1. Instantaneous centre of a body rolling with sliding on a stationary curved surface lies
(a) at the point of contact
(b) on the common normal at the point of contact
(c) on the common tangent at the point of contact
(d) at the centre of curvature of the stationary surface
(1 Mark, 1992)

Ans: b
2. The number of degrees of freedom of a five link plane mechanism with five revolute pairs as shown in the figure is:
(a) 3
(b) 4
(c) 2
(d) 1
(2 Mark, 1993)

Ans: c
Number of links (l) = 5
Number of joints (j) = 5
Number of higher pairs (h) = 0
Degree of freedom (F) = 3(l – 1) – 2j – h
=> F = 3(5 – 1) – 2(5) – 0 = 2
3. Figure shows a quick return mechanism. The crank OA rotates clockwise uniformly. OA = 2 cm, OO’ = 4 cm. The ratio of time for forward motion to that for return motion is:
(a) 0.5
(b) 2.0
(c) \sqrt { 2 }
(d) 1
(2 Mark, 1995)

Ans: b
Here,\frac { \alpha }{ 2 } ={ cos }^{ 1 }\left( \frac { 2 }{ 4 } \right)
=> \frac { \alpha }{ 2 } ={ 60 }^{ 0 }
=> \alpha ={ 120 }^{ 0 }
Again, \beta ={ 360 }^{ 0 }{ 120 }^{ 0 }={ 240 }^{ 0 }
Now, Ratio of time for forward motion to that return motion = \frac { \beta }{ \alpha } =\frac { { 240 }^{ 0 } }{ { 120 }^{ 0 } } = 2
4. A rod of length 1 m is sliding in a corner as shown in figure. At an instant when the rod makes an angle of 60 degrees with the horizontal plane, the velocity of point A on the rod is 1 m/s. The angular velocity of the rod at this instant is
(a) 2 rad/s
(b) 1.5 rad/s
(c) 0.5 rad/s
(d) 0.75 rad/s
(2 Mark, 1996)

Ans: a
5. The cross head velocity (Vp) in the slider crank mechanism, for the position shown in the figure is:
(1 Mark, 1997)

Ans: b
6. Consider the triangle formed by the connecting rod and the crank of an IC engine as the two sides of the triangle. If the maximum area of this triangle occurs when the crank angle is 75°, the ratio of connecting rod length to crank radius is:
(a) 5
(b) 4
(c) 3.73
(d) 3
(1 Mark, 1998)

Ans: c
7. For the planar mechanism shown in Figure, select the most appropriate choice for the motion of link 2 when link 4 is moved upwards.
(a) Link 2 rotates clockwise
(b) Link 2 rotates counter – clockwise
(c) Link 2 does not move
(d) Link 2 motion cannot be determined
(1 Mark, 1999)

Ans: b
8. For the audio cassette mechanism shown in figure, where is the instantaneous centre of rotation (point) of the two spools?
(a) Point P lies to the left of both the spools but a infinity along the line joining A and H.
(b) Point P lies in between the two spools on the line joining A and H, such that PH =2AP.
(c) Point P lies to the right of both the spools on the line joining A and H, such that AH = HP.
(d) Point P lies at the intersection of the line joining B and C and the line joining G and F.
(2 Mark, 1999)

Ans: c
Data for Q.9 – 10 are given below.
The circular disc shown in its plan view in the figure rotates in a plane parallel to the horizontal plane about the point O at a uniform angular velocity ω. Two other points A and B are located on the line OZ at distances r_{A} and r_{B} from O respectively.
9. The velocity of point B with respect to point A is a vector of magnitude
(a) 0
(b) ω(r_{B} − r_{A} ) and direction opposite to the direction of motion of point B.
(c) ω(r_{B} − r_{A} ) and direction same as the direction of motion of point B.
(d) ω(r_{B} − r_{A} ) and direction being from 0 to Z.
(2 Mark, 2003)

Ans: c
10. The acceleration of point B with respect to point A is a vector of magnitude
(a) 0
(b) ω(r_{B}^{2} −r_{A}^{2} ) and direction same as the direction of motion of point B
(c) ω^{2}(r_{B} − r_{A} ) and direction opposite to the direction of motion of point B
(d) ω^{2}(r_{B} − r_{A} ) and direction being from Z to O.
(2 Mark, 2003)

