction.

The maximum frictional force, which comes into play, when a body just begins to slide over

the surface of the other body, is known as limiting friction.

4. The friction experienced by a body, when at rest, is known as static friction.

a) True

b) False

Answer: a

Explanation: The friction, experienced by a body, when at rest, is known as static friction.

The friction, experienced by a body, when in motion, is known as dynamic friction.

The maximum frictional force, which comes into play, when a body just begins to slide over

the surface of the other body, is known as limiting friction.

5. The dynamic friction is the friction experienced by a body, when the body

a) is in motion

b) is at rest

c) just begins to slide over the surface of the other body

d) none of the mentioned

Answer: a

Explanation: The friction, experienced by a body, when at rest, is known as static friction.

The friction, experienced by a body, when in motion, is known as dynamic friction.

The maximum frictional force, which comes into play, when a body just begins to slide over

the surface of the other body, is known as limiting friction.

6. The static friction

a) bears a constant ratio to the normal reaction between the two surfaces

b) is independent of the area of contact, between the two surfaces

c) always acts in a direction, opposite to that in which the body tends to move

d) all of the mentioned

Answer: d

Explanation: The laws of static friction are:

a) The force of friction always acts in a direction, opposite to that in which the body tends to move.

b) The magnitude of the force of friction is exactly equal to the force, which tends to move.

c) The force of friction is independent of the area of contact, between the two surfaces.

d) The force of friction depends upon the roughness of the surfaces.

7. Which of the following statements regarding laws governing the friction between dry surfaces are correct?

a) The friction force is dependent on the materials of the contact surfaces.

b) The friction force is directly proportional to the normal force.

c) The friction force is independent of the area of contact.

d) All of the mentioned

Answer: d

Explanation: The laws of friction between dry surfaces are:

a) The force of friction always acts in a direction, opposite to that in which the body tends to move.

b) The magnitude of the force of friction is exactly equal to the force, which tends to move.

c) The force of friction is independent of the area of contact, between the two surfaces.

d) The force of friction depends upon the roughness of the surfaces.

8. The angle of the inclined plane at which the body just begins to slide down the plane, is called helix angle.

a) True

b) False

Answer: b

Explanation: The angle of the inclined plane at which the body just begins to slide down the plane, is called angle of repose.

9. The angle which the normal reaction makes with the resultant reaction is called angle of friction.

a) True

b) False

Answer: a

Explanation: The angle of the inclined plane at which the body just begins to slide down the plane, is called angle of repose. The angle which the normal reaction makes with the resultant reaction is called angle of friction.

Answer: b

Explanation: The angle of the inclined plane at which the body just begins to slide down the plane, is called angle of repose. The angle which the normal reaction makes with the resultant reaction is called angle of friction.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Friction Clutches”.

1. A jaw clutch is essentially a

a) positive action clutch

b) cone clutch

c) friction clutch

d) disc clutch

Answer: a

Explanation: The positive clutches are used when a positive drive is required. The simplest type of a positive clutch is a jaw or claw clutch.

2. The material used for lining of friction surfaces of a clutch should have _____________ coefficient of friction.

a) low

b) high

c) medium

d) none of the mentioned

Answer: b

Explanation: The material should have a high and uniform coefficient of friction.

3. The torque developed by a disc clutch is given by

a) T = 0.25 µ.W.R

b) T = 0.5 µ.W.R

c) T = 0.75 µ.W.R

d) T = µ.W.R

Answer: d

Explanation: T = µ.W.R

where W = Axial force with which the friction surfaces are held together ;

µ = Coefficient of friction ; and

R = Mean radius of friction surfaces.

4. In case of a multiple disc clutch, if n 1 are the number of discs on the driving shaft and n 2 are the number of the discs on the driven shaft, then the number of pairs of contact surfaces will be

a) n 1 + n 2

b) n 1 + n 2 – 1

c) n 1 + n 2 + 1

d) none of the mentioned

Answer: b

Explanation: If n 1 are the number of discs on the driving shaft and n 2 are the number of the discs on the driven shaft, then the number of pairs of contact surfaces will be

n 1 + n 2 – 1.

5. The cone clutches have become obsolete because of

a) small cone angles

b) exposure to dirt and dust

c) difficulty in disengaging

d) all of the mentioned

Answer: d

Explanation: A cone clutch, was extensively used in automobiles, but now-a-days it has been replaced completely by the disc clutch. In a cone clutch, the driver is keyed to the driving shaft by a sunk key and has an inside conical surface or face which exactly fits into the outside conical surface of the driven.

6. The axial force (W e ) required for engaging a cone clutch is given by

a) W n sin α

b) W n µ

c) W n µ

d) none of the mentioned

Answer: c

Explanation: Axial force required for engaging the clutch = W n µ

where W n = Normal force acting on the contact surfaces,

α = Face angle of the cone, and

µ = Coefficient of friction.

7. In a centrifugal clutch, the force with which the shoe presses against the driven member is the ___________ of the centrifugal force and the spring force.

a) difference

b) sum

c) ratio

d) none of the mentioned

Answer: a

Explanation: The force with which the shoe presses against the driven member is the difference of the centrifugal force and the spring force. The increase of speed causes the shoe to press harder and enables more torque to be transmitted.

Answer: a

Explanation: Since the operating centrifugal force is a function of square of angular velocity, the friction torque for accelerating a load is also a function of square of speed driving member.

Answer: a

Explanation: ȵ = tanα/tanɸ

ɸ = angle of friction,

α = Helix angle or lead angle

tanɸ = 0.15

ɸ = 8.53 0

ȵ = 74% .

Sanfoundry Global Education & Learning Series – Machine Kinematics.

To practice all areas of Machine Kinematics, here is complete set of 1000+ Multiple Choice Questions and Answers .

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Belt, Rope and Chain Drives”.

1. The velocity ratio of two pulleys connected by an open belt or crossed belt is

a) directly proportional to their diameters

b) inversely proportional to their diameters

c) directly proportional to the square of their diameters

d) inversely proportional to the square of their diameters

Answer: b

Explanation: It is the ratio between the velocities of the driver and the follower or driven.

Let d 1 = Diameter of the driver,

d 2 = Diameter of the follower,

N 1 = Speed of the driver in r.p.m., and

N 2 = Speed of the follower in r.p.m.

∴ Length of the belt that passes over the driver, in one minute

= π d 1 .N 1

Similarly, length of the belt that passes over the follower, in one minute

= π d 2 . N 2

Since the length of belt that passes over the driver in one minute is equal to the length of belt that passes over the follower in one minute, therefore

π d 1 .N 1 = π d 2 . N 2

∴ Velocity ratio, N 2 /N 1 = d 1 /d 2 .

2. Two pulleys of diameters d 1 and d 2 and at distance x apart are connected by means of an open belt drive. The length of the belt is

a) π /2 (d 1 + d 2 ) 2x + (d 1 + d 2 ) 2 /4x

b) π /2 (d 1 – d 2 ) 2x + (d 1 – d 2 ) 2 /4x

c) π /2 (d 1 + d 2 ) 2x + (d 1 – d 2 ) 2 /4x

d) π /2 (d 1 – d 2 ) 2x + (d 1 + d 2 ) 2 /4x

Answer: c

Explanation: None.

3. In a cone pulley, if the sum of radii of the pulleys on the driving and driven shafts is constant, then

a) open belt drive is recommended

b) cross belt drive is recommended

c) both open belt drive and cross belt drive are recommended

d) the drive is recommended depending upon the torque transmitted

Answer: b

Explanation: In a cross belt drive, both the pulleys rotate in opposite directions. If sum of the radii of the two pulleys be constant, then length of the belt required will also remain constant, provided the distance between centres of the pulleys remain unchanged.

4. Due to slip of the belt, the velocity ratio of the belt drive

a) decreases

b) increases

c) does not change

d) none of the mentioned

Answer: a

Explanation: The result of the belt slipping is to reduce the velocity ratio of the system. As the slipping of the belt is a common phenomenon, thus the belt should never be used where a definite velocity ratio is of importance.

5. When two pulleys of different diameters are connected by means of an open belt drive, then the angle of contact taken into consideration should be of the

a) larger pulley

b) smaller pulley

c) average of two pulleys

d) none of the mentioned

Answer: b

Explanation: None.

6. The power transmitted by a belt is maximum when the maximum tension in the belt  is equal to

a) T C

b) 2T C

c) 3T C

d) 4T C

Answer: c

Explanation: When the power transmitted is maximum, 1/3rd of the maximum tension is absorbed as centrifugal tension.

T = 3T C

where T C = Centrifugal tension.

7. The velocity of the belt for maximum power is

a) √T/3m

b) √T/4m

c) √T/5m

d) √T/6m

Answer: a

Explanation: We know that T 1 = T– T C and for maximum power T C = T/3

T 1 = T – T/3 = 2T/3

the velocity of the belt for the maximum power, v = √T/3m

where m = Mass of the belt in kg per metre length.

8. The centrifugal tension in belts

a) increases power transmitted

b) decreases power transmitted

c) have no effect on the power transmitted

d) increases power transmitted upto a certain speed and then decreases

Answer: c

Explanation: None.

9. When the belt is stationary, it is subjected to some tension, known as initial tension. The value of this tension is equal to the

a) tension in the tight side of the belt

b) tension in the slack side of the belt

c) sum of the tensions in the tight side and slack side of the belt

d) average tension of the tight side and slack side of the belt

Answer: d

Explanation: When the driver starts rotating, it pulls the belt from one side  and delivers it to the other side . The increased tension in one side of the belt is called tension in tight side and the decreased tension in the other side of the belt is called tension in the slack side.

Answer: d

Explanation: It is given by p = d sin (180 0 /T).

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Types of Belts – 1”.

1. In a cone pulley, if the sum of radii of the pulleys on the driving and driven shafts is constant, then

a) open belt drive is recommended

b) crossed belt drive is recommended

c) both open belt drive and crossed belt drive is recommended

d) the drive is recommended depending upon the torque transmitted

Answer: b

Explanation: Cone pulley drive, is used for changing the speed of the driven shaft while the main or driving shaft runs at constant speed. This is accomplished by shifting the belt from one part of the steps to the other.

2. Due to slip of belt, the velocity ratio of the belt drive increases.

a) True

b) False

Answer: b

Explanation: The result of the belt slipping is to reduce the velocity ratio of the system.

3. When two pulleys of different diameters are connected by means of an open belt, the angle of contact at the _________pulley must be taken into consideration.

a) smaller

b) larger

c) medium

d) none of the mentioned

Answer: a

Explanation: None.

4. The power transmitted by a belt is maximum when the maximum tension in the belt is __________of centrifugal tension.

a) one-third

b) two-third

c) double

d) three times

Answer: d

Explanation: When the power transmitted is maximum, 1/3rd of the maximum tension is absorbed as centrifugal tension.

5. The velocity of the belt for maximum power is

a) T/3

b) T.g/3

c) √T/3m

d) √3m/T

Answer: c

Explanation: None.

6. The centrifugal tension on the belt has no effect on the power transmitted.

a) True

b) False

Answer: a

Explanation: None.

7. V-belts are usually used for

a) long drives

b) short drives

c) long and short drives

d) none of the mentioned

Answer: b

Explanation: V-belt is mostly used in factories and workshops where a great amount of power is to be transmitted from one pulley to another when the two pulleys are very near to each other.

8. In a multiple V-belt drive, if one of the belt is broken, then we should replace

a) the broken belt only

b) all the belts

c) the broken belt and the belts on either side of it

d) none of the mentioned

Answer: b

Explanation: In multiple V-belt drive, all the belts should stretch at the same rate so that the load is equally divided between them. When one of the set of belts break, the entire set should be replaced at the same time. If only one belt is replaced, the new unworn and unstressed belt will be more tightly stretched and will move with different velocity.

Answer: c

Explanation: None.

This set of Machine Kinematics Question Bank focuses on “Types of Belts – 2”.

1. In a multiple V- belt drive, when a single belt is damaged, it is preferable to change the complete set to

a) reduce vibration

b) reduce slip

c) ensure uniform loading

d) ensure proper alignment

Answer: c

Explanation: For uniform loading it is better to change the complete set of V-belt drive.

2. In a multiple V- belt drive, all the belts should stretch at the same rate.

a) True

b) False

Answer: a

Explanation: It may be noted that in multiple V-belt drive, all the belts should stretch at the same rate so that the load is equally divided between them.

3. The ratio of the driving tensions for V-belts is _____________ times that of flat belts.

a) sin β

b) cos β

c) cosec β

d) sec β

Answer: c

Explanation: None.

4. The ratio of driving tensions for rope drive is same as that of V-belt drive.

a) True

b) False

Answer: a

Explanation: None.

5. Creep in belt drive is due to

a) weak material of the belt

b) weak material of the pulley

c) uneven extensions and contractions of the belt when it passes from tight side to slack side

d) expansion of the belt

Answer: c

Explanation: None.

6. The centrifugal tension in belts

a) increases power transmitted

b) decreases power transmitted

c) have no effect on power transmitted

d) increases power transmitted upto a certain speed and then decreases

Answer: c

Explanation: In a high speed flat belt transmission, it would probably help. It is unlikely to add any significant power transmission in V- belts, as they rely on the wedging action of the belts in the pulley grooves. As the need for greater power transmission increases in a V- belt drive, the belts wedge harder into the pulleys, to respond.

7. When the belt is stationary, it is subjected to some tension known as initial tension. The value of this tension is equal to the

a) tension in the tight side of the belt

b) tension in the slack side of the belt

c) sum of the tensions on the tight side and slack side of the belt

d) average tension of the tight side and slack side of the belt

Answer: d

Explanation: None.

Answer: a

Explanation: п/16 x s s x d 3 = l x d/4 x s s x d/2

or, l/d = п/2.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “V-Belts”.

1. The included angle for the V-belt is usually

a) 20° – 30°

b) 30° – 40°

c) 40° – 60°

d) 60° – 80°

Answer: b

Explanation: The V-belts are made of fabric and cords moulded in rubber and covered with fabric and rubber. These belts are moulded to a trapezoidal shape and are made endless. These are particularly suitable for short drives. The included angle for the V-belt is usually from 30° to 40°.

2. The V-belts are particularly suitable for _____________ drives.

a) short

b) long

c) medium

d) none of the mentioned

Answer: a

Explanation: The V-belts are made of fabric and cords moulded in rubber and covered with fabric and rubber. These belts are moulded to a trapezoidal shape and are made endless. These are particularly suitable for short drives.

3. The groove angle of the pulley for V-belt drive is usually

a) 20° – 25°

b) 25° – 32°

c) 32° – 38°

d) 38° – 45°

Answer: c

Explanation: A small groove angle will require more force to pull the belt out of the groove which will result in loss of power and excessive belt wear due to friction and heat. Hence the selected groove angle is a compromise between the two. Usually the groove angles of 32° to 38° are used.

