## GATE ME solved questions on Planar Mechanism(Theory of Machines)

**Question #1**

For an Oldham coupling used between two shafts, which among the following statements are correct?

I. Torsional load is transferred along shaft axis.

II. A velocity ratio of 1:2 between shafts is obtained without using gears.

III. Bending load is transferred transverse to shaft axis.

IV. Rotation is transferred along shaft axis.

(A) I and III

(B) I and IV

(C) II and III

(D) II and IV

**[GATE 2018 S1, 1 mark]**

**Question #2**

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 __________.

**[GATE 2018 S1, 1 mark]**

**Question #3**

In a rigid body in plane motion, the point R is accelerating with respect to point P at 10∠180 m/s . If the instantaneous acceleration of point Q is zero, the acceleration (in m/s ) of point R is

(A) $8\angle 233^{o}$

(B) $10\angle 225^{o}$

(C) $10\angle 217^{o}$

(D) $8\angle 217^{o}$

**[GATE 2018 S2, 2 marks]**

**Question #4**

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 counterclockwise. The magnitude of the total acceleration (in m/s ) of point P of the block with respect to fixed point O is ________

**[GATE 2017 S2, 2 marks]**

**Question #5**

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 VA of the slider at A is 2 m/s, the velocity of the midpoint of the rod at this instant is ___________ m/s.

**[GATE 2016 S2, 2 marks]**

**Question #6**

A rigid link PQ is undergoing plane motion as shown in the figure (VP and VQ are non-zero). 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

**[GATE 2016 S3, 1 mark]**

**Question #7**

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

**[GATE 2016 S3, 1 mark]**

**Question #8**

A wheel of radius r rolls without slipping on a horizontal surface shown below. If the velocity of point P is 10 m/s in the horizontal direction, the magnitude of velocity of point Q (in m/s) is ______

**[GATE 2015 Set 1, 1 mark]**

**Question #9**

The number of degrees of freedom of the planetary gear train shown in the figure is the number of degrees of freedom of the planetary gear train shown in the figure is

(A) 0

(B) 1

(C) 2

(D) 3

**[GATE 2015 Set 2, 1 mark]**

**Question #10**

In the figure, link 2 rotates with constant angular velocity ω2. A slider link 3 moves outwards with a constant relative velocity VQ/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) 2 $\omega _2$ VQ/P; direction of VQ/P rotated by 90° in the direction of ω2

(B)$\omega _2$ VQ/P; direction of VQ/P rotated by 90° in the direction of ω2

(C) 2 $\omega _2$ VQ/P; direction of VQ/P rotated by 90° opposite to the direction of ω2

(D) $\omega _2$ VQ/P; direction of VQ/P rotated by 90° opposite to the direction of ω2

**Question #11**

In the given problem, the direction of $\vec{V}_{slider}$ is upward and the direction of $\omega $ is clockwise. So, the direction of $a_c$ will be 90 ^{o }_{ }in the direction of $\omega $.

The number of degrees of freedom of the linkage shown in the figure is

(A) −3

(B) 0

(C) 1

(D) 2

**[GATE 2015 Set 3, 2 marks]**

**Question #12**

Figure shows a wheel rotating about O2. Two points A and B located along the radius of wheel have speeds of 80 m/s and 140 m/s respectively. The distance between the points A and B is 300 mm. The diameter of the wheel (in mm) is ________

**[GATE 2015 Set 3, 2 marks]**

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