Category: Machine Kinematics Objective Questions

Machine Kinematics test 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: None

9. An automobile steering gear is an example of
a) sliding pair
b) rolling pair
c) lower pair
d) higher pair
Answer: c
Clarification: None

10. A pair is said to be kinematic pair, if the relative motion between them is completely or successfully constrained.
a) True
b) False
Answer: a
Clarification: 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.

To practice all areas of Machine Kinematics for tests,

Machine Kinematics Multiple Choice Questions 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 90⁰ 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
Clarification: 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
Clarification: None.

3. The magnitude of tangential acceleration is equal to
a) velocity² x crank radius
b) velocity²/ crank radius
c) (velocity/ crank radius)²
d) velocity x crank radius²
Answer: b
Clarification: The magnitude of tangential acceleration is equal to velocity²/ 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
Clarification: 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
Clarification: The magnitude of tangential acceleration is equal to velocity²/ 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/sec²
b) 250m/sec²
c) 1000m/sec²
d) 2000m/sec²
Answer: a
Clarification: Corioli’s component = 2Vω
= 2 x 10 x 25 = 500500m/sec².

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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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 90⁰
b) lags the sliding velocity vector by 90⁰
c) is along the sliding velocity vector by 90⁰
d) leads the sliding velocity vector by 180⁰
Answer: a
Clarification: 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
Clarification: None.

15. Klein’s construction is useful to determine
a) velocity of various parts
b) acceleration of various parts
c) displacement of various parts
d) angular acceleration of various parts
Answer: b
Clarification: Klien’s construction can be used to determine acceleration.

Machine Kinematics Multiple Choice Questions 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
Clarification: Consider that a body A of weight (W) 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 (α – φ)
b) P = W tan (α + φ)
c) P = W cos (α – φ)
d) P = W cos (α + φ)
Answer: b
Clarification: 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 (α + φ)
where α = Helix angle, and
φ = Angle of friction.

3. The efficiency of a screw jack is given by
a) tan (α + φ)/tan α
b) tan α / tan (α + φ)
c) tan (α − φ)/ tan α
d) tan α/ tan (α − φ)
Answer: b
Clarification: Efficiency, η = Ideal effort/ Actual effort
= P₀ / P
= W tanα/ W tan(α + φ)
= tan α / tan (α + φ).

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
Clarification: 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
Clarification: The efficiency of a screw jack is maximum when sin (2α + φ) 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
Clarification: Maximum efficiency, η_max = sin (90º – φ + φ) – sinφ/sin (90º – φ + φ) + 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: A Hooke’s joint is used to connect two shafts, which are intersecting at a small angle.

Machine Kinematics Question Bank 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
Clarification: 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
Clarification: 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
Clarification: None.

4. The ratio of driving tensions for rope drive is same as that of V-belt drive.
a) True
b) False
Answer: a
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: None.

8. A pulley is connected to a power transmission shaft of diameter d by means of a rectangular sunk key of width w and length l. The width of the key is taken as d/4. For full power transmission, the shearing strength of the key is equal to the torsional shearing strength of the shaft. The ratio of the length of the key to the diameter of the shaft (l/d) is
a) п/4
b) п/6
c) п/2
d) п
Answer: a
Clarification: п/16 x s_s x d³ = l x d/4 x s_s x d/2
or, l/d = п/2.

To practice Machine Kinematics Question Bank,

Machine Kinematics Problems 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 20⁰ full depth involute teeth will be
a) 12
b) 14
c) 18
d) 24
Answer: c
Clarification: The minimum number of teeth on the pinion in order to avoid interference for 14.5⁰ full depth involute are 32 and for 20⁰ 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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) (r² + R²) cosɸ/2
b) (r² + R²) sinɸ/2
c) (r + R) cosɸ/2
d) (r + R) sinɸ/2
Answer: d
Clarification: None.

7. The maximum efficiency of spiral gears is
a) sin (ϴ + ɸ) + 1/cos(ϴ – ɸ) +1
b) cos(ϴ – ɸ) +1/sin (ϴ + ɸ) + 1
c) cos (ϴ + ɸ) + 1/cos(ϴ – ɸ) +1
d) cos(ϴ – ɸ) +1/cos (ϴ + ɸ) + 1
Answer: c
Clarification: The maximum efficiency of spiral gears is
cos (ϴ + ɸ) + 1/cos(ϴ – ɸ) +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
Clarification: 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
Clarification: The speed ratio (or velocity 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
Clarification: The speed ratio (or velocity 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
Clarification: 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
Clarification: 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 (i.e. first driver) and the last gear (i.e. last driven or follower) 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
Clarification: When the axes of the first gear (i.e. first driver) and the last gear (i.e. last driven or follower) are co-axial, then the gear train is known as reverted gear train.

14. The gear train usually employed in clocks is a
a) simple gear train
b) reverted gear train
c) sun and planet gear
d) differential gear
Answer: b
Clarification: 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).

To practice all areas of Machine Kinematics Problems,

Advanced Machine Kinematics Questions and Answers 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
Clarification: Loss of kinetic energy during inelastic collision is given by
m₁m₂/(2(m₁+ m₂) (u₁² – u₂²)
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
Clarification: 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
Clarification: Loss of kinetic energy during inelastic collision with coefficient of restitution is given by
m₁m₂/(2(m₁+ m₂) (u₁² – u₂²)(1-e²))
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
Clarification: Common velocity during inelastic collision is given by
m₁u₁ + m₂u₂/(m₁+ m₂) = 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
Clarification: Velocity during elastic collision is given by
m₁u₁ + m₂u₂/(m₁+ m₂) = v
substituting the values we get
V = 2.5 m/s
v₁ = 2V – u₁
v₁ = 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: Velocity during elastic collision is given by
m₁u₁ + m₂u₂/(m₁+ m₂) = v
substituting the values we get
V = 2.5 m/s
v₂ = 2V – u₂
v₂ = 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
Clarification: Velocity during elastic collision is given by
m₁u₁ + m₂u₂/(m₁+ m₂) = v
substituting the values we get
V = 2.5 m/s
v₂ = 2(1+e)V – eu₂
v₂ = 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
Clarification: Velocity during elastic collision is given by
m₁u₁ + m₂u₂/(m₁+ m₂) = v
substituting the values we get
V = 2.5 m/s
v₁ = 2(1+e)V – eu₁
v₁ = 2.2 m/s.

12. Which of the following cases momentum is conserved?
a) Perfectly elastic collision
b) Inelastic collision with 0c) Perfectly inelastic collision
d) Momentum is always conserved
Answer: d
Clarification: 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 0c) Perfectly inelastic collision
d) Momentum is always conserved
Answer: a
Clarification: 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.

To practice advanced questions and answers on all areas of Machine Kinematics,