Ans: d
11. In the figure shown, the relative velocity of link 1 with respect to link 2 is 12 m/sec. Link 2 rotates at a constant speed of 120 rpm. The magnitude of Coriolis component of acceleration of link 1 is
(a) 302 m/s^{2}
(b) 604 m/s^{2}
(c) 906 m/s^{2}
(d) 1208 m/s^{2}
(2 Mark, 2003)

Ans: a
12. 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 the single slidercrank chain
(1 Mark, 2003)

Ans: d
13. The lengths of the links of a 4bar linkage with revolute pairs only 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
(1 Mark, 2003)

Ans: a
14. For a mechanism shown below, the mechanical advantage for the given configuration is
(a) 0
(b) 0.5
(c) 1.0
(d) \infty
(1 Mark, 2004)

Ans: d
15. The figure below shows a planar mechanism with single degree of freedom. The instant center 24 for the given configuration is located at a position
(a) L
(b) M
(c) N
(d) \infty
(2 Mark, 2004)

Ans: d
16. Match the following.
(a) P2, Q3, R1, S4
(b) P3, Q2, R4, S1
(c) P4, Q1, R2, S3
(d) P4, Q3, R1, S2
(2 Mark, 2004)

Ans: c
17. Match the following with respect to spatial mechanisms.
(b) P5, Q4, R3
(c) P2, Q3, R1
(d) P4, Q5, R3
(2 Mark, 2004)

Ans: c
18. 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
(1 Mark, 2005)

Ans: c
Common Data for Questions 19, 20, 21:
An instantaneous configuration of a fourbar mechanism, whose plane is horizontal, is shown in the figure below. At this instant, the angular velocity and angular acceleration of link O_{2}A are ω = 8rad/s and α = 0, respectively, and the driving torque (τ) is zero. The link O_{2}A is balanced so that its center of mass falls at O_{2}.
19. Which kind of 4bar mechanism is O_{2}ABO_{4} ?
(a) Doublecrank mechanism
(b) Crankrocker mechanism
(c) Doublerocker mechanism
(d) Parallelogram mechanism
(2 Mark, 2005)

Ans: b
20. At the instant considered, what is the magnitude of the angular velocity of O_{4}B?
(a) 1 rad/s
(b) 3 rad/s
(c) 8 rad/s
(d) 64/3 rad/s
(2 Mark, 2005)

Ans: b
21. At the same instant, if the component of the force at joint A along AB is 30 N, then the magnitude of the joint reaction at O_{2}
(a) is zero
(b) is 30 N
(c) is 78 N
(d) cannot be determined from the given data
(2 Mark, 2005)

Ans: d
22. For a fourbar linkage in toggle position, the value of mechanical advantage is:
(a) 0.0
(b) 0.5
(c) 1.0
(d) \infty
(1 Mark, 2006)

Ans: d
23. The number of inversions for a slider crank mechanism is:
(a) 6
(b) 5
(c) 4
(d) 3
(1 Mark, 2006)

Ans: c
24. Match the items in columns I and II.
(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
(2 Mark, 2006)

Ans: b
25. Match the items in columns I and II.
(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
(2 Mark, 2006)

Ans: d
26. In a fourbar 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 \le P + Q
(b) S + L > P + Q
(c) S + P \le L + Q
(d) S + P > L + Q
(2 Mark, 2006)

Ans: a
27. The input link O_{2}P of a four bar linkage is rotated at 2 rad/s in counter clockwise direction as shown below. The angular velocity of the coupler PQ in rad/s, at an instant when \angle { O }_{ 4 }{ O }_{ 2 }P = 180^{0}, is
(a) 4
(b) 2\sqrt { 2 }
(c) 1
(d) 1/\sqrt { 2 }
(2 Mark, 2007)

Ans: c
Statement for Linked Answer Questions.
A quick return mechanism is shown below. The crank OS is driven at 2 rev/s in counterclockwise direction.
28. If the quick return ratio is 1 : 2, then the length of the crank in mm is
(a) 250
(b) 250\sqrt { 3 }
(c) 500\sqrt { 3 }
(d) 500
(2 Mark, 2007)

