Category: Machine Kinematics Objective Questions

Machine Kinematics Multiple Choice Questions 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(n – 1) – 2j
B. Displacement relation of Hook’e joint 2. x = R[ (1 – cosϴ) + sin²ϴ/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
Clarification: 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(n – 1) – 2j
Displacement equation of reciprocating engine piston – x = R[ (1 – cosϴ) + sin²ϴ/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
Clarification: Only statement 1 is correct.

3.The speed of driving shaft of a Hooke’s Joint of angle 19.5⁰ 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
Clarification: N_max = N/cosα = 500/cos19.5⁰ = 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: Slider crank chain often finds applications in most of the reciprocating machinery.

9. f = 3 (n – 1) – 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
Clarification: None.

10. Which of the following are examples of forced closed kinematic pairs?
1. Cam and roller mechanism
2. Door closing mechanism
3. Slider crank mechanism
4. Automotive clutch operating mechanism
Select the correct answer using the codes given below:
a) 1,2 and 4
b) 1 and 3
c) 2,3 and 4
d) 1,2,3 and 4
Answer: c
Clarification: Except statement 1 all are examples of forced closed kinematic pairs.

Machine Kinematics Multiple Choice Questions 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
Clarification: 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
Clarification: 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
Clarification: 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(α − φ)/tanα
b) tanα/tan (α − φ)
c) tan(α + φ)/tanα
d) tanα/tan (α + φ)
Answer: d
Clarification: Efficiency, η = Ideal effort/Actual effort = tanα/tan (α + φ).

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 (μ) is
a) μ > tan α
b) μ = sin α
c) μ = cot α
d) μ = cosec α
Answer: a
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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.

10. 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
Clarification: 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.

Machine Kinematics Multiple Choice Questions 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
Clarification: 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
Clarification: 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
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.
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
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.

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
Clarification: 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 (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.
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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: Working depth is twice of addendum and whole depth is sum of addendum and dedendum.

10. Tooth thickness on pitch line of involute gear in terms of module (m) is equal to
a) 1.157 m
b) 1.167 m
c) 2 m
d) 1.5708
Answer: d
Clarification: Tooth thickness = 1.5708 x module.

Machine Kinematics Multiple Choice Questions 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
Clarification: 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
Clarification: Centre distance in mm = m/2 (T₁ + T₂)
= 6/2 (60 + 20)
= 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: Involute system is very interference prone.

10. A spur gear transmits 10 kW at a pitch line velocity of 10 m/s; driving gear has a diameter of 1.0 m. Find the tangential force between the driver and the follower, and the transmitted torque respectively.
a) 1 kN and 0.5 kN-m
b) 10 kN and 5 kN-m
c) 0.5 kN and 0.25 kN-m
d) 1 kN and 1 kN-m
Answer: a
Clarification: Power transmitted = Force × Velocity
Force = 10 x 10³/10
= 1000 N/m
Torque Transmitted = Force x diameter/2
= 1000 x 1/2
= 500 N-m
= 0.5 kN-m

Machine Kinematics Interview Questions and Answers on “Linear Velocity – 2”.

1. The unit of linear acceleration is
a) kg-m
b) m/s
c) m/s²
d) rad/s²
Answer: c
Clarification: Linear acceleration, a = dv/dt
unit of dv = m/s
and dt = s
therefore, dv/dt = m/s²

2. The angular velocity (in rad/s) 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
Clarification: 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 (omega). 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) ω².r
d) ω²/r
Answer: a
Clarification: 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
Clarification: When a particle moves along a straight path, then the radius of curvature is infinitely great. This means that v²/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
Clarification: 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
Clarification: 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
Clarification: 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.

8. When the motion of a body is along a curved path, it is called
a) translatory motion
b) plane motion
c) culvilinear motion
d) none of the mentioned
Answer: b
Clarification: 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.