4. A V-belt designated by A-914-50 denotes

a) a standard belt

b) an oversize belt

c) an undersize belt

d) none of the mentioned

Answer: a

Explanation: a V-belt marked A – 914 – 50 denotes a standard belt of inside length 914 mm and a pitch length 950 mm. A belt marked A – 914 – 52 denotes an oversize belt by an amount of  = 2 units of grade number.

5. The wire ropes make contact at

a) bottom of groove of the pulley

b) sides of groove of the pulley

c) sides and bottom of groove of the pulley

d) any where in the groove of the pulley

Answer: a

Explanation: The wire ropes run on grooved pulleys but they rest on the bottom of the grooves and are not wedged between the sides of the grooves.

6. Which of the following statements are correct regarding power transmission through V-belts?

 V-belts are used at the high-speed end.

 V-belts are used at the low-speed end.

 V-belts are of standard lengths.

 V-angles of pulleys and belts are standardized.

Select the correct answer using the code given below.

a) 1 and 3 only

b) 2 and 4 only

c) 2, 3 and 4

d) 1, 3 and 4

Answer: d

Explanation: Advantages of V -belts

V-belts are used at the high-speed end.

 V-belts are used at the high-speed end.

 V-belts are of standard lengths.

 V-angles of pulleys and belts are standardized

7. The creep in a belt drive is due to the

a) material of the pulleys

b) material of the belt

c) unequal size of the pulleys

d) unequal tension in tight and slack sides of the belt

Answer: d

Explanation: The belt always has an initial tension when installed over the pulleys. This initial tension is same throughout the belt length when there is no motion. During rotation of the drive, tight side tension is higher than the initial tension and slack side tension is lower than the initial tension.

Answer: b

Explanation: The V-belt may be operated in either direction with tight side of the belt at the top or bottom. The centre line may be horizontal, vertical or inclined.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Chain Drives”.

1. What is the purpose of using steel chains?

a) To avoid slipping

b) To avoid friction

c) To avoid accelerated motion

d) To avoid jerks

Answer: a

Explanation: In belt and rope drives, it is observed that slipping may take place. In order to avoid the issue of slipping, steel chains are being used.

2. The chains are made up of rigid links which are hinged together in order to avoid flexibility for warping around the driving and driven wheels.

a) True

b) False

Answer: b

Explanation: The chains are made up of rigid links which are hinged together in order to provide the necessary flexibility for warping around the the two sets of wheels, i.e. driving and driven wheels.

3. The toothed wheels in chain drives are known as ______

a) Sprockets

b) Sprockers

c) V-belt

d) V- chain

Answer: a

Explanation: The wheels and the chain are subjected to a constraint to move together without slipping and ensures perfect velocity ratio. The toothed wheels are known as sprocket wheels or sprockets.

4. Which of the following is true regarding chain drives?

a) The chain drives may be used when the distance between the shafts is less

b) The production cost of chains is relatively low

c) The chain drive needs low maintenance

d) The chain drive has no velocity fluctuations

Answer: b

Explanation: The chain drives may be used when the distance between the shafts is less. This is an advantage of using a chain drive over belt or rope drives.

5. The distance between hinge centres of two corresponding links is known as _______

a) Pitch

b) Pitch circle diameter

c) Sprocket length

d) Sprocker diameter

Answer: a

Explanation: Pitch ‘p’ of the chain is the linear distance between the hinge centre of a link and the corresponding hinge centre of the adjacent link. It is usually denoted by p.

6. In the figure given below, what the quantity ‘p’ is known as _________

machine-kinematics-questions-answers-chain-drives-q6

a) Pitch

b) Pitch circle diameter

c) Sprocket length

d) Sprocker diameter

Answer: a

Explanation: In the given figure the quantity p is the Pitch. Pitch of the chain is the distance between the hinge centre of a link and the corresponding hinge centre of the adjacent link.

7. The diameter of the circle on which the hinge centres of the chain lie is known as _______

a) Pitch

b) Pitch circle diameter

c) Sprocket length

d) Sprocker diameter.

Answer: a

Explanation: Pitch circle diameter of the chain sprocket is the diameter of the circle on which the hinge centres of the chain lie, when the chain is wrapped round a sprocket.

8. Pitch of the chain lies on the arc of the pitch circle.

a) True

b) False

Answer: b

Explanation: Since the links of the chain are rigid, therefore pitch of the chain does not lie on the arc of the pitch circle. Thus, the given statement is false.

9. Which of the following chains fall under the category of hoisting and hauling chains?

a) Chain with oval links

b) Closed joint chain

c) Detachable chain

d) Block chain

Answer: a

Explanation: Chains with oval links are used only at low speeds such as in chain hoists and in anchors for marine works. Hence it falls under the above mentioned category.

10. Which of the following chain is used to provide elevation continuosly?

a) Conveyor chains

b) Power transmitting chains

c) Hoisting chains

d) Hauling chains

Answer: a

Explanation: Conveyer chains are are used for elevating and conveying the materials continuously. The conveyor chains are of the following two types : Detachable or hook joint type chain and Closed joint type chain.

11. Which of the following chains are used for transmission of power, when the distance between the centres of shafts is short?

a) Chain with oval links

b) Closed joint chain

c) Detachable chain

d) Block chain

Answer: d

Explanation: Block chains are used for transmission of power, when the distance between the centres of shafts is relatively short. These chains provide efficient lubrication.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Advantages and Disadvantages of Chain Drive Over Belt or Rope Drive”.

1. The advantages of the V-belt drive over flat belt drive are

a) The V-belt drive gives compactness due to the small distance between the centres of pulleys.

b) The drive is positive, because the slip between the belt and the pulley groove is negligible.

c) Since the V-belts are made endless and there is no joint trouble, therefore the drive is smooth.

d) all of the mentioned

Answer: d

Explanation: Following are the advantages of the V-belt drive over flat belt drive:

a) The V-belt drive gives compactness due to the small distance between the centres of pulleys.

b) The drive is positive, because the slip between the belt and the pulley groove is negligible.

c) Since the V-belts are made endless and there is no joint trouble, therefore the drive is smooth.

d) It provides longer life, 3 to 5 years.

e) It can be easily installed and removed.

f) The operation of the belt and pulley is quiet.

g) The belts have the ability to cushion the shock when machines are started.

h) The high velocity ratio  may be obtained.

i) The wedging action of the belt in the groove gives high value of limiting ratio of tensions.

2. The disadvantages of the V-belt drive over flat belt drive are

a) The V-belt drive cannot be used with large centre distances.

b) The V-belts are not so durable as flat belts.

c) The construction of pulleys for V-belts is more complicated than pulleys for flat belts.

d) all of the mentioned

Answer: d

Explanation: Following are the disadvantages of the V-belt drive over flat belt drive :

a) The V-belt drive cannot be used with large centre distances.

b) The V-belts are not so durable as flat belts.

c) The construction of pulleys for V-belts is more complicated than pulleys for flat belts.

d) Since the V-belts are subjected to certain amount of creep, therefore these are not suitable for constant speed application such as synchronous machines, and timing devices.

e) The belt life is greatly influenced with temperature changes, improper belt tension and mismatching of belt lengths.

f) The centrifugal tension prevents the use of V-belts at speeds below 5 m/s and above 50m/s.

3. The advantages of the V-belt drive over flat belt drive are

a) It provides longer life, 3 to 5 years.

b) It can be easily installed and removed.

c) The operation of the belt and pulley is quiet.

d) all of the mentioned

Answer: d

Explanation: Following are the advantages of the V-belt drive over flat belt drive:

a) The V-belt drive gives compactness due to the small distance between the centres of pulleys.

b) The drive is positive, because the slip between the belt and the pulley groove is negligible.

c) Since the V-belts are made endless and there is no joint trouble, therefore the drive is smooth.

d) It provides longer life, 3 to 5 years.

e) It can be easily installed and removed.

f) The operation of the belt and pulley is quiet.

g) The belts have the ability to cushion the shock when machines are started.

h) The high velocity ratio  may be obtained.

i) The wedging action of the belt in the groove gives high value of limiting ratio of tensions.

4. The disadvantages of the V-belt drive over flat belt drive are

a) Since the V-belts are subjected to certain amount of creep, therefore these are not suitable for constant speed application such as synchronous machines, and timing devices.

b) The belt life is greatly influenced with temperature changes, improper belt tension and mismatching of belt lengths.

c) The centrifugal tension prevents the use of V-belts at speeds below 5 m/s and above 50m/s.

d) all of the mentioned

Answer: d

Explanation: Following are the disadvantages of the V-belt drive over flat belt drive :

a) The V-belt drive cannot be used with large centre distances.

b) The V-belts are not so durable as flat belts.

c) The construction of pulleys for V-belts is more complicated than pulleys for flat belts.

d) Since the V-belts are subjected to certain amount of creep, therefore these are not suitable for constant speed application such as synchronous machines, and timing devices.

e) The belt life is greatly influenced with temperature changes, improper belt tension and mismatching of belt lengths.

f) The centrifugal tension prevents the use of V-belts at speeds below 5 m/s and above 50m/s.

5. The distance between the hinge centre of a link and the corresponding hinge centre of the adjacent link is called

a) pitch of the chain

b) bush roller chain

c) block chain

d) none of the mentioned

Answer: a

Explanation: A bush roller chain, consists of outer plates or pin link plates, inner plates or roller link plates, pins, bushes and rollers.

The distance between the hinge centre of a link and the corresponding hinge centre of the adjacent link is called pitch of the chain.

6. Industrial rotors will not have uniform diameter throughout their lengths.

a) True

b) False

Answer: a

Explanation: Industrial rotors are not uniform, because of fitment of pulleys, gears, belt etc.

7. For cutting multi-start threads, the speed ratio is expressed in terms of the lead of the job thread and lead of the lead screw threads.

a) True

b) False

Answer: a

Explanation: During multi-start thread cutting operation, speed is reduced to one-third to one-fourth of that in turning operation.

8. Which one of the following is a positive drive?

a) Crossed flat belt drive

b) Rope drive

c) V-belt drive

d) Chain drive

Answer: d

Explanation: The chains are mostly used to transmit motion and power from one shaft to another, when the centre distance between their shafts is short such as in bicycles, motor cycles, agricultural machinery, conveyors, rolling mills, road rollers etc.

9. The chain drive transmits ____________ power as compared to belt drive.

a) more

b) less

c) equal

d) none of the mentioned

Answer: a

Explanation: Following are the advantages and disadvantages of chain drive over belt or rope drive:

1. As no slip takes place during chain drive, hence perfect velocity ratio is obtained.

2. Since the chains are made of metal, therefore they occupy less space in width than a belt or rope drive.

3. It may be used for both long as well as short distances.

4. It gives a high transmission efficiency .

5. It gives less load on the shafts.

6. It has the ability to transmit motion to several shafts by one chain only.

7. It transmits more power than belts.

8. It permits high speed ratio of 8 to 10 in one step.

9. It can be operated under adverse temperature and atmospheric conditions.

10. The relation between the pitch of the chain  and pitch circle diameter of the sprocket  is given by

a) p = D sin(90 0 /T)

b) p = D sin(120 0 /T)

c) p = D sin(180 0 /T)

d) p = D sin(360 0 /T)

Answer: c

Explanation: None.

11. In order to have smooth operation, the minimum number of teeth on the smaller sprocket, for moderate speeds, should be

a) 15

b) 17

c) 21

d) 25

Answer: b

Explanation: In order to have smooth operation, the minimum number of teeth on the smaller sprocket or pinion may be taken as 17 for moderate speeds and 21 for high speeds.

12. The speed of the sprocket reduces as the chain pitch _____________ for a given number of teeth.

a) increases

b) decreases

c) remains same

d) none of the mentioned

Answer: a

Explanation: The r.p.m. of the sprocket reduces as the chain pitch increases for a given number of teeth.

Answer: b

Explanation: Greater angle of articulation will lead to breaking of chain & reduction in life of the chain.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Pulleys”.

1. In a wheel and differential axle, the diameter of the effort wheel is 400 mm. The radii of the load axles are 150mm and 100 mm respectively. The diameter of the rope is 10 mm. Find the load which can be lifted by an effort of 100 N, assuming an efficiency of the machine to be 75%.

a) 800 N

b) 725 N

c) 615 N

d) none of the mentioned

Answer: c

Explanation: Diameter of effort wheel, D = 400 mm

Diameter of longer axle, d 1 = 2 x 150 = 300 mm

Diameter of the smaller axle, d 2 = 2 x 100 = 200 mm

Diameter of the rope, d r = 10 mm

therefore, V.R. = 2(D + d r )/(d 1 + d r ) – (d 2 + d r )

= 2/  – 

= 820/100 = 8.2

Effort, P = 100 N

ȵ = 75%

Let W = load which can be lifted by the machine

ȵ = M.A./V.R.

0.75 = W/P x 8.2

W = 0.75 x 100 x 8.2 = 615 N.

2. Four movable pulleys are arranged as in the first system. If the weight of each pulley is 5 N, calculate the effort which can lift a load of 10 kN.

a) 629.7 N

b) 615 N

c) 625 N

d) none of the mentioned

Answer: a

Explanation: We know that M.A. = 2 n W/W + w(2 n – 1)

where W = load to be lifted

w = weight of each pulley

n = no. of movable pulleys

therefore, M.A. = 2 4 x 10000/10000 + 5(2 4 – 1) = 10000/P

P = 10000 + 5(2 4 – 1)/ 2 4 = 629.7 N.

3. A person weighing 600 N platform attached to the lower block of a system of 5 pulleys arranged in the second system. The platform and the lower block weigh 100N. The man himself supports by exerting a downward pull at the free end of the rope. Neglecting friction, the minimum pull of the man will be

a) 1000 N

b) 200 N

c) 116.7 N

d) none of the mentioned

Answer: c

Explanation: n = total number of pulleys in the system = 5

W = 600 N

Weight of the lower block and platform = 100 N

Total weight = 600 + 100 = 700 N

Let the pull exerted by the man be P newton.

Due to this pull the effective load on the lower platform will reduce to 

nP = effective load = 700 – P

therefore, 5P = 700 -P

5P = 700

P = 116.7 N.

4. Five pulleys are arranged in the second system of pulleys. When not loaded the effort required to raise the movable block is 35N. Further wastage in friction increases the pull at the rate of 3% of the load lifted. What is the effort required to raise a load of 2kN?

a) 500 N

b) 400 N

c) 495 N

d) none of the mentioned

Answer: c

Explanation: n = no. of pulleys = 5

Frictional effort at zero loading = 35N

Frictional effort at 2 kN loading = 35 + 2000 x 3/100 = 95 N

When the system is considered frictionless nP = W

5P = 2000

P = 400 N

Hence total effort = 400 + 95 = 495 N.