Ans: a
29. The angular speed of PQ in rev/s when the block R attains maximum speed during forward stroke (stroke with slower speed) is
(a) 1/3
(b) 2/3
(c) 2
(d) 3
(2 Mark, 2007)

Ans: b
30. A Planner mechanism has 8 links and 10 rotary joints. The number of degrees of freedom of the mechanism, using Gruebler’s criterion is
(a) 0
(b) 1
(c) 2
(d) 3
(2 Mark, 2008)

Ans: b
31. A simple quick return mechanism is shown in the figure. The forward to return ratio of the quick return mechanism is 2:1. If the radius of the crank O_{1}P is 125 mm, then the distance ‘d’ (in mm) between the crank centre to lever pivot centre point should be
(a) 144.3
(b) 216.5
(c) 240.0
(d) 250.0
(1 Mark, 2009)

Ans: d
32. Match the approaches given below to perform stated kinematics / dynamics analysis of machine.
(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
(2 Mark, 2009)

Ans: b
33. For the configuration shown, the angular velocity of link AB is 10 rad/s counter clockwise. The magnitude of the relative sliding velocity (in ms^{1}) of slider B with respect to rigid link CD is
(a) 0
(b) 0.86
(c) 1.25
(d) 2.5
(2 Mark, 2010)

Ans: d
34. Mobility of a statically indeterminate structure is
(a) ≤ −1
(b) 0
(c) 1
(d) ≥ 2
(1 Mark, 2010)

Ans: a
35. 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
(1 Mark, 2010)

Ans: c
36. Which of the following statements is INCORRECT?
(a) Grashof’s rule states that for a planar crankrocker 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 mobility of a planar mechanism to be one.
(1 Mark, 2010)

Ans: a
37. For the fourbar linkage shown in the figure, the angular velocity of link AB is 1 rad/s. the length of link CD is 1.5 times the length of link AB. In the configuration shown, the angular velocity of link CD in rad/s is
(a) 3
(b) 3/2
(c) 1
(d) 2/3
(2 Mark, 2011)

Ans: d
38. A double – parallelogram mechanism is shown in the figure. Note that PQ is a single link. The mobility of the mechanism is
(a) 1
(b) 0
(c) 1
(d) 2
(1 Mark, 2011)

Ans: c
39. A solid disc of radius r rolls without slipping on a horizontal floor with angular velocity ω and angular acceleration α. The magnitude of the acceleration of the point of contact on the disc is
(a) zero
(b) rα
(c) \sqrt { { (r\alpha ) }^{ 2 }{ +(r\omega ) }^{ 2 } }
(d) rω^{2}
(1 Mark, 2012)

Ans: d
41. A link OB is rotating with a constant angular velocity of 2 rad/s in counter clockwise direction and a block is sliding radially outward on it with an uniform velocity of 0.75 m/s with respect to the rod, as shown in the figure below. If OA = 1 m, the magnitude of the absolute acceleration of the block at location A in m/s^{2} is
(a) 3
(b) 4
(c) 5
(d) 6
(1 Mark, 2013)

Ans: c
42. A planar closed kinematic chain is formed with rigid links PQ = 2.0 m, QR = 3.0 m, RS = 2.5 m and SP = 2.7 m with all revolute joints. The link to be fixed to obtain a double rocker (rockerrocker) mechanism is
(a) PQ
(b) QR
(c) RS
(d) SP
(1 Mark, 2013)

Ans: c
43. An offset slidercrank mechanism is shown in the figure at an instant. Conventionally, the Quick Return Ratio (QRR) is considered to be greater than one. The value of QRR is __.
(2 Mark, 2014[1])

Ans: 1.25
44. A rigid link PQ of length 2 m rotates about the pinned end Q with a constant angular acceleration of 12 rad/s^{2}. When the angular velocity of the link is 4 rad/s, the magnitude of the resultant acceleration (in m/s^{2}) of the end P is _______.
(2 Mark, 2014[2])

