Category: Machine Kinematics Objective Questions

Machine Kinematics Multiple Choice Questions 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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 (52 – 50) = 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
Clarification: 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?
(i) V-belts are used at the high-speed end.
(ii) V-belts are used at the low-speed end.
(iii) V-belts are of standard lengths.
(iv) 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
Clarification: Advantages of V -belts
V-belts are used at the high-speed end.
(i) V-belts are used at the high-speed end.
(ii) V-belts are of standard lengths.
(iii) 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
Clarification: 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.

8. In order to have a good grip on the pulley, the V-belt should touch the bottom of the groove in the pulley.
a) True
b) False
Answer: b
Clarification: 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.

Machine Kinematics Multiple Choice Questions 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
Clarification: When equal bevel gears (having equal teeth and equal pitch angles) 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
Clarification: 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
Clarification: 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
Clarification: 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 (T) is
a) 1/sin θ
b) 1/cos θ
c) 1/tan θ
d) sin θ cos θ
Answer: b
Clarification: (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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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.

10. The axial thrust on the worm (W_A) is given by
a) W_A = W_T . tan φ
b) W_A = W_T / tan φ
c) W_A = W_T . tan λ
d) W_A = W_T / tan λ
Answer: d
Clarification: 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.

Machine Kinematics Multiple Choice Questions 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
Clarification: 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
Clarification: At mean the value of x = 0. Therefore, it is maximum at mean position.
V_max = ω.r.

3. The velocity of a particle (v) moving with simple harmonic motion, at any instant is given by
a) ω √r² − x²
b) ω √x² − r²
c) ω² √r² − x²
d) ω²√x² − r²
Answer: a
Clarification: Velocity of any particle v_N = vsinθ = ω.rsinθ = ω √r² − x².

4. The maximum acceleration of a particle moving with simple harmonic motion is
a) ω
b) ω.r
c) ω².r
d) ω²/r
Answer: c
Clarification: Acceleration, a_N = ω².rcosθ = ω².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
Clarification: 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
Clarification: 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/k²_G +h²
b) 1/2π √k²_G +h²/g.h
c) 2π√g.h/k²_G +h²
d) 2π√k²_G +h²/g.h
Answer: a
Clarification: 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/k²_G +h²
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/ k²_G +h²
b) k²_G +h²/h
c) h²/k²_G +h²
d) k²_G +h²/h²
Answer: b
Clarification: By comparing the frequencies of simple pendulum to compound pendulum we get the equivalent length of simple pendulum as k²_G +h²/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) h²/k_G
d) k²_G/h
Answer: d
Clarification: 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 k²_G/h. The distance between the centre of suspension and the centre of percussion is equal to the equivalent length of a simple pendulum.

10. The frequency of oscillation of a torsional pendulum is
a) 2πk_G/r √g/I
b) r/2πk_G√g/I
c) 2πk_G/r√I/g
d) r/2πk_G√I/g
Answer: b
Clarification: None.

Machine Kinematics Multiple Choice Questions on “Mechanism – 1”.

1. A type-writer constitutes a machine.
a) True
b) False
Answer: b
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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 (n) of a mechanism having plane motion is
a) n = (l – 1) – j
b) n = 2(l – 1) – 2j
c) n = 3(l – 1) – 2j
d) n = 4(l – 1) – 3j
Answer: c
Clarification: None

8. The mechanism forms a structure, when the number of degrees of freedom (n) is equal to
a) 0
b) 1
c) 2
d) -1
Answer: a
Clarification: 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
Clarification: Four bar chain or quadric cycle chain consists of four links, each of them forms a turning pair.

10. The mechanism in which two are turning pairs and two are sliding pairs, is called a
a) double slider crank chain
b) elliptical trammel
c) scotch yoke mechanism
d) all of the mentioned
Answer: d
Clarification: 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

Machine Kinematics Multiple Choice Questions 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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
Clarification: 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.