5. Five pulleys are arranged in the second system of pulleys. When not loadwd the effort required to raise the movable block is 35N. Further wastage in friction increases the pull at the rate of 3% of the load lifted. What is the efficiency of the system at 2kN?

a) 80%

b) 80.81%

c) 80.50%

d) none of the mentioned

Answer: b

Explanation: n = no. of pulleys = 5

Frictional effort at zero loading = 35N

Frictional effort at 2 kN loading = 35 + 2000 x 3/100 = 95 N

When the system is considered frictionless nP = W

5P = 2000

P = 400 N

Hence total effort = 400 + 95 = 495 N

Efficiency at this load = effort without friction/effort with friction

= 400/495 x 100

= 80.81%.

6. In a weston differential pulley block, the number of recesses in the smaller wheel is 9/10 of that of the larger wheel. If the efficiency of the machine is 50%, find the load lifted by an effort of 300N.

a) 2000N

b) 3000N

c) 4000N

d) none of the mentioned

Answer: b

Explanation: Let the recesses in the larger wheel, n 1 = 10

Recesses in the smaller wheel, n 2 = 9/10 x 10 = 9

V.R. = 2n 1 /n 1 – n 2 = 2×10/10 – 9 = 20

and mechanical advantage M.A. = W/P

= W/300

efficiency = M.A./V.R.

0.5 = W/300×20

W = 3000N.

7. If the velocity ratio for an open belt drive is 8 and the speed of driving pulley is 800 r.p.m, then considering an elastic creep of 2% the speed of the driven pulley is

a) 104.04 r.p.m

b) 102.04 r.p.m

c) 100.04 r.p.m

d) 98.04 r.p.m

Answer: d

Explanation: Velocity Ratio = Velocity of belt on driver/Velocity of belt on driven

Velocity of belt on driven = 800/8 = 100 r.p.m

Elastic creep = velocity of belt at driven pulley – Velocity of driven pulley

0.02 × Vp = [100-Vp] Vp = 100/1.02 = 98.04r.p.m.

8. If the angle of wrap on smaller pulley of diameter 250 mm is 120 0 and diameter of larger pulley is twice the diameter of smaller pulley, then the centre distance between the pulleys for an open belt drive is

a) 1000 mm

b) 750 mm

c) 500 mm

d) 250 mm

Answer: d

Explanation: sin α = /2c

Angle of wrap on smaller pulley = п – 2α

2п/3 = п – 2sin -1 /2c

c = 250 mm.

9. In short open-belt drives, an idler pulley is used in order to decrease the angle of contact on the smaller pulley for higher power transmission.

a) True

b) False

Answer: b

Explanation: In short open-belt drives, an idler pulley is used in order to increase the angle of contact on the smaller pulley for higher power transmission.

Answer: b

Explanation: Arms of a pulley in belt drive are subjected to complete reversal of stresses and is designed for bending in the plane of rotation.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Toothed Gearing – 1”.

1. The two parallel and coplanar shafts are connected by gears having teeth parallel to the axis of the shaft. This arrangement is called

a) spur gearing

b) helical gearing

c) bevel gearing

d) spiral gearing

Answer: a

Explanation: The two parallel and co-planar shafts connected by the gears. These gears are called spur gears and the arrangement is known as spur gearing. These gears have teeth parallel to the axis of the wheel as shown in Fig. 12.1. Another name given to the spur gearing is helical gearing, in which the teeth are inclined to the axis.

2. The type of gears used to connect two non-parallel non-intersecting shafts are

a) spur gears

b) helical gears

c) spiral gears

d) none of the mentioned

Answer: c

Explanation: The two non-intersecting and non-parallel i.e. non-coplanar shaft connected by gears. These gears are called skew bevel gears or spiral gears and the arrangement is known as skew bevel gearing or spiral gearing. This type of gearing also have a line contact, the rotation of which about the axes generates the two pitch surfaces known as hyperboloids.

3. An imaginary circle which by pure rolling action, gives the same motion as the actual gear, is called

a) addendum circle

b) dedendum circle

c) pitch circle

d) clearance circle

Answer: c

Explanation: Pitch circle is an imaginary circle which by pure rolling action, would give the same motion as the actual gear.

Addendum circle is the circle drawn through the top of the teeth and is concentric with the pitch circle.

Dedendum circle is the circle drawn through the bottom of the teeth. It is also called root circle.

4. The size of a gear is usually specified by

a) pressure angle

b) circular pitch

c) diametral pitch

d) pitch circle diameter

Answer: d

Explanation: Pitch circle diameter is the diameter of the pitch circle. The size of the gear is usually specified by the pitch circle diameter. It is also known as pitch diameter.

5. The radial distance of a tooth from the pitch circle to the bottom of the tooth, is called

a) dedendum

b) addendum

c) clearance

d) working depth

Answer: a

Explanation: Addendum is the radial distance of a tooth from the pitch circle to the top of the tooth.

Dedendum is the radial distance of a tooth from the pitch circle to the bottom of the tooth.

6. The product of the diametral pitch and circular pitch is equal to

a) 1

b) 1/π

c) π

d) 2π

Answer: c

Explanation: Diametral pitch, p d = T/D = π/p c

where, p c = circular pitch.

7. The module is the reciprocal of

a) diametral pitch

b) circular pitch

c) pitch diameter

d) none of the mentioned

Answer: a

Explanation: It is the ratio of the pitch circle diameter in millimeters to the number of teeth.

It is usually denoted by m. Mathematically,

Module, m = D /T.

8. Which is the incorrect relationship of gears?

a) Circular pitch × Diametral pitch = π

b) Module = P.C.D/No.of teeth

c) Dedendum = 1.157 module

d) Addendum = 2.157 module

Answer: d

Explanation: None.

9. If the module of a gear be m, the number of teeth T and pitch circle diameter D, then

a) m = D/T

b) D = T/m

c) m = D/2T

d) none of the mentioned

Answer: a

Explanation: Module, m = D /T.

Answer: b

Explanation: When equal bevel gears  connect two shafts whose axes are mutually perpendicular, then the bevel gears are known as mitres.

This set of Machine Kinematics Questions and Answers for Entrance exams focuses on “Toothed Gearing – 2”.

1. The condition of correct gearing is

a) pitch line velocities of teeth be same

b) radius of curvature of two profiles be same

c) common normal to the pitch surface cuts the line of centres at a fixed point

d) none of the mentioned

Answer: c

Explanation: The fundamental condition of correct gearing is the common normal at the point of contact between a pair of teeth must always pass through the pitch point.

2. Law of gearing is satisfied if

a) two surfaces slide smoothly

b) common normal at the point of contact passes through the pitch point on the line joining the centres of rotation

c) number of teeth = P.C.D. / module

d) addendum is greater than dedendum

Answer: b

Explanation: Law of gearing says that the common normal at the point of contact between a pair of teeth must always pass through the pitch point.

3. Involute profile is preferred to cyloidal because

a) the profile is easy to cut

b) only one curve is required to cut

c) the rack has straight line profile and hence can be cut accurately

d) none of the mentioned

Answer: b

Explanation: The face and flank of involute teeth are generated by a single curve where as in cycloidal

gears, double curves  are required for the face and flank respectively.

Thus the involute teeth are easy to manufacture than cycloidal teeth. In involute system, the basic rack has straight teeth and the same can be cut with simple tools.

4. The contact ratio for gears is

a) zero

b) less than one

c) greater than one

d) none of the mentioned

Answer: c

Explanation: The theoretical minimum value for the contact ratio is one, that is there must always be at least one pair of teeth in contact for continuous action.

5. The maximum length of arc of contact for two mating gears, in order to avoid interference, is

a)  sin φ

b)  cos φ

c)  tan φ

d) none of the mentioned

Answer: c

Explanation: Interference may only be prevented, if the addendum circles of the two mating gears cut the

common tangent to the base circles between the points of tangency.

maximum length of arc of contact =  tan φ

where r = Pitch circle radius of pinion,

R = Pitch circle radius of driver, and

φ = Pressure angle.

6. When the addenda on pinion and wheel is such that the path of approach and path of recess are half of their maximum possible values, then the length of the path of contact is given by

a)  sin φ/2

b)  cos φ/2

c)  tan φ/2

d)  cot φ/2

Answer: a

Explanation: In case the addenda on pinion and wheel is such that the path of approach and path of recess are half of their maximum possible values, then

Path of approach, KP = 1/2 MP.

7. Interference can be avoided in involute gears with 20° pressure angle by

a) cutting involute correctly

b) using as small number of teeth as possible

c) using more than 20 teeth

d) using more than 8 teeth

Answer: c

Explanation: None.

8. The ratio of face width to transverse pitch of a helical gear with α as the helix angle is normally

a) more than 1.15/tan α

b) more than 1.05/tan α

c) more than 1/tan α

d) none of the mentioned

Answer: a

Explanation: None.

9. The maximum efficiency for spiral gears is

a) sin  + 1/ cos  + 1

b) cos  + 1/sin  + 1

c) cos  + 1/ cos  + 1

d) cos  + 1/cos  + 1

Answer: c

Explanation: η max = cos  + 1/ cos  + 1

where θ = Shaft angle, and φ = Friction angle.

Answer: d

Explanation: None.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Law of Gearing – 1”.

1. The two parallel and coplaner shafts are connected by gears having teeth parallel to the axis of the shaft. This arrangement is known as

a) spur gearing

b) helical gearing

c) bevel gearing

d) spiral gearing

Answer: a

Explanation: The two parallel and co-planar shafts connected by the gears. These gears are called spur gears and the arrangement is known as spur gearing.

2. The arrangement is called bevel gearing, when two __________ are connected by gears.

a) tension in the tight side of the belt

b) tension in the slack side of the belt

c) sum of the tensions on the tight side and slack side of the belt

d) average tension of the tight side and slack side of the belt

Answer: a

Explanation: The two non-parallel or intersecting, but coplanar shafts connected by gears. These gears are called bevel gears and the arrangement is known as bevel gearing.

3. When two non-intersecting and non-coplaner shafts are connected by gears,the arrangement is known as helical gearing.

a) True

b) False

Answer: b

Explanation: The two parallel and co-planar shafts connected by the gears. These gears are called spur gears and the arrangement is known as spur gearing. These gears have teeth parallel to the axis of the wheel. Another name given to the spur gearing is helical gearing.

4. The gears are termed as medium velocity gears, if their peripheral velocity is

a) 1-3 m/s

b) 3-15 m/s

c) 15-30 m/s

d) 30-50 m/s

Answer: b

Explanation: The gears having velocity less than 3 m/s are termed as low velocity gears and gears having velocity between 3 and 15 m/s are known as medium velocity gears.

5. An imaginary circle which by pure rolling action, gives the same motion as the actual gear, is called

a) addendum circle

b) dedendum circle

c) pitch circle

d) clearance circle

Answer: c

Explanation: Addendum circle is the circle drawn through the top of the teeth and is concentric with the pitch circle.

Dedendum circle is the circle drawn through the bottom of the teeth. It is also called root circle.

Pitch circle is an imaginary circle which by pure rolling action, would give the same motion as the actual gear.

6. The size of a gear is usually specified by

a) pressure angle

b) circular pitch

c) diametral pitch

d) pitch circle diameter

Answer: d

Explanation: Pitch circle diameter is the diameter of the pitch circle. The size of the gear is usually specified by the pitch circle diameter. It is also known as pitch diameter.

7. The radial distance of a tooth from the pitch circle to the bottom of the tooth is called

a) dedendum

b) addendum

c) clearance

d) working depth

Answer: a

Explanation: Dedendum is the radial distance of a tooth from the pitch circle to the bottom of the tooth.

Addendum is the radial distance of a tooth from the pitch circle to the top of the tooth.

8. The addendum is the radial distance of tooth from the pitch circle to the top of the tooth.

a) True

b) False

Answer: a

Explanation: Dedendum is the radial distance of a tooth from the pitch circle to the bottom of the tooth.

Addendum is the radial distance of a tooth from the pitch circle to the top of the tooth.

9. The working depth of a gear is radical distance from the

a) pitch circle to the bottom of a tooth

b) pitch circle to the top of a tooth

c) top of a tooth to the bottom of a tooth

d) addendum circle to the clearance circle

Answer: d

Explanation: Working depth is the radial distance from the addendum circle to the clearance circle. It is equal to the sum of the addendum of the two meshing gears.

Answer: c

Explanation: Clearance is the radial distance from the top of the tooth to the bottom of the tooth, in a meshing gear. A circle passing through the top of the meshing gear is known as clearance circle.

This set of Machine Kinematics Questions and Answers for Campus interviews focuses on ” Law of Gearing – 2″.

1. A side and face cutter 125 mm diameter has 10 teeth. It operates at a cutting speed of 14 m/min with a table traverse 100 mm/min. The feed per tooth of the cutter is

a) 10 mm

b) 2.86 mm

c) 0.286 mm

d) 0.8 mm

Answer: c

Explanation: пDN = 14,

N = 14000/3.14 x 125 = 35.65

Feed for tooth = table traverse/ N x no. of teeth = 100/35.65 x 10 = 0.286 mm.

2. Consider the following statements in case of reverted gear train:

1. The direction of rotation of the first and the last gear is the same.

2. the direction of rotation of the first and the last gear is opposite.

3. The first and the last gears are on the same shaft.

4. The first and the last gears are on separate but co-axial shafts.

Which of these statements is/are correct?

a) 1 and 3

b) 2 and 3

c) 2 and 4

d) 4 alone

Answer: d

Explanation: Only fourth statement is correct.

3. The dynamic load on a gear is due to

1. inaccurancies of tooth spacing

2. irregularities in tooth profile

3. deflection of the teeth under load

4. type of service

Which of the above statements are correct?

a) 1,2 and 3

b) 2,3 and 4

c) 1,3 and 4

d) 1,2 and 4

Answer: a

Explanation: The dynamic load on a gear is due to

1. inaccurancies of tooth spacing

2. irregularities in tooth profile

3. deflection of the teeth under load.

4. Consider the following statements:

A 20 0 stub tooth system is generally preferred in spur gears as it results in

1. stronger teeth

2. lesser number of teeth on the pinion

3. lesser chances of surface fatigue failure

4. reduction of interference

Which of the above statements are correct?

a) 1,2 and 4

b) 3 and 4

c) 1 and 3

d) 1,2,3 and 4

Answer: a

Explanation: A 20 0 stub tooth system is generally preferred in spur gears as it results in

1. stronger teeth

2. lesser number of teeth on the pinion

3. reduction of interference.