Ans: 40
45. A slidercrank mechanism with crank radius 60 mm and connecting rod length 240 mm is shown in figure. The crank is rotating with a uniform angular speed of 10 rad/s, counter clockwise. For the given configuration, the speed (in m/s) of the slider is _______.
(2 Mark, 2014[3])

Ans: 0.617
46. In a certain slidercrank mechanism, lengths of crank and connecting rod are equal. If the crank rotates with a uniform angular speed of 14 rad/s and the crank length is 300 mm, the maximum acceleration of the slider (in m/s^{2}) is ___.
(2 Mark, 2015[2])

Ans: 117.5
47. The number of degrees of freedom of the planetary gear train shown in the figure is
(a) 0
(b) 1
(c) 2
(d) 3
(1 Mark, 2015[2])

Ans: 2
Explanation:
F = 3(N – 1) – 2j – h
F = 3(4 – 1) – 2(3) – 1
F = 2
47. In the figure, link 2 rotates with constant angular velocity ω_{2}. A slider link 3 moves outwards with a constant relative velocity V_{Q/P}, where Q is a point on slider 3 and P is a point on link 2. The magnitude and direction of Coriolis component of acceleration is given by
(a) 2ω_{2} V_{Q/P}; direction of V_{Q/P} rotated by 90° in the direction of ω_{2}
(b) ω_{2} V_{Q/P}; direction of V_{Q/P} rotated by 90° in the direction of ω_{2}
(c) 2ω_{2} V_{Q/P}; direction of V_{Q/P} rotated by 90° opposite to the direction of ω_{2}
(d) ω_{2} V_{Q/P}; direction of V_{Q/P} rotated by 90° opposite to the direction of ω_{2}
(1 Mark, 2015[3])

Ans: a
48. A slider crank mechanism with crank radius 200 mm and connecting rod length 800 mm is shown. The crank is rotating at 600 rpm in the counter clockwise direction. In the configuration shown, the crank makes an angle of 90^{0} with the sliding direction of the slider, and a force of 5 kN is acting on the slider. Neglecting the inertia forces, the turning moment on the crank (in kNm) is ______.
(2 Mark, 2016[1])

Ans: 1
49. The rod AB, of length 1 m, shown in the figure is connected to two sliders at each end through pins. The sliders can slide along QP and QR. If the velocity V_{A} of the slider at A is 2 m/s, the velocity of the midpoint of the rod at this instant is _____ m/s.
(2 Mark, 2016[2])

Ans: 1
50. The number of degrees of freedom in a planar mechanism having n links and j simple hinge joints is
(a) 3(n − 3) − 2j
(b) 3(n − 1) − 2j
(c) 3n − 2j
(d) 2j − 3n + 4
(1 Mark, 2016[3])

Ans: b
51. A rigid link PQ is undergoing plane motion as shown in the figure (V_{P} and V_{Q} are nonzero). V_{QP} is the relative velocity of point Q with respect to point P.
Which one of the following is TRUE?
(a) V_{QP} has components along and perpendicular to PQ
(b) V_{QP }has only one component directed from P to Q
(c) V_{QP} has only one component directed from Q to P
(d) V_{QP} has only one component perpendicular to PQ
(1 Mark, 2016[3])

Ans: d
52. Block 2 slides outward on link 1 at a uniform velocity of 6 m/s as shown in the figure. Link 1 is rotating at a constant angular velocity of 20 radian/s counter clockwise. The magnitude of the total acceleration ( in m/s^{2}) of point P of the block with respect to fixed point O is ______.
(2 Mark, 2017[2])

Ans: 243.32
53. In a slidercrank mechanism, the lengths of the crank and connecting rod are 100 mm and 160 mm, respectively. The crank is rotating with an angular velocity of 10 radian/s counter clockwise. The magnitude of linear velocity (in m/s) of the piston at the instant corresponding to the configuration shown in the figure is _____.
(1 Mark, 2017[2])

Ans: 1
54. A four bar mechanism is made up of links of length 100, 200, 300 and 350 mm. If the 350 mm link is fixed; the number of links that can rotate fully is ____.
(1 Mark, 2018[1])