5. An involute rack with 20 0 pressure angle meshes with a pinion of 14.5 0 pressure angle.

a) True

b) False

Answer: b

Explanation: Such a matching is impossible.

6. When a pair of spur gears of the same material is in mesh, the design is based on pinion.

a) True

b) False

Answer: a

Explanation: For a pair of gears of the same material in mesh, the strength factor of the pinion is less than that of the gear.

7. Consider the following modifications regarding avoiding the interference between gears:

1. The centre distance between meshing gears be increased

2. Addendum of the gear be modified

3. Teeth should be undercut slightly at the root

4. Pressure angle should be increased

5. Circular pitch be increased

Which of these are effective in avoiding interference?

a) 1,2 and 3

b) 2,3,4 and 5

c) 1,4 and 5

d) 3,4 and 5

Answer: a

Explanation: None.

8. In a reverted gear train, two gears P and Q are meshing, Q-R is a compound gear, and R and S are meshing. The modules of P and R are 4 mm and 5 mm respectively. The numbers of teeth in P, Q and r are 20, 40 and 25 respectively. The number of teeth in S is

a) 23

b) 35

c) 50

d) 53

Answer: a

Explanation: C = 1/2m 1 (z p + z q ) = 1/2m 2 (z r + z s )

4 = 5(25 + z s )

z s = 23.

9. When two spur gears having involute profiles on their teeth engage, the line of action is tangential to the

a) pitch circles

b) dedendum circles

c) addendum circles

d) base circles

Answer: a

Explanation: None.

Answer: b

Explanation: 2d p + d s = d a

2z p + z s = z a

2 x 20 + z s = 100

z s = 60.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Gear Trains”.

1. In a simple gear train, if the number of idle gears is odd, then the motion of driven gear will

a) be same as that of driving gear

b) be opposite as that of driving gear

c) depend upon the number of teeth on the driving gear

d) none of the mentioned

Answer: a

Explanation: The speed ratio and the train value, in a simple train of gears, is independent of the size and number of intermediate gears. These intermediate gears are called idle gears, as they do not effect the speed ratio or train value of the system.

2. The train value of a gear train is

a) equal to velocity ratio of a gear train

b) reciprocal of velocity ratio of a gear train

c) always greater than unity

d) always less than unity

Answer: b

Explanation: Train value = Speed of the last driven or follower/Speed of the first driver.

3. When the axes of first and last gear are co-axial, then gear train is known as

a) simple gear train

b) compound gear train

c) reverted gear train

d) epicyclic gear train

Answer: c

Explanation: When the axes of the first gear  and the last gear  are co-axial, then the gear train is known as reverted gear train.

When there are more than one gear on a shaft, as shown in Fig. 13.2, it is called a compound train.

4. In a clock mechanism, the gear train used to connect minute hand to hour hand, is

a) epicyclic gear train

b) reverted gear train

c) compound gear train

d) simple gear train

Answer: b

Explanation: The reverted gear trains are used in automotive transmissions, lathe back gears, industrial speed reducers, and in clocks (where the minute and hour hand shafts are co-axial.

5. In a gear train, when the axes of the shafts, over which the gears are mounted, move relative to a fixed axis, is called

a) simple gear train

b) compound gear train

c) reverted gear train

d) epicyclic gear train

Answer: d

Explanation: In an epicyclic gear train, the axes of the shafts, over which the gears are mounted, may move relative to a fixed axis.

When the axes of the first gear  and the last gear  are co-axial, then the gear train is known as reverted gear train.

When there are more than one gear on a shaft, as shown in Fig. 13.2, it is called a compound train of gear.

6. A differential gear in an automobile is a

a) simple gear train

b) epicyclic gear train

c) compound gear train

d) none of the mentioned

Answer: b

Explanation: The epicyclic gear trains are useful for transmitting high velocity ratios with gears of moderate size in a comparatively lesser space. The epicyclic gear trains are used in the back gear of lathe, differential gears of the automobiles, hoists, pulley blocks, wrist watches etc.

7. A differential gear in automobilies is used to

a) reduce speed

b) assist in changing speed

c) provide jerk-free movement of vehicle

d) help in turning

Answer: d

Explanation: For turning differential gears are used.

8. The gear train usually employed in clocks is a

a) reverted gear train

b) simple gear train

c) sun and planet gear

d) differential gear

Answer: a

Explanation: In reverted gear train and last gear train is on the same axis. Such an arrangement has application on speed reducers clocks and machine tools.

9. The working depth of an involute gear is equal to

a) addendum

b) dedendum

c) addendum + dedendum

d) 2 x addendum

Answer: d

Explanation: Working depth is twice of addendum and whole depth is sum of addendum and dedendum.

Answer: d

Explanation: Tooth thickness = 1.5708 x module.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Types of Gear Trains”.

1. A fixed gear having 200 teeth is in mesh with another gear having 50 teeth. The two gears are connected by an arm. The number of turns made by the smaller gear for one revolution of arm about the centre of bigger gear is

a) 2

b) 4

c) 3

d) none of the mentioned

Answer: b

Explanation: N 1 = 200

N 2 = 50

Number of turns = N 1 /N 2

= 200/50 = 4.

2. Number of teeth on a wheel per unit of its pitch diameter is called

a) module

b) diametral pitch

c) circular pitch

d) none of the mentioned

Answer: b

Explanation: None.

3. The type of gears used to connect two non parallel and non intersecting shafts is

a) Spur gear

b) Helical gear

c) Bevel gear

d) Spiral gear

Answer: d

Explanation: Spiral gear is used connect two non parallel and non intersecting shafts. Spur gear is used to connect two parallel and coplanar shafts.

4. To connect two parallel and coplanar shafts the following type of gearing is used

a) Spur gear

b) Bevel gear

c) Spiral gear

d) None of the mentioned

Answer: a

Explanation: Spiral gear is used connect two non parallel and non intersecting shafts. Spur gear is used to connect two parallel and coplanar shafts.

5. In which of the following type of gear train the first gear and the last gear are co-axial.

a) Simple gear train

b) Compound gear train

c) Reverted gear train

d) None of the mentioned

Answer: c

Explanation: When the axes of the first gear  and the last gear  are co-axial, then the gear train is known as reverted gear train.

6. Which gear train is used for higher velocity ratios in a small space?

a) Simple gear train

b) Compound gear train

c) Reverted gear train

d) Epicyclic gear train

Answer: d

Explanation: The epicyclic gear trains are useful for transmitting high velocity ratios with gears of moderate size in a comparatively lesser space. The epicyclic gear trains are used in the back gear of lathe, differential gears of the automobiles, hoists, pulley blocks, wrist watches etc.

7. Which type of gear train is used in clock mechanism to join hour hand and minute hand?

a) Simple gear train

b) Compound gear train

c) Reverted gear train

d) Epicyclic gear train

Answer: d

Explanation: The epicyclic gear trains are used in the back gear of lathe, differential gears of the automobiles, hoists, pulley blocks, wrist watches etc.

8. The gear used to convert rotary motion into translating motion is

a) Worm and wheel

b) Crown gear

c) Rack and pinion

d) Spiral Bevel gear

Answer: c

Explanation: Rack and pinion gears are used to convert rotation into linear motion. The flat, toothed part is the rack and the gear is the pinion. A piston coaxial to the rack provides hydraulic assistance force, and an open centered rotary valve controls the assist level.

9. The circular pitch of a gear is given by

a) Πd/t

b) Πd/2t

c) 2Πd/t

d) Πd/3t

Answer: a

Explanation: The distance measured along the pitch circle from a point on one tooth to the corresponding point on an adjacent tooth is called circular pitch.

P c = Πd/t

Where d=diameter of pitch circle

t=number of teeth.

Answer: b

Explanation: None.

This set of Machine Kinematics Questions & Answers for Exams focuses on “The Differential & Torques in Epicyclic Gear Trains”.

1. To split the engine torque in two ways, which of the following device is used?

a) Clutch

b) Brake

c) Final drive

d) Differential

Answer: d

Explanation: The differential is a device that splits the engine torque two ways, allowing each output to spin at a different speed and hence considered as an immensely important device in the modern vehicles.

2. Two wheelers are also equipped with a differential.

a) True

b) False

Answer: b

Explanation: The differential is found on all modern cars and trucks, and also in many all-wheel-drive vehicles. Two wheelers do not have a differential.

3. Which of the following device allows the wheels of a car to rotate at two different speeds?

a) Clutch

b) Brake

c) Final drive

d) Differential

Answer: d

Explanation: The differential is a device that splits the engine torque two ways, allowing each output to spin at a different speed. The differential plays an integral role in how a car makes turns.

4. Which of the following is true regarding a differential?

a) The outer wheel rotates at a higher speed than the inner wheel

b) The outer wheel rotates at a lower speed than the inner wheel

c) Both the wheels rotate at the same speed

d) Front wheels rotate at a lower speed than rear wheel

Answer: a

Explanation: Since the outer wheels of a car has to travel a greater distance, the outer wheel must rotate at a higher speed in order to prevent slipping.

5. The ratio of speeds between gears is dependent upon the _________

a) Ratio of teeth between the two adjoining gears

b) Ratio of teeth between the two alternate gears

c) Ratio of acceleration

d) Ratio of velocity

Answer: a

Explanation: The ratio of speeds between gears is dependent upon the ratio of teeth between the two adjoining gears such that w 1 x N 1 = w 2 x N 2 where w 1 is the teeth of gear one and N 1 is the speed.

6. On a straight road motion, what is the purpose served by differential?

a) Equal torque to all the wheels

b) More torque to front wheels

c) More torque to rear wheels

d) More torque to opposite wheels

Answer: a

Explanation: When the car is traveling straight, both wheels travel at the same speed. This is done by providing equal torque to all the wheels.

7. Input torque acts on which of the following member?

a) Driven member

b) Driving member

c) Fixed member

d) Reciprocating member

Answer: b

Explanation: If the rotating parts of an epicyclic gear trains does not undergo any acceleration then it is kept in equilibrium by an externally applied torques. The input torque is one of them and acts on the driving member.

8. Resisting torque acts on which of the following member?

a) Driven member

b) Driving member

c) Fixed member

d) Reciprocating member

Answer: a

Explanation: If the rotating parts of an epicyclic gear trains does not undergo any acceleration then it is kept in equilibrium by an externally applied torques. The input torque is one of them and acts on the driven member.

9. Braking torque acts on which of the following member?

a) Driven member

b) Driving member

c) Fixed member

d) Reciprocating member

Answer: c

Explanation: If the rotating parts of an epicyclic gear trains does not undergo any acceleration then it is kept in equilibrium by an externally applied torques. The input torque is one of them and acts on the fixed member.

10. If the input power is increased to two times, what will be the effect of it on the fixed member power?

a) Has a 0 value

b) Increases by two times

c) Increases by 4 times

d) Decreases by two times

Answer: a

Explanation: Since the fixed member does not rotate, the power transmitted by it is 0. As a result of this it remains unaffected by change in input power.

11. If the ratio of angular velocities of the driven and driving torque is one, find the Braking torque

a) 0

b) 2

c) 4

d) 8

Answer: a

Explanation: We know the relation

T 2 = -T 1 ω 1 /ω 2

since the velocity ratio is 1

we have T 2 + T 1 = 0

now

T 3 = T 2 + T 1

Therefore, T 3 = 0.

12. The angular speed of the driven member is twice the driving member, if the input torque is 100 N-m,

Find the load torque magnitude in N-m.

a) 50

b) 100

c) 200

d) 25

Answer: a

Explanation: We know the relation

T 2 = -T 1 ω 1 /ω 2

since the velocity ratio is 1 ⁄ 2

we have T 2 = 50 N-m.

13. Fixing torque’s value is independent of the load torque.

a) True

b) False

Answer: b

Explanation: Fixing torque or the braking torque or the Holding torque generally represented by T 3 has a value

T 3 = -(T 2 + T 1 )

therefore its value is dependent on the load torque.

14. Load torque is directly proportional to the input angular velocity.

a) True

b) False

Answer: a

Explanation: We know that Load torque is given by

T 2 = -T 1 ω 1 /ω 2 where ω 1 is the input angular velocity. Hence the given statement is correct.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Systems of Gear Teeth”.

1. The face of the tooth is the

a) surface of the top of tooth

b) surface of tooth above the pitch surface

c) width of tooth below the pitch surface

d) width of tooth measured along the pitch circle

Answer: b

Explanation: Face of tooth is the surface of the gear tooth above the pitch surface.

Flank of tooth is the surface of the gear tooth below the pitch surface.

2. The flank of the tooth is the surface of the tooth _____________ the pitch surface.

a) above

b) below

c) on

d) none of the mentioned

Answer: b

Explanation: Face of tooth is the surface of the gear tooth above the pitch surface.

Flank of tooth is the surface of the gear tooth below the pitch surface.

3. The ratio of the number of teeth to the pitch circle diameter in millimeters, is called

a) circular pitch

b) diametral pitch

c) module

d) none of the mentioned

Answer: b

Explanation: Diametral pitch is the ratio of number of teeth to the pitch circle diameter in millimetres.

Circular pitch is the distance measured on the circumference of the pitch circle from a point of one tooth to the corresponding point on the next tooth.

4. The ratio of the pitch circle diameter in millimeters to the number of teeth, is called circular pitch.

a) True

b) False

Answer: b

Explanation: Diametral pitch is the ratio of number of teeth to the pitch circle diameter in millimetres.

Circular pitch is the distance measured on the circumference of the pitch circle from a point of one tooth to the corresponding point on the next tooth.

5. The product of the diametral pitch and circular pitch is equal to

a) 1

b) 1/п

c) п

d) 2п

Answer: c

Explanation: None.

6. The product of the diametral pitch and module is equal to one.

a) True

b) False

Answer: a

Explanation: None.

7. The module is the reciprocal of diametral pitch.

a) True

b) False

Answer: a

Explanation: Diametral pitch is the ratio of number of teeth to the pitch circle diameter in millimetres.

Module is the ratio of the pitch circle diameter in millimeters to the number of teeth.

8. The dedendum circle diameter is equal to

a) pitch circle dia. x cosɸ

b) addendum circle dia. x cosɸ

c) clearance circle dia. x cosɸ

d) pitch circle dia. x sinɸ

Answer: a

Explanation: It is the circle drawn through the bottom of the teeth. It is also called root circle.

Root circle diameter = Pitch circle diameter × cos φ, where φ is the pressure angle.

9. The contact ratio is the ratio of

a) length of pair of contact to the circular pitch

b) length of arc of contact to the circular pitch

c) length of arc of approach to the circular pitch

d) length of arc of recess to the circular pitch

Answer: b

Explanation: The ratio of the length of arc of contact to the circular pitch is known as contact ratio i.e. number of pairs of teeth in contact.

Answer: a

Explanation: None.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Spur Gears”.

1. The gears are termed as medium velocity gears, if their peripheral velocity is

a) 1–3 m / s

b) 3–15 m / s

c) 15–30 m / s

d) 30–50 m / s

Answer: b

Explanation: The gears having velocity less than 3 m/s are termed as low velocity gears and gears having velocity between 3 and 15 m / s are known as medium velocity gears. If the velocity of gears is more than 15 m / s, then these are called high speed gears.

2. The size of gear is usually specified by

a) pressure angle

b) pitch circle diameter

c) circular pitch

d) diametral pitch

Answer: b

Explanation: It is the diameter of the pitch circle. The size of the gear is usually specified by the pitch circle diameter. It is also called as pitch diameter.

3. A spur gear with pitch circle diameter D has number of teeth T. The module m is defined as

a) m = d / T

b) m = T / D

c) m = π D / T

d) m = D.T

Answer: a

Explanation: Module is the ratio of the pitch circle diameter in millimetres to the number of teeth. It is usually denoted by m. Mathematically,

Module, m = D / T.

4. In a rack and pinion arrangement, the rack has teeth of _______________ shape.

a) square

b) trepazoidal

c) oval

d) circular

Answer: b

Explanation: None.

5. The radial distance from the _______________ to the clearance circle is called working depth.

a) addendum circle

b) dedendum circle

c) pitch circle

d) none of the mentioned

Answer: a

Explanation: Working depth is radial distance from the addendum circle to the clearance circle. It is equal to the sum of the addendum of the two meshing gears.

6. The product of the diametral pitch and circular pitch is equal to

a) 1

b) 1/π

c) π

d) π × No. of teeth

Answer: c

Explanation: Diametral pitch, p d =T/D = π/p c

Circular pitch, p c = πD/T

Therefore, p d x p c = π.

7. The backlash for spur gears depends upon

a) module

b) pitch line velocity

c) tooth profile

d) both  and 

Answer: d

Explanation: Backlash is the difference between the tooth space and the tooth thickness, as measured on the pitch circle.

8. The contact ratio for gears is

a) zero

b) less than one

c) greater than one

d) none of the mentioned

Answer: c

Explanation: The ratio of the length of arc of contact to the circular pitch is known as contact ratio i.e. number of pairs of teeth in contact.

9. If the centre distance of the mating gears having involute teeth is increased, then the pressure angle

a) increases

b) decreases

c) remains unchanged

d) none of the mentioned

Answer: a

Explanation: The pressure angle increases with the increase in centre distance.

10. The form factor of a spur gear tooth depends upon

a) circular pitch only

b) pressure angle only

c) number of teeth and circular pitch

d) number of teeth and the system of teeth

Answer: d

Explanation: Form factor is independent of the size of the tooth and depends only on the number of teeth on a gear and the system of teeth.

11. Lewis equation in spur gears is used to find the

a) tensile stress in bending

b) shear stress

c) compressive stress in bending

d) fatigue stress

Answer: c

Explanation: None.

12. The minimum number of teeth on the pinion in order to avoid interference for 20° stub system is

a) 12

b) 14

c) 18

d) 32

Answer: b

Explanation: None.

13. The allowable static stress for steel gears is approximately ____________ of the ultimate tensile stress.

a) one-fourth

b) one-third

c) one-half

d) double

Answer: b

Explanation: The allowable static stress (σ o ) for steel gears is approximately one-third of the ultimate tensile strength

(σ u ) i.e. σ o = σ u / 3.

14. Lewis equation in spur gears is applied

a) only to the pinion

b) only to the gear

c) to stronger of the pinion or gear

d) to weaker of the pinion or gear

Answer: d

Explanation: The Lewis equation is applied only to the weaker of the two wheels .

Answer: b

Explanation: For safety, against tooth breakage, the static tooth load should be greater than the dynamic load.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Comparison Between Involute and Cycloidal Gears”.

1. The velocity of sliding _____________ the distance of the point of contact from the pitch point.

a) is directly proportional to

b) is inversaly proportional to

c) is equal to cosɸ multiplied by

d) does not depend upon

Answer: a

Explanation: The velocity of sliding is the velocity of one tooth relative to its mating tooth along the common tangent at the point of contact.

2. In involute gears, the pressure angle is

a) dependent on the size of teeth

b) dependent on the size of gears

c) always constant

d) always variable

Answer: c

Explanation: None

3. In full depth 14 0 involute system, the smallest number of teeth in a pinion which meshes with rack without interference is

a) 12

b) 16

c) 25

d) 32

Answer: d

Explanation: The minimum number of teeth on the pinion in order to avoid interference for 14.5 0 full depth involute are 32 and for 20 0 full depth involute teeth are 18.

4. The pressure angle for involute gears depends upon the size of teeth.

a) True

b) False

Answer: b

Explanation: In a gear drive, the shape of the tooth depends upon the pressure angle.

5. The contact ratio is given by

a) Length of the path of approach/Circular pitch

b) Length of the path of recess/Circular pitch

c) Length of the arc of contact/Circular pitch

d) Length of the arc of approach/cosɸ

Answer: c

Explanation: None

6. For an involute gear, the ratio of base circle radius and pitch circle radius is equal to

a) sinɸ

b) cosɸ

c) secɸ

d) cosecɸ

Answer: b

Explanation: None

7. Which of the following statement is correct for gears?

a) The addendum is less than the dedendum

b) The pitch circle diameter is the product of module and number of teeth

c) The contact ratio means the number of pairs of teeth in contact

d) All of the mentioned

Answer: d

Explanation: None

8. In a gear having involute teeth, the normal to the involute is a tangent to the

a) pitch circle

b) base circle

c) addendum circle

d) dedendum circle

Answer: b

Explanation: Addendum circle is the circle drawn through the top of the teeth and is concentric with the pitch circle.

Dedendum circle is the circle drawn through the bottom of the teeth. It is also called root circle.

Pitch circle is an imaginary circle which by pure rolling action, would give the same motion as the actual gear.

9. The centre distance between two meshing involute gears is equal to

a) sum of base circle radii/cosɸ

b) difference of base circle radii/cosɸ

c) sum of pitch circle radii/cosɸ

d) difference of pitch circle radii/cosɸ

Answer: a

Explanation: None

Answer: a

Explanation: None

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Standard Proportions of Gear Systems”.

1. If T is the actual number of teeth on a helical gear and φ is the helix angle for the teeth, the formative number of teeth is written as

a) T sec 3 φ

b) T sec 2 φ

c) T/sec 3 φ

d) T cosec φ

Answer: a

Explanation: The formative or equivalent number of teeth for a helical gear may be defined as the number of teeth that can be generated on the surface of a cylinder having a radius equal to the radius of curvature at a point at the tip of the minor axis of an ellipse obtained by taking a section of the gear in the normal plane. Mathematically, formative or equivalent number of teeth on a helical gear,

T sec 3 φ

2. In helical gears, the distance between similar faces of adjacent teeth along a helix on the pitch cylinders normal to the teeth, is called

a) normal pitch

b) axial pitch

c) diametral pitch

d) module

Answer: a

Explanation: Normal pitch is the distance between similar faces of adjacent teeth along a helix on the pitch cylinders normal to the teeth.

Axial pitch is the distance, parallel to the axis, between similar faces of adjacent teeth.

3. In helical gears, the right hand helices on one gear will mesh ____________ helices on the other gear.

a) right hand

b) left hand

c) opposite

d) none of the mentioned

Answer: b

Explanation: A helical gear has teeth in form of helix around the gear. Two such gears may be used to connect two parallel shafts in place of spur gears. The helixes may be right handed on one gear and left handed on the other.

4. The helix angle for single helical gears ranges from

a) 10° to 15°

b) 15° to 20°

c) 20° to 35°

d) 35° to 50°

Answer: c

Explanation: In single helical gears, the helix angle ranges from 20° to 35°, while for double helical gears, it may be made upto 45°.

5. The helix angle for double helical gears may be made up to

a) 45°

b) 60°

c) 75°

d) 90°

Answer: a

Explanation: In single helical gears, the helix angle ranges from 20° to 35°, while for double helical gears, it may be made upto 45°.

6. The outside diameter of an involute gear is equal to pitch circle diameter plus

a) 2 addendum

b) 2 dedendum

c) 3.1416 module

d) 2.157 module

Answer: a

Explanation: Addendum is the portion of gear tooth above the pitch circle diameter . Therefore outside diameter of involute gear = PCD + 2 addendum.

7. Pick out the false statement about relationships of spur gears.

a) Pitch diameter = module x No. of teeth

b) Module = 25.4/diametral pitch

c) dedendum = 1.25 x module

d) Base pitch = module x п x sinɸ

Answer: d

Explanation: The false statement is

Base pitch = module x п x sinɸ

Correct relationship of base pitch = module x п x cosɸ

8. Which of the following is not the correct property of involute curve?

a) The form or shape pf an involute curve depends upon the diameter of base circle from which it is derived

b) The angular motion of two involute gear teeth rotating at a uniform rate will be uniform, irrespective of the centre distance

c) The relative rate of motion between driving and driven gears having involute tooth curves, is established by the diameters of their pitch circles

d) the pitch diameters of mating involute gears are directly proportional to the diameters of their respective base circles

Answer: c

Explanation: All statements except at  are correct. The correct statement for  is – The relative rate motion between driving and driven gears having involute tooth curves, is established by the diameters of their base circles.

9. Which of the following gear ratio does not result in hunting tool

a) 77/20

b) 76/21

c) 75/22

d) 71/25

Answer: d

Explanation: When several pairs of gears operating at the same centre distance are required to have hunting ratios, this can be accomplished by having the sum of the teeth in each pair equal to a prime number.

Answer: d

Explanation: The correct relationship is chordal thickness = a + t 2 /4D

This set of Machine Kinematics Problems focuses on “Minimum Number of Teeth on a Pinion for Involute Rack in Order to Avoid Interference”.

1. The minimum number of teeth on the pinion which will mesh with any gear without interference for 20 0 full depth involute teeth will be

a) 12

b) 14

c) 18

d) 24

Answer: c

Explanation: The minimum number of teeth on the pinion in order to avoid interference for 14.5 0 full depth involute are 32 and for 20 0 full depth involute teeth are 18.

2. In gears, interference takes place when

a) the tip of a tooth of a mating gear digs into the portion between base and root circles

b) gears do not move smoothly in the absence of lubrication

c) pitch of the gears is not same

d) gear teeth are undercut

Answer: a

Explanation: Interference occurs when the number of teeth on the smaller of the two meshing gears is less than a required minimum.

3. An involute pinion and gear are in mesh. If both have the same size of addendum, then there will be an interference between the

a) tip of the gear tooth and flank of pinion

b) tip of the pinion and flank of gear

c) flanks of both gear and pinion

d) tip of both gear and pinion

Answer: a

Explanation: The phenomenon when the tip of a tooth under cuts the root on its mating gear, is known as interference.

4. Which of the following statement is correct for involute gears?

a) The interference is inherently absent

b) The variation in centre distance of shafts increases radial force

c) A convex flank is always in contact with concave flank

d) The pressure angle is constant throughout the teeth engagement

Answer: d

Explanation: None.

5. The interference may only be avoided if the addendum circles of the two mating gears cut the common tangent to the base circles between the points of tangency.

a) True

b) False

Answer: a

Explanation: None.

6. When the addenda on pinion and wheel is such that the path of approach and path of recess are half of their maximum possible values, then the length of the path of contact is given by

a) (r 2 + R 2 ) cosɸ/2

b) (r 2 + R 2 ) sinɸ/2

c)  cosɸ/2

d)  sinɸ/2

Answer: d

Explanation: None.

7. The maximum efficiency of spiral gears is

a) sin 𝛳ɸ + 1/cos𝛳ɸ +1

b) cos𝛳ɸ +1/sin 𝛳ɸ + 1

c) cos 𝛳ɸ + 1/cos𝛳ɸ +1

d) cos𝛳ɸ +1/cos 𝛳ɸ + 1

Answer: c

Explanation: The maximum efficiency of spiral gears is

cos 𝛳ɸ + 1/cos𝛳ɸ +1

where, ϴ = Shaft angle

and ɸ = Friction angle.

8. The contact ratio for gears is

a) zero

b) less than one

c) greater than one

d) infinity

Answer: c

Explanation: The theoretical minimum value for the contact ratio is one, that is there must always be at least one

pair of teeth in contact for continuous action.

9. In a simple train of wheels, if the number of intermediate wheels is odd, the motion of the follower will be same as that of the driver.

a) True

b) False

Answer: a

Explanation: The speed ratio  of gear train is the ratio of the speed of the driver to

the speed of the driven or follower. But if the number of intermediate gears are even, the motion of the driven or follower will be in the opposite direction of the driver.

10. In a simple train of wheels, the velocity ratio _____________ the intermediate wheels.

a) depends upon

b) is independent of

c) is equal to

d) none of the mentioned

Answer: b

Explanation: The speed ratio  of gear train is the ratio of the speed of the driver to

the speed of the driven or follower and ratio of speeds of any pair of gears in mesh is the inverse of

their number of teeth.

11. The train value of a gear train is

a) equal to velocity ratio of a gear train

b) reciprocal of velocity ratio of a gear train

c) always greater than unity

d) always less than unity

Answer: b

Explanation: The train value is the reciprocal of speed ratio.

12. When the axes of the first and the last wheels are co-axial, then the train is known as

a) simple train of wheels

b) compound train of wheels

c) reverted gear train

d) epicyclic gear train

Answer: c

Explanation: When there is only one gear on each shaft, it is known as simple gear train.

When there are more than one gear on a shaft, it is called a compound train of gear.

When the axes of the first gear  and the last gear  are co-axial, then the gear train is known as reverted gear train.

13. When the axes of the shafts, over which the gears are mounted, move relative to a fixed axis, then the train is known as reverted gear train.

a) True

b) False

Answer: b

Explanation: When the axes of the first gear  and the last gear  are co-axial, then the gear train is known as reverted gear train.

Answer: b

Explanation: The reverted gear trains are used in automotive transmissions, lathe back gears, industrial speed reducers, and in clocks .

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Worm Gears”.

1. When bevel gears having equal teeth and equal pitch angles connect two shafts whose axes intersect at right angle, then they are known as

a) angular bevel gears

b) crown bevel gears

c) internal bevel gears

d) mitre gears

Answer: d

Explanation: When equal bevel gears  connect two shafts whose axes intersect at right angle, then they are known as mitre gears.