Ans: 1
55. A slider crank mechanism is shown in the figure. At some instant, the crank angle is 45^{0} and a force of 40 N is acting towards the left on the slider. The length of the crank is 30 mm and the connecting rod is 70 mm. Ignoring the effect of gravity, friction and inertial forces, the magnitude of the crankshaft torque (in Nm) needed to keep the mechanism in equilibrium is _____ (correct to two decimal places).
(2 Mark, 2018[1])

Ans: 1.105
56. In a rigid body in plane motion, the point R is accelerating with respect to point P at 10∠180^{0} m/s^{2}. If the instantaneous acceleration of point Q is zero, the acceleration (in m/s^{2}) of point R is
(a) 8∠233^{0}
(b) 10∠225^{0}
(c) 10∠217^{0}
(d) 8∠217^{0}
(2 Mark, 2018[2])

Ans: d
57. A rigid rod of length 1 m is resting at an angle θ = 45^{0} as shown in the figure. The end P is dragged with a velocity of U = 5 m/s to the right. At the instant shown, the magnitude of the velocity V (in m/s) of point Q as it moves along the wall without losing contact is
(a) 5
(b) 6
(c) 8
(d) 10
(2 Mark, 2018[2])

Ans: a
58. In a four bar planar mechanism shown in the figure, AB = 5 cm, AD = 4 cm and DC = 2 cm. In the configuration shown, both AB and DC are perpendicular to AD. The bar AB rotates with an angular velocity of 10 rad/s. The magnitude of angular velocity (in rad/s) of bar DC at this instant is
(a) 25
(b) 15
(c) 10
(d) 0
(2 Mark, 2019[1])

Ans: a
59. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the instant shown, edge QR is parallel to the xaxis, and the body moves such that velocities of points P and R are V_{P} and V_{R}, in the x and y directions, respectively. The magnitude of the angular velocity of the body is
(a) 2V_{R}
(b) 2V_{P}
(c) V_{R}/\sqrt { 3 }
(d) V_{P}/\sqrt { 3 }
(1 Mark, 2019[2])

Ans: a
60. The crank of a slidercrank mechanism rotates counter clockwise (CCW) with a constant angular velocity ω, as sown. Assume the length of the crank to be r. Using exact analysis. The acceleration of the slider in the ydirection, at the instant shown, where the crank is parallel to xaxis, is given by
(a) –ω^{2}r
(b) 2ω^{2}r
(c) ω^{2}r
(d) 2ω^{2}r
(2 Mark, 2019[2])

Ans: c
61. A four bar mechanism is shown in the figure. The link numbers are mentioned near the links, input link 2 is rotating anticlockwise with a constant angular speed ω_{2}. Length of different links are:
O_{2}O_{4} = O_{2}A = L
AB = O_{4}B = \sqrt { 2 } L
The magnitude of the angular speed of the output link 4 is ω_{4} at the instant when link 2 makes an angle of 90° with O_{2}O_{4} as shown. The ratio \frac { { \omega }_{ 4 } }{ { \omega }_{ 2 } } is ____ (round off to two decimal places).
(2 Mark, 2019[2])

Ans: 0.79
We know, { \omega }_{ 4 }\left( { I }_{ 24 }{ I }_{ 14 } \right) ={ \omega }_{ 2 }\left( { I }_{ 24 }{ I }_{ 12 } \right)
=> \frac { { \omega }_{ 4 } }{ { \omega }_{ 2 } } =\frac { { I }_{ 24 }{ I }_{ 12 } }{ { I }_{ 24 }{ I }_{ 14 } }
=> \frac { { \omega }_{ 4 } }{ { \omega }_{ 2 } } =\frac { x }{ x+L }
=> \frac { { \omega }_{ 4 } }{ { \omega }_{ 2 } } =\frac { 1 }{ 1+\frac { L }{ x } }
=> \frac { { \omega }_{ 4 } }{ { \omega }_{ 2 } } =\frac { 1 }{ 1+tan\theta }
=> \frac { { \omega }_{ 4 } }{ { \omega }_{ 2 } } =\frac { 1 }{ 1+tan15 } = 0.79