When the bevel gears connect two shafts whose axes intersect at an angle other than a right angle, then they are known as angular bevel gears.

2. The face angle of a bevel gear is equal to

a) pitch angle – addendum angle

b) pitch angle + addendum angle

c) pitch angle – dedendum angle

d) pitch angle + dedendum angle

Answer: b

Explanation: Face angle is the angle subtended by the face of the tooth at the cone centre. It is denoted by ‘φ’. The face angle is equal to the pitch angle plus addendum angle.

3. The root angle of a bevel gear is equal to

a) pitch angle – addendum angle

b) pitch angle + addendum angle

c) pitch angle – dedendum angle

d) pitch angle + dedendum angle

Answer: c

Explanation: Root angle is the angle subtended by the root of the tooth at the cone centre. It is denoted by ‘θ R ’. It is equal to the pitch angle minus dedendum angle.

4. If b denotes the face width and L denotes the cone distance, then the bevel factor is written as

a) b / L

b) b / 2L

c) 1 – 2 b.L

d) 1 – b / L

Answer: d

Explanation: Bevel factor = 1 – b / L.

5. For a bevel gear having the pitch angle θ, the ratio of formative number of teeth (T E ) to actual number of teeth  is

a) 1/sin θ

b) 1/cos θ

c) 1/tan θ

d) sin θ cos θ

Answer: b

Explanation: (T E )/T = 1/cos θ.

6. The worm gears are widely used for transmitting power at ______________ velocity ratios between non-intersecting shafts.

a) high

b) low

c) medium

d) none of the mentioned

Answer: a

Explanation: The worm gears are widely used for transmitting power at high velocity ratios between non-intersecting shafts that are generally, but not necessarily, at right angles.

7. In worm gears, the angle between the tangent to the thread helix on the pitch cylinder and the plane normal to the axis of worm is called

a) pressure angle

b) lead angle

c) helix angle

d) friction angle

Answer: b

Explanation: Lead angle is the angle between the tangent to the thread helix on the pitch cylinder and the plane normal to the axis of the worm. It is denoted by λ.

8. The normal lead, in a worm having multiple start threads, is given by

a) l N = l / cos λ

b) l N = l . cos λ

c) l N = l

d) l N = l tan

Answer: b

Explanation: The term normal pitch is used for a worm having single start threads. In case of a worm having multiple start threads, the term normal lead (l N ) is used, such that

l N = l . cos λ

where l N = Normal lead,

l = Lead, and

λ = Lead angle.

9. The number of starts on the worm for a velocity ratio of 40 should be

a) single

b) double

c) triple

d) quadruple

Answer: a

Explanation: For number of starts from 36 and above we have single velocity ratio. For 12 to 36 we have double velocity ratio, for 8 to 12, we have triple velocity ratio and for 6 to 12 we have quadruple velocity ratio.

Answer: d

Explanation: Axial force or thrust on the worm,

W A = W T / tan λ = Tangential force on the worm gear

where W T = Tangential force acting on the worm,

φ = Pressure angle, and

λ = Lead angle.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Types of Gears”.

1. The gears used for parallel shaft arrangement are

a) mitre gear

b) face gear

c) spur gears on helical gears

d) none of the mentioned

Answer: c

Explanation: Bevel gears are the gears used for intersecting shaft arrangement.

The gears used for parallel shaft arrangement are spur gears on helical gears.

2. _____________ are the gears used for intersecting shaft arrangement.

a) bevel gears

b) beveloid gears

c) mitre gears

d) none of the mentioned

Answer: a

Explanation: Bevel gears are the gears used for intersecting shaft arrangement.

The gears used for parallel shaft arrangement are spur gears on helical gears.

3. ________________ are gears used for skew arrangement.

a) spur gears on helical gears

b) helical, worm, or hypoid gears

c) mitre gears

d) none of the mentioned

Answer: b

Explanation: Helical, worm, or hypoid gears are gears used for skew arrangement.

Bevel gears are the gears used for intersecting shaft arrangement.

4. Bevel gears used for connecting intersecting shafts at 90 0 and having speed ratio 1 : 1 is known as

a) bevel gears

b) beveloid gears

c) mitre gears

d) none of the mentioned

Answer: c

Explanation: Bevel gears used for connecting intersecting shafts at 90 0 and having speed ratio 1 : 1 is known as mitre gears.

Bevel gears with basic pressure angle of 20 0 with long and short addendums for ratios other than 1:1 to avoid undercut pinions and to increase strength are gleason bevel gears.

5. Tapered involute gears which can couple intersecting shafts, skew shafts, and parallel shafts are known as

a) bevel gears

b) beveloid gears

c) mitre gears

d) none of the mentioned

Answer: b

Explanation: Tapered involute gears which can couple intersecting shafts, skew shafts, and parallel shafts are known as beveloid gears.

The gears used for parallel shaft arrangement are spur gears on helical gears.

6. Gears having teeth cut on the rotating face plane of the gear and mate with standard involute spur gears are known as

a) mitre gear

b) face gear

c) spur gears on helical gears

d) none of the mentioned

Answer: b

Explanation: Worm gears are used for obtaining large speed reduction between non-intersecting shafts making an angle of 90 0 with each other.

Gears having teeth cut on the rotating face plane of the gear and mate with standard involute spur gears are known as face gears.

7. ____________ gears are used for obtaining large speed reduction between non-intersecting shafts making an angle of 90 0 with each other.

a) worm gears

b) beveloid gears

c) mitre gears

d) none of the mentioned

Answer: a

Explanation: Worm gears are used for obtaining large speed reduction between non-intersecting shafts making an angle of 90 0 with each other.

Gears having teeth cut on the rotating face plane of the gear and mate with standard involute spur gears are known as face gears.

8. Bevels connecting shafts other than 90 0 are

a) worm gears

b) angular bevel gears

c) mitre gears

d) none of the mentioned

Answer: b

Explanation: Bevels connecting non-intersecting shafts are skew bevel gears.

Bevels connecting shafts other than 90 0 are angular bevel gears.

9. Bevels connecting non-intersecting shafts are

a) skew bevel gears

b) angular bevel gears

c) mitre gears

d) none of the mentioned

Answer: a

Explanation: Bevels connecting non-intersecting shafts are skew bevel gears.

Bevels connecting shafts other than 90 0 are angular bevel gears.

Answer: c

Explanation: Bevel gears used for connecting intersecting shafts at 90 0 and having speed ratio 1 : 1 is known as mitre gears.

Bevel gears with basic pressure angle of 20 0 with long and short addendums for ratios other than 1:1 to avoid undercut pinions and to increase strength are gleason bevel gears.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Bevel Gears”.

1. The bevel gears are used to connect

a) two parallel shafts

b) two intersecting shafts

c) two non intersecting shafts

d) none of the mentioned

Answer: b

Explanation: Two intersecting shafts are connected by bevel gears and pitch cylinders in spur gears.

2. Bevel gears with shafts angle of 90 0 are termed as

a) zerol gears

b) angular bevel gears

c) mitre gears

d) hypoid gears

Answer: c

Explanation: The bevel gears with shaft angle 90 0 are termed as Mitre gears. The bevel gears with any other shaft angle are termed as angular bevel gears.

3. The bevel gears used for connecting non intersecting shafts are

a) mitre gears

b) hypoid gears

c) spiral bevel gears

d) zerol gears

Answer: b

Explanation: The bevel gears used for connecting non intersecting shafts are hypoid gears. The bevel gears with shaft angle 90 0 are termed as Mitre gears.

4. Face width of the bevel gear is usually equal to

a) 10 modules

b) pitch cone radius/3

c) pitch cone radius/2

d) none of the mentioned

Answer: b

Explanation: For correctly designed gears the face width should not be more than 1/3 the slant length, i.e. pitch cone radius.

5. Formative number of teeth on bevel gears is equal to

a) 2 x actual number of teeth

b) actual number of teeth/ cosɸ

c) actual number of teeth/cosα

d) actual number of teeth/cosϴ

Answer: d

Explanation: None.

6. Lewis Equation for bevel gear is corrected for

a) variation in p.c.d.

b) variation in tooth thickness

c) taking care of axial thrust

d) variation in torque acting on the tooth

Answer: a

Explanation: As radius of bevel gear varies along the width, the torque does not produce the same tangential force.

7. Ratio factor Q in wear load equation of bevel gear is given by

a) 2gear ratio G/G + 1

b) 2ratio of formative number of teeth of gear and pinion G

c) G + 1/G ‘ +1

d) 2G ‘ /G

Answer: b

Explanation: None.

8. Bevel factor should not be less than

a) 0.75

b) 0.8

c) 0.67

d) 0.76

Answer: c

Explanation: None.

9. Pitch cone angle of pinion of straight tooth bevel gear pair with ratio 1.732 is

a) 25 0

b) 30 0

c) 60 0

d) none of the mentioned

Answer: c

Explanation: None.

10. The face width of the bevel gear is 0.3 times the radius of pitch cone. Here the bevel factor must be

a) 1.3

b) 3

c) 0.7

d) 1.7

Answer: c

Explanation: Face width = Pitch cone radius/3

therefore, bevel factor = 0.7.

Answer: c

Explanation: Spur gears are connected by pitch cylinders and therefore, they can interchange.

This set of Machine Kinematics Questions and Answers for Aptitude test focuses on “Bevel Gears – 2”.

1. The mathematical form of the bevel tooth profile which closely resembles a spherical involute but is fundamentally different is

a) crown

b) back cone

c) octoid

d) none of the mentioned

Answer: c

Explanation: Octoid is the mathematical form of the bevel tooth profile which closely resembles a spherical involute but is fundamentally different is

The sharp corner orming the outside diameter is crown.

2. The angle formed between an element of the pitch cone and the bevel gear axis is

a) shaft angle

b) pitch angle

c) spiral angle

d) none of the mentioned

Answer: b

Explanation: The angle between the tooth trace and an element of the pitch cone, corresponding to helix angle in helical gears is spiral angle.

The angle formed between an element of the pitch cone and the bevel gear axis is pitch angle.

3. The angle between the tooth trace and an element of the pitch cone, corresponding to helix angle in helical gears is

a) shaft angle

b) pitch angle

c) spiral angle

d) none of the mentioned

Answer: c

Explanation: The angle between the tooth trace and an element of the pitch cone, corresponding to helix angle in helical gears is spiral angle.

The angle formed between an element of the pitch cone and the bevel gear axis is pitch angle.

4. The diameter and plane of rotation surface or shaft centre which is used for locating the gear blank during fabrication of the gear teeth is known as

a) crown

b) back cone

c) generating mounting surface

d) none of the mentioned

Answer: c

Explanation: The diameter and plane of rotation surface or shaft centre which is used for locating the gear blank during fabrication of the gear teeth is known as generating mounting surface.

5. The sharp corner orming the outside diameter is

a) crown

b) back cone

c) octoid

d) none of the mentioned

Answer: a

Explanation: The sharp corner orming the outside diameter is crown.

The length of teeth along the cone distance is face width.

6. The angle between elements of the face cone and pitch cone is

a) addendum angle

b) pitch angle

c) spiral angle

d) none of the mentioned

Answer: a

Explanation: The angle between mating bevel gear axes, also the sum of the two pitch angles is spiral angle.

The angle between elements of the face cone and pitch cone is addendum angle.

7. The angle between mating bevel gear axes, also the sum of the two pitch angles is

a) shaft angle

b) pitch angle

c) spiral angle

d) none of the mentioned

Answer: c

Explanation: The angle between mating bevel gear axes, also the sum of the two pitch angles is spiral angle.

The angle between elements of the face cone and pitch cone is addendum angle.

8. The length of teeth along the cone distance is

a) crown

b) face width

c) octoid

d) none of the mentioned

Answer: b

Explanation: The length of teeth along the cone distance is face width.

The sharp corner orming the outside diameter is crown.

9. The angle of a cone whose elements are tangent to a sphere containing a trace of the pitch circle is

a) crown

b) back cone

c) octoid

d) none of the mentioned

Answer: b

Explanation: The angle between elements of the root cone and pitch cone is dedendum angle.

The angle of a cone whose elements are tangent to a sphere containing a trace of the pitch circle is back cone.

Answer: b

Explanation: The angle between elements of the root cone and pitch cone is dedendum angle.

The angle of a cone whose elements are tangent to a sphere containing a trace of the pitch circle is back cone.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Gearing”.

1. Radial distance between the pitch circle and the top of the tooth is known as

a) pitch

b) addendum

c) base circle

d) none of the mentioned

Answer: b

Explanation: The circle from which an involute curve is generated is known as base circle.

Radial distance between the pitch circle and the top of the tooth is known as addendum.

2. The circle from which an involute curve is generated is known as

a) pitch

b) addendum

c) base circle

d) none of the mentioned

Answer: c

Explanation: The circle from which an involute curve is generated is known as base circle.

Radial distance between the pitch circle and the top of the tooth is known as addendum.

3. Length of the arc of the pitch circle between the centres or other corresponding points of adjacent teeth is known as

a) pitch

b) circular pitch

c) base circle

d) none of the mentioned

Answer: b

Explanation: Length of the arc of the pitch circle between the centres or other corresponding points of adjacent teeth is known as circular pitch.

The circle from which an involute curve is generated is known as base circle.

Radial distance between the pitch circle and the top of the tooth is known as addendum.

4. The curve formed by the point on a circle as it rolls along a straight line is known as

a) cycloid

b) addendum

c) base circle

d) none of the mentioned

Answer: a

Explanation: Length of the arc of the pitch circle between the centres or other corresponding points of adjacent teeth is known as circular pitch.

The circle from which an involute curve is generated is known as base circle.

The curve formed by the point on a circle as it rolls along a straight line is known as cycloid.

5. That surface of the tooth which is between the pitch circle and the top of the tooth is known as

a) cycloid

b) addendum

c) face of tooth

d) none of the mentioned

Answer: c

Explanation: The circle from which an involute curve is generated is known as base circle.

The curve formed by the point on a circle as it rolls along a straight line is known as cycloid.

That surface of the tooth which is between the pitch circle and the top of the tooth is known as face of tooth.

6. The distance between similar, equally spaced tooth surfaces, in a given direction and along a given curve or line is known as

a) pitch

b) addendum

c) base circle

d) none of the mentioned

Answer: a

Explanation: The curve formed by the point on a circle as it rolls along a straight line is known as cycloid.

That surface of the tooth which is between the pitch circle and the top of the tooth is known as face of tooth.

The distance between similar, equally spaced tooth surfaces, in a given direction and along a given curve or line is known as pitch.

7. The angle between a tooth profile and a radial line at its pitch point is known as

a) pressure angle

b) dedendum angle

c) spiral angle

d) none of the mentioned

Answer: a

Explanation: The angle subtended at the centre of a base circle from the origin of an involute to the point of tangency of the generatrix from any point on the same involute is known as roll angle.

The angle between a tooth profile and a radial line at its pitch point is known as pressure angle.

8. The angle subtended at the centre of a base circle from the origin of an involute to the point of tangency of the generatrix from any point on the same involute is known as

a) pressure angle

b) dedendum angle

c) roll angle

d) none of the mentioned

Answer: c

Explanation: The angle subtended at the centre of a base circle from the origin of an involute to the point of tangency of the generatrix from any point on the same involute is known as roll angle.

The angle between a tooth profile and a radial line at its pitch point is known as pressure angle.

9. Surface of the gear between the fillets of adjacent teeth is known as

a) cycloid

b) addendum

c) bottom land

d) none of the mentioned

Answer: c

Explanation: Surface of the gear between the fillets of adjacent teeth is known as bottom land.

Answer: b

Explanation: The angle subtended at the centre of a base circle from the origin of an involute to the point of tangency of the generatrix from any point on the same involute is known as roll angle.

The angle between a tooth profile and a radial line at its pitch point is known as pressure angle.

The angle, at the base cylinder of an involute gear, that the tooth makes with the gear axis is known as base helix angle.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Standard Spur Gears – 1”.

1. Lewis equation for design of involute gear tooth predicts the dynamic load capacity of a cantilever beam of uniform strength.

a) True

b) False

Answer: b

Explanation: Lewis equation for design of involute gear tooth predicts the static load capacity of a cantilever beam of uniform strength.

2. For a pair of gears in mesh, pressure angle and module must be different to satisfy the condition of interchangeability and correct gearing.

a) True

b) False

Answer: b

Explanation: For a pair of gears in mesh, pressure angle and module must be same to satisfy the condition of interchangeability and correct gearing.

3. In skew bevel gears, the axes are

a) non-parallel and non-intersecting, and teeth are curved

b) non-parallel and non-intersecting, and teeth are straight

c) intersecting, and teeth are curved and oblique

d) intersecting, and teeth are curved and can be ground

Answer: a

Explanation: Skew bevel gears imply non-parallel, non-intersecting and curved them.

4. In case the number of teeth on two bevel gears in mesh is 30 and 60 respectively, then the pitch cone angle of the gear will be

a) tan -1 2

b) п/2 + tan -1 2

c) п/2 – tan -1 0.5

d) tan -1 0.5

Answer: d

Explanation: tanɸ = N P /N G

N P = No. of teeth of pinion

N G = No. of teeth of gear

ɸ = Pitch cone angle

ɸ = tan -1 

ɸ = tan -1 0.5.

5. Consider the following statements:

The axes of spiral bevel gear are non-parallel and intersecting.

1. The most common pressure angle for spiral bevel gear is 20 o .

2. The most common spiral angle for spiral bevel gear is 35 o .

3. Spiral bevel gears are generally interchangeable.

4. Spirals are noisy and recommended for low speeds of 10 m/s.

Which of the above statements are correct?

a) 1 and 4

b) 1 and 2

c) 2 and 3

d) 3 and 4

Answer: a

Explanation: Commonly used pressure angle is 20 o , spiral gear operation is noisy hence recommended for low speed operation.

6. Consider the following statements:

In case of helical gears, teeth are cut at an angle to the axis of rotation of the gears.

1. Helix angle introduces another ratio called axial contact ratio.

2. Transverse contact ratio is equal to axial contact ratio in helical gears.

3. Large transverse contact ratio does not allow multiple teeth to share the load.

4. Large axial contact ratio will cause larger axial force component.

Which of the above statements are correct?

a) 1 and 2

b) 2 and 3

c) 1 and 4

d) 3 and 4

Answer: c

Explanation: Transverse contact ratio may not be equal to axial contact ratio. Larger contact ratio means sharing of multiple teeth.

7. A worm gear set is designed to have pressure angle of 30 0 which is equal to the helix angle. The efficiency of the worm gear set at an interface friction of 0.05 is

a) 87.9%

b) 77.9%

c) 67.9%

d) 57.9%

Answer: a

Explanation: ȵ = tanλɸ/cosɸtanλ + μ

tanλ = -μ + √1 + μ 2

tanλ = - + √1 +  2

tanλ = 0.9512

ȵ = 89.1%

So most suitable option is ‘a’.

8. The use of straight or curved external gear teeth in mesh with internal teeth in gear and spline couplings is specifically employed accommodate

a) torsional misalignment

b) parallel misalignment

c) angular misalignment

d) substantial axial movements between shafts

Answer: c

Explanation: Straight or curved external gear teeth are used to correct the angular misalignment.

9. A planetary gear train is gear train having

a) a relative motion of axes and the axis of at least one of the gears also moves relative to the frame

b) no relative motion of axes and no relative motion of axes with respect to the frame

c) no relative motion of axes and the axis of at least one of the gears also moves relative to the frame

d) a relative motion of axes and none of the axes of gears has relative motion with the frame

Answer: a

Explanation: Planetary gear train ensures the relative motion of at least one axis w.r.t. the frame.

Answer: d

Explanation: T = w cosɸ x d/2

6000 = 50000 x 0.94 x d/2

d = 0.25 m.

This set of Machine Kinematics Assessment Questions and Answers focuses on “Standard Spur Gears – 2”.

1. A spur gear of 40 teeth is machined in a gear hobbing machine using a double start hob cutter. The speed ratio between the hob and the blank is

a) 1:20

b) 1:40

c) 40:1

d) 20:1

Answer: d

Explanation: None.

2. A helical gear has the active face width equal to b pitch p and helix angle α. What should be the minimum value of b in order that contact is maintained across the entire active face of the gear?

a) p cosα

b) p secα

c) p tanα

d) p cotα

Answer: d

Explanation: b > p/tanα

b > p cotα.

3. Match the type of gears with their most appropriate description.

Type of gear Description

P. Helical 1. Axes non parallel and intersecting

Q. Spiral 2. Axes parallel and teeth are inclined to the axis

R. Hypoid 3. Axes parallel and teeth are parallel to the axis

S. Rack and pinion 4. Axes are perpendicular and intersecting,and teeth are inclined to the axis

5. Axes are perpendicular and used for large speed reduction

6. Axes parallel and one of the gears has infinite radius

a) P-2, Q- 4, R- 1, S- 6

b) P-1, Q- 4, R- 5, S- 6

c) P-2, Q- 6, R- 4, S- 2

d) P-6, Q- 3, R- 1, S- 5

Answer: a

Explanation: Helical – Axes parallel and teeth are inclined to the axis

Spiral – Axes are perpendicular and intersecting,and teeth are inclined to the axis

Hypoid – Axes non parallel and intersecting

Rack and pinion – Axes parallel and one of the gears has infinite radius.

4. Tooth interference in an external in volute spur gear pair can be reduced by

a) Decreasing center distance between gear pair

b) Decreasing module

c) Decreasing pressure angle

d) Increasing number of gear teeth

Answer: d

Explanation: There are several ways to avoid interfering:

i. Increase number of gear teeth

ii. Modified involutes

iii. Modified addendum

iv. Increased centre distance .

5. Interference in a pair of gears is avoided, if the addendum circles of both the gears intersect common tangent to the base circles within the points of tangency.

a) True

b) False

Answer: a

Explanation: None.

6. Twenty degree full depth involute profiled 19-tooth pinion and 37-tooth gear are in mesh. If the module is 5 mm, the centre distance between the gear pair will be

a) 140 mm

b) 150 mm

c) 280 mm

d) 300 mm

Answer: a

Explanation: Centre distance = D 1 + D 2 /2 = mT 1 + mT 2 /2 = 5/2

= 140 mm.

7. If the drive efficiency is 80%, then torque required on the input shaft to create 1000 N output thrust is

a) 20 Nm

b) 25 Nm

c) 32 Nm

d) 50 Nm

Answer: b

Explanation: Module m = 2,

D/T = 2

∴ D = 80 × 2 = 160 mm

2F = 1000, or F = 500 N

Let T 1 be the torque applied by motor.

TT 2 be the torque applied by gear.

∴ Power transmission = 80%

Now, T 1 ω 1 2 x ω 2 /0.8

T 1 = 25 N-m.

8. If the pressure angle of the rack is 20°, then force acting along the line of action between the rack and the gear teeth is

a) 250 N

b) 342 N

c) 532 N

d) 600 N

Answer: c

Explanation: Pcos φ = F

∴ Force acting along the line of action,

P = F/cos φ

= 500/cos20°

= 532 N.

9. Two mating spur gears have 40 and 120 teeth respectively. The pinion rotates at 1200 rpm and transmits a torque of 20 Nm. The torque transmitted by the gear is

a) 6.6 Nm

b) 20 Nm

c) 40 Nm

d) 60Nm

Answer: d

Explanation: We know, N 1 /N 2 = T 1 /T 2

N 1 = speed of pinion

N 2 = speed of gear wheel

T 1 = number of teeth of gear

T 2 = number of teeth of pinion

1200/N 2 = 120/40

N 2 = 400 r.p.m.

Since power transmitted by both gear will be equal

T 1 ω 1 2 x ω 2

torque transmitted by gear, = 60 N-m.

Answer: b

Explanation: Centre distance = D 1 + D 2 /2 = mT 1 + mT 2 /2

= m/2(T 1 + T 2 )

= 2/2 x 99 = 99 mm.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Length Of Arc of Contact”.

1. If the centre distance between a pair of spur gears in mesh is 240 mm and the pinion moves five times faster than the gear, then the pitch circle diameters of pinion and gear respectively are

a) 40mm and 200 mm

b) 80mm and 400 mm

c) 60mm and 300 mm

d) 50mm and 250 mm

Answer: b

Explanation: r p + r g = 240

r p /r g = 5

r g = 200 mm, d g = 400 mm

r p = 40 mm, d p = 80 mm.

2. Pressure angle of involute gears does not exceed 25 0 , since

a) this will lead to unwanted radial force

b) the number of teeth to avoid undercutting will be very high

c) no cutters are available

d) gear will become too small

Answer: a

Explanation: Pressure angle of involute gears does not exceed 25 0 , since Gear is curved.

3. Worm and worm wheel drive can be reversible.

a) True

b) False

Answer: a

Explanation: If friction angle > lead angle we cannot determine whether drive is reversible or not.

4. Two involute gears are designed to mesh for a given centre distance and a given angular velocity ratio . During assembly, the centre distance has increased slightly. Then which of the following changes occur?

 Velocity ratio changes

 Pressure angle changes

 Pitch circle diameter changes

 Working depth changes

 Base circle radius changes

Select the correct answer using the code given below.

a) 1, 2 and 3

b) 2, 3 and 4

c) 2 and 5

d) 3 and 5

Answer: b

Explanation: When Centre to centre distance increases then pressure angle, depth, pitch circle diameter changes. Velocity ratio and base circle radius will remain same.

5. Which of the following statements are correct for mating gears with involute profiles?

 The pressure angle, from the start of the engagement to the end of the engagement, remains constant.

 The pressure angle is maximum at the beginning of the engagement, reduces to zero at pitch point, starts decreasing and again becomes maximum at the end of the engagement.

 The face and flank of the teeth are generated by a single curve and the normal to this curve at any point is tangent to the base circle of the gear.

 The centre distance for a pair of mating gears can be varied within limits without altering the velocity ratio.

Select the correct answer using the code given below.

a) 1, 3 and 4

b) 1 and 3 only

c) 2 and 4 only

d) 2,3 and 4

Answer: a

Explanation: The pressure angle varies only for cycloidal gears.

6. The velocity ratio in the case of the compound train of wheels is equal to

a) No. of teeth on first driver/No.of teeth on last follower

b) No. of teeth on last follower/No.of teeth on first driver

c) Product of teeth on the drivers/Product of teeth on the followers

d) Product of teeth on the followers/Product of teeth on the drivers

Answer: c

Explanation: In compound trains, velocity ratio = Product of teeth on the drivers/Product of teeth on the followers.

7. Match list I with list II

List I List II

A. Compound train 1. Hart mechanism

B. Quick return mechanism 2. Coriolis force

C. Exact straight line motion 3. Transmission of motion around bends and corners

D. Approximate straight line motion 4. Watt mechanism

a) A-1,B-2,C-3,D-4

b) A-3,B-2,C-1,D-4

c) A-3,B-4,C-1,D-2

d) A-1,B-4,C-3,D-2

Answer: b

Explanation: Compound train – Transmission of motion around bends and corners

Quick return mechanism – Coriolis force

Exact straight line motion – Hart mechanism

Approximate straight line motion – Watt mechanism.

8. Consider the following statements:

When two gears are meshing, the clearance is given by the

1. difference between dedendum of one gear and addendum of the mating gear.

2. difference between total and the working depth of a gear tooth.

3. distance between the bottom land of one gear and the top land of the mating gear.

4. difference between the radii of the base circle and the dedendum circle.

Which of these statements are correct?

a) 1,2 and 3

b) 2,3 and 4

c) 1,3 and 4

d) 1,2 and 4

Answer: d

Explanation: the clearance can be found by following points 1,2 and 4.

9. In a simple gear train, if the number of idler gears is odd, then the direction of motion of driven gear will

a) be same as that of the driving gear

b) be opposite to that of the driving gear

c) depend upon the number of teeth on the driving gear

d) depend upon the total number of teeth on all gears of the train

Answer: a

Explanation: In case of odd number of gears in a simple gear train, then the direction of motion of driven gear will be same as that of driving gear.

Answer: a

Explanation: T A ω A = T B ω B

50 x 100 = T B x 250

or, T B = 20 kNm

Torque on C will be same as on B but in inverse direction.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Reverted Gear Train”.

1. Gearing contact is which one of the following?

a) Sliding contact

b) Sliding contact, only rolling at pitch point

c) Rolling contact

d) Rolling and sliding at each point of contact

Answer: b

Explanation: When pair of teeth touch at the pitch point ,they have for the instant pure rolling action. At any other position they have the sliding action.

2. An external gear with 60 teeth meshes with a pinion of 20 teeth, module being 6 mm. What is the centre distance in mm?

a) 120

b) 180

c) 240

d) 300

Answer: c

Explanation: Centre distance in mm = m/2 (T 1 + T 2 )

= 6/2 

= 240 mm

3. Which one of the following is true for involute gears?

a) Interference is inherently absent

b) Variation in centre distance of shafts increases radial force

c) A convex flank is always in contact with concave flank

d) Pressure angle is constant throughout the teeth engagement

Answer: d

Explanation: For involute gears, the pressure angle is constant throughout the teeth engagement.

4. In involute gears the pressure angle is

a) Dependent on the size of teeth

b) dependent on the size of gears

c) Always constant

d) always variable

Answer: c

Explanation: The pressure angle is always constant in involute gears.

5. Consider the following statements:

1. A stub tooth has a working depth larger than that of a full-depth tooth.

2. The path of contact for involute gears is an arc of a circle.

Which of the statements given above is/are correct?

a) Only 1

b) Only 2

c) Both 1 and 2

d) Neither 1 nor 2

Answer: d

Explanation: 1. A stub tooth has a working depth lower than that of a full-depth tooth.

2. The path of contact for involute gears is a line.

6. Consider the following statements regarding the choice of conjugate teeth for the profile of mating gears:

1. They will transmit the desired motion

2. They are difficult to manufacture.

3. Standardisation is not possible

4. The cost of production is low.

Which of these statements are correct?

a) 1, 2 and 3

b) 1, 2 and 4

c) 2, 3 and 4

d) 1, 3 and 4

Answer: a

Explanation: Cost of production of conjugate teeth, being difficult to manufacture is high.

7. Common contact ratio of a pair of spur pinion and gear is

a) Less than 1·0

b) Equal to 1

c) Between 2 and 3

d) Greater than 3

Answer: c

Explanation: The ratio of the length of arc of contact to the circular pitch is known as contact ratio i.e. number of pairs of teeth in contact. The contact ratio for gears is greater than one. Contact ratio should be at least 1.25. For maximum smoothness and quietness, the contact ratio should be between 1.50 and 2.00. High-speed applications should be designed with a face-contact ratio of 2.00 or higher for best results.

8. In gears, interference takes place when

a) The tip of a tooth of a mating gear digs into the portion between base and root circles

b) Gears do not move smoothly in the absence of lubrication

c) Pitch of the gear is not same

d) gear teeth are undercut

Answer: a

Explanation: In gears, interference takes place when the tip of a tooth of a mating gear digs into the portion between base .and root circle.

9. Consider the following characteristics:

1. Small interference

2. Strong tooth.

3. Low production cost

4. Gear with small number of teeth.

Those characteristics which are applicable to stub 20° involute system would include

a) 1 alone

b) 2, 3 and 4

c) 1, 2 and 3

d) 1, 2, 3 and 4

Answer: b

Explanation: Involute system is very interference prone.

Answer: a

Explanation: Power transmitted = Force × Velocity

Force = 10 x 10 3 /10

= 1000 N/m

Torque Transmitted = Force x diameter/2

= 1000 x 1/2

= 500 N-m

= 0.5 kN-m

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Contact Ratio”.

1. The tooth profile most commonly used in gear drives for power transmission is

a) A cycloid

b) An involute

c) An ellipse

d) A parabola

Answer: b

Explanation: It is due to easy manufacturing.

2. There are six gears A, B, C, D, E, F in a compound train. The numbers of teeth in the gears are 20, 60, 30, 80, 25 and 75 respectively. The ratio of the angular speeds of the driven  to the driver  of the drive is

a) 1/24

b) 1/8

c) 4/15

d) 12

Answer: a

Explanation: The ratio of angular speeds of F to A = T A .T C .T E /T B .T D .T F

= 20 x 30 x 25/60 x 80 x 75

= 1/24.

3. A fixed gear having 100 teeth meshes with another gear having 25 teeth, the centre lines of both the gears being joined by an arm so as to form an epicyclic gear train. The number of rotations made by the smaller gear for one rotation of the arm is

a) 3

b) 4

c) 5

d) 6

Answer: c

Explanation: Revolution of 25 teeth gear = 1 + T 100 /T 25

= 1 + 100/25 =5.

4. Speed reduction in a gear box is achieved using a worm and worm wheel. The worm wheel has 30 teeth and a pitch diameter of 210 mm. If the pressure angle of the worm is 20 o , what is the axial pitch of the worm?

a) 7 mm

b) 22 mm

c) 14 mm

d) 63 mm

Answer: b

Explanation: m = 210/30 = 7

P = πm = 22/7 x 7

= 22 mm

Axial pitch = circular pitch of the worm wheel = πm.

5. A speed reducer unit consists of a double-threaded worm of pitch = 11 mm and a worm wheel of pitch diameter = 84 mm. The ratio of the output torque to the input to rque is

a) 7·6

b) 12

c) 24

d) 42

Answer: a

Explanation: Output torque/Input torque = pitch diameter of worm wheel/ pitch of worm

= 84/11

= 7.6.

6. A pair of gears forms a rolling pair.

a) True

b) False

Answer: b

Explanation: In rolling pair one link rolls over another fixed link.

7. Spiral bevel gears designed to be used with an offset in their shafts are called ‘hypoid gears’

a) True

b) False

Answer: a

Explanation: The pitch surfaces of such gears are hyperboloids of revolution.

8. Gears with involute tooth profile transmit constant velocity ratios between shafts connected by them.

a) True

b) False

Answer: a

Explanation: For involute gears, the common normal at the point of contact between pairs of teeth always passes through the pictch point.

9. In the case of spur gears, the mating teeth execute pure rolling motion with respect to each other from the commencement of engagement to its termination.

a) True

b) False

Answer: a

Explanation: The involute profiles of the mating teeth are conjugate profiles which obey the law of gearing.

10. A pair of helical gears has fewer teeth in contact as compared to an equivalent pair of spur gears.

a) True

b) False

Answer: b

Explanation: In spur gears, the contact between meshing teeth occurs along the entire face width of the tooth, resulting in a sudden application of the load which, in turn, results in impact conditions and generates noise.

This set of Machine Kinematics Multiple Choice Questions & Answers  focuses on “Interference”.

1. Which of the following is a disadvantage of involute gears?

a) Occurrence of interference

b) Non occurrence of interference

c) Pressure angle remains constant

d) Face and flank are generated by single curve

Answer: a

Explanation: The disadvantage of the involute teeth is that the interference occurs. This may be avoided by altering the heights of addendum and dedendum of the mating teeth.

2. By changing the angle of obliquity of the teeth, interference can be avoided.

a) True

b) False

Answer: a

Explanation: Interference can be avoided by changing the obliquity of the teeth or alternatively altering the height of the addendum. Failure to do so will result in the occurrence of interference.

3. The phenomenon when the tip of tooth undercuts the root on its mating gear is known as _______

a) Involution

b) Interference

c) Cycloidal motion

d) Undercutting

Answer: a

Explanation: The phenomenon when the tip of tooth undercuts the root on its mating gear is known as interference. This is generally observed in involute profiles.

4. In which of the following gears, interference occurs?

a) Cycloidal

b) Involute

c) Epi cycloidal

d) Hypo-cycloidal

Answer: b

Explanation: Interference occurs in involute gears which is one of its disadvantages amongst many advantages. This happens when the pinion has a low number of teeth.

5. For the same pitch, which of the following statement is true?

a) Cycloidal gears are stronger than involute gears

b) Involute gears are stronger than cycloidal gears

c) Both cycloidal and Involute gears have equal strength

d) Cycloidal gears are stronger for lower pitch only

Answer: a

Explanation: Cycloidal teeth have wider flanks, as a consequence the cycloidal gears are stronger than the involute gears, provided the pitch is the same. That is why cycloidal gears are used for cast teeth.

6. If the point of contact between the two teeth is always on the involute profiles of both the teeth, then which of the phenomenon will occur?

a) Avoidance of interference

b) Occurrence of interference

c) Increase in length of path of contact

d) Increase in length of arc of contact

Answer: a

Explanation: The interference may only be avoided, if the point of contact between the two teeth is always on the involute profiles of both the teeth.

7. Given,

Involute profile teeths of mating gear: 20 and 40

Pressure angle = 20°

module = 10mm

The constraint: The addendum on each wheel is to be made of such a length that the line of contact on each side of the pitch point has half the maximum possible length.

Find the addendum height for the larger gear wheel in mm.

a) 6.5

b) 6

c) 6.8

d) 7

Answer: a

Explanation: r = m.t/2 = 100mm

R = 200mm

Using the constraint we find that

Ra = 206.5mm

Therefore

Addendum height = 6.5mm.

8. Given:

Involute profile teeths of mating gear: 20 and 40

Pressure angle = 20°

module = 10mm

The constraint: The addendum on each wheel is to be made of such a length that the line of contact on each side of the pitch point has half the maximum possible length.

Find the addendum height for the smaller gear wheel in mm.

a) 6.4

b) 6.2

c) 6.3

d) 6

Answer: b

Explanation: r = m.t/2 = 100mm

R = 200mm

Using the constraint we find that

ra = 106.2mm

Therefore

Addendum height = 6.2mm.

9. Given:

Involute profile teeths of mating gear: 20 and 40

Pressure angle = 20°

module = 10mm

The constraint: The addendum on each wheel is to be made of such a length that the line of contact on each side of the pitch point has half the maximum possible length.

Find the length of path of contact in mm.

a) 56.4

b) 56.2

c) 56.3

d) 51.3

Answer: d

Explanation: r = m.t/2 = 100mm

R = 200mm

We know that length of path of contact = sinΦ/2

= 51.3mm.

10. Given:

Involute profile teeths of mating gear: 20 and 40

Pressure angle = 20°

module = 10mm

The constraint: The addendum on each wheel is to be made of such a length that the line of contact on each side of the pitch point has half the maximum possible length.

Find the length of arc of contact in mm.

a) 56.4

b) 54.6

c) 56.3

d) 51.3

Answer: b

Explanation: r = m.t/2 = 100mm

R = 200mm

We know that length of path of contact = sinΦ/2

= 51.3mm

Arc of contact = length of path of contact / cosΦ

= 54.6mm.

11. Given:

Involute profile teeths of mating gear: 20 and 40

Pressure angle = 20°

module = 10mm

The constraint: The addendum on each wheel is to be made of such a length that the line of contact on each side of the pitch point has half the maximum possible length.

Find the contact ratio.

a) 1.23

b) 1.52

c) 1.74

d) 1.97

Answer: c

Explanation: r = m.t/2 = 100mm

R = 200mm

We know that length of path of contact = sinΦ/2

= 51.3mm

Pitch = πx10 = 31.42

Contact ratio = length of path of contact/pitch

= 1.74.

This set of Machine Kinematics Puzzles focuses on “Path of Contact”.

1. Which of the following is a commonly used pressure angle in gears?

a) 20

b) 10

c) 12

d) 17

Answer: a

Explanation: The pressure angle is the angle between the tangent to the pitch circles and the line drawn normal  to the surface of the gear teeth. It has a set of standard values which is accepted globally, 20° is one of them.

2. Addendum circle of the gear wheel has the shortest radius.

a) True

b) False

Answer: b

Explanation: Addendum circle of the gear wheel has the largest radius, the base circle has the smallest radius. Addendum of the gear plays a vital role in determining whether interference will take place or not.

3. Which of the following is true for Length of arc of contact?

a) Sum of Arc of recess and Arc of approach

b) Difference of arc of approach and arc of recess

c) Twice the arc of approach

d) Twice the arc of recess

Answer: a

Explanation: The arc of contact is given by the sum of Length of arc of approach and length of arc of recess. Numerically it is the ratio of length of path of contact and the cosine of the pressure angle.

4. Which of the following is true for Length of path of contact?

a) Sum of path of recess and path of approach

b) Difference of path of approach and path of recess

c) Twice the arc of approach

d) Twice the path of recess

Answer: a

Explanation: The path of contact is given by the sum of Length of path of approach and length of path of recess. Numerically it is dependent on pitch radius, addendum radius and the sine of pressure angle.

5. From the following data, find the addendum in mm:

Teeth on each wheel: 40

Pressure angle: 20°

Module: 6mm

Arc of contact/ pitch: 1.75

a) 6.12

b) 6.51

c) 6.61

d) 6.81

Answer: a

Explanation: Pc = πm = 18.85mm

Arc of contact = 1.75xp = 33mm

Length of path of contact = cosΦx Arc of contact

From another relation of length of path of contact we get

Ra = 126.12 mm

R = 120mm

Therefore addendum = 6.12mm.

6. From the following data:

Teeth on pinion: 30

Teeth on gear: 80

Pressure angle: 20°

Module: 12mm

Addendum: 10mm

Find the length of path of contact in mm.

a) 52.3

b) 55.4

c) 53.2

d) 54.5

Answer: a

Explanation: R = mT/2 = 480mm

r = mt/2 = 180mm

Addendum radius of pinion = 190mm

Addendum radius of gear = 490mm

Using the relation for length of path of approach

We get path of approach = 27.3mm

Path of recess = 25mm

adding both we get total length of path of contact

= 52.3mm.

7. From the following data:

Teeth on pinion: 30

Teeth on gear: 80

Pressure angle: 20°

Module: 12mm

Addendum: 10mm

Find the length of arc of contact in mm.

a) 52.333

b) 55.66

c) 53.22

d) 54.55

Answer: b

Explanation: R = mT/2 = 480mm

r = mt/2 = 180mm

Addendum radius of pinion = 190mm

Addendum radius of gear = 490mm

Using the relation for length of path of approach

We get path of approach = 27.3mm

Path of recess = 25mm

adding both we get total length of path of contact

= 52.3mm

Length of arc of contact = length of path of contact / cosΦ

= 55.66mm.

8. Maximum sliding velocity is the sum of angular velocities and its product with the length of path of contact.

a) True

b) False

Answer: b

Explanation: Maximum sliding velocity is the sum of angular velocities and its product with the length of path of appraoch.

Vs = (ω 2 + ω 1 )x.

9. From the following data:

Teeth on pinion: 30

Teeth on gear: 80

Pressure angle: 20°

Module: 12mm

Addendum: 10mm

Find the contact ratio.

a) 1.5

b) 1.75

c) 2

d) 1,33

Answer: b

Explanation: R = mT/2 = 480mm

r = mt/2 = 180mm

Addendum radius of pinion = 190mm

Addendum radius of gear = 490mm

Using the relation for length of path of approach

We get path of approach = 27.3mm

Path of recess = 25mm

adding both we get total length of path of contact

= 52.3mm

Length of arc of contact = length of path of contact / cosΦ

Contact ratio = Length of arc of contact/Pc

=1.75.

10. Find maximum sliding velocity in cm/s from the given data

addendum = 1 module = 5mm

Pitch line speed = 1.2m/s

Pressure angle of involute profile: 20 degrees

Tp = 20

Gear ratio = 2

a) 45.5

b) 46.8

c) 45.1

d) 47.2

Answer: a

Explanation: We know that

V = ω 1 r = ω 2 R

120/ = ω 1

ω 1 = 24 rad/s

similarly

ω 2 = 12 rad/s

Now maximum sliding velocity = (ω 2 + ω 1 )x

= 455.4 mm/s

= 45.5 cm/s.