GATE Past Year Questions: Kinematics of Mechanisms | Theory of Machines (TOM) - Mechanical Engineering PDF Download

Q1: At the instant when OP is vertical and AP is horizontal, the link OD is rotating counter clockwise at a constant rate ω=7rad/s, Pin P on link OD sides in the slot BC of link ABC which is hinged at A, and cause a clockwise rotation of the link ABC. The magnitude of angular velocity of link  ABC for the instant is _____  rad/s (rounded off to 2 decimal places).  [GATE ME 2024]

Ans: (11.3 to 12.7)
7 x 134. 49 = ω₃ x 77.65
ω₃ = 12.124 ≈ 12.12rad/sec

Q1: The wheels and axle system lying on a rough surface is shown in the figure.

Each wheel has diameter 0.8 m and mass 1 kg. Assume that the mass of the wheel is concentrated at rim and neglect the mass of the spokes. The diameter of axle is 0.2 m and its mass is 1.5 kg. Neglect the moment of inertia of the axle and assume g = 9.8m/s² . An effort of 10 N is applied on the axle in the horizontal direction shown at mid span of the axle. Assume that the wheels move on a horizontal surface without slip. The acceleration of the wheel axle system in horizontal direction is ________ m/s ² (round off to one decimal place). [GATE ME 2021 SET-2]
Ans: (1.3 to 1.4)
IG = 2 x (M x r²)
= 2 x 1 x 0.4² = 0.32 kg/m²
ΣF = m . a
⇒ 10 - f = 3.5 x a...(i) 
ΣF = I .a
⇒ 10  x 0.1 - f x 0.4 = 0.32 x a/0.4 ....(ii)
[As there is no slip ∴ a = r α 
 Solving (i) and (ii),
∴ a = 5 m/s²

Q2: Consider the mechanism shown in the figure. There is rolling contact without slip between the disc and ground.

Select the correct statement about instantaneous centers in the mechanism. [GATE ME 2021 SET-2]
(a) Only points P, Q, and S are instantaneous centers of mechanism
(b) Only points P, Q, S and T are instantaneous centers of mechanism
(c) Only points P, Q, R, S, and U are instantaneous centers of mechanism
(d) All points P, Q, R, S, T and U are instantaneous centers of mechanism
Ans: (d) 

Points P, Q, R, S, T and U are instantaneous centers of mechanism.

Q1: The number of qualitatively distinct kinematic inversions possible for a Grashof chain with four revolute pairs is  [GATE ME 2020, SET-2]
(a) 1
(b) 2
(c) 3
(d) 4
Ans: (c)
They are:
1. Double crank mechanism
2. Crank-rocker mechanism
3. Double rocker mechanism

Q3: Question 5 The 2 kg block shown in figure (top view) rests on a smooth horizontal surface and is attached to a massless elastic cord that has a stiffness 5 N/m. 
The cord hinged at O is initially unstretched and always remains elastic. The block is given a velocity v of 1.5 m/s perpendicular to the cord. The magnitude of velocity in m/s of the block at the instant the cord is stretched by 0.4 m is [GATE ME 2020 SET-1]
(a) 0.83
(b) 1.07 
(c) 1.36 
(d) 1.5
Ans: (c)
Energy conservation

⇒ 2 x 1.5² = 2 x V_O² + 5 x 0.4²
VO = 1.360m/s

Q4: A four bar mechanism is shown below

For the mechanism to be a crank-rocker mechanism, the length of the link PQ can be  [GATE ME 2020 SET-1]
(a) 80 mm
(b) 200 mm
(c) 300 mm
(d) 350 mm
Ans: (a)

For Crank-Rocker mechanism, shortest link must be crank and adjacent to fixed as well as Grashoff's law must be satisfied. 
If l = 80mm then shortest will be = 80 mm 
as well as (80 + 600) <(400 + 300)
Therefore law is satisfied.
⇒ l = 80 mm

Question for GATE Past Year Questions: Kinematics of Mechanisms

Try yourself:For the planar mechanism shown in figure select the most appropriate choice for the motion of link 2 when link 4 is moved upwards.

[1999]

• A.

  Link 2 rotates clockwise
• B.

  Link 2 rotates counter clockwise
• C.

  Link 2 does not move
• D.

  Link 2 motion cannot be determined

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Question for GATE Past Year Questions: Kinematics of Mechanisms

Try yourself:For the audio Cassette mechanism shown in figure given below where is the instantaneous centre of rotation (P) of the two spools?

[1999]

• A.

  Point P lies to the left of both the spools but at infinity along the line joining A and H
• B.

  Point P lies in between the two spools on the line joint 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

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Question for GATE Past Year Questions: Kinematics of Mechanisms

Try yourself:Figure shows a quick return mechanism. The cranks OA rotates clockwise uniformly. OA = 2 cm, OO' = 4 cm. The ratio of time for forward motion to that for return motion is

[1995]

• A.

  0.5
• B.

  2.0
• C.

  √2
• D.

  1

Explanation

Ratio of time of forward motion to return motion

(Given OD = 2 cm, OO' = 4 cm, sin α = 2/4 = 0.5 ⇒ α = 30°) 

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Question for GATE Past Year Questions: Kinematics of Mechanisms

Try yourself: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 1m/ s. The angular velocity of the rod at this instant is

[1996]

• A.

  2 rad/s
• B.

  1.5 rad/s
• C.

  0.5 rad/s
• D.

  0.75 rad/s

Explanation

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Question for GATE Past Year Questions: Kinematics of Mechanisms

Try yourself:An instantaneous configuration of a four-bar mechanism, whose plane is horizontal, is shown in the figure below. At this instant, the angular velocity and angular acceleration of link O₂A are ω = 8 rad/s and α = 0, respectively, and the driving torque (τ) is zero. The link O₂A is balanced so that its centre of mass falls at O₂.

Which kind of 4-bar mechanism is O₂ABO₄?

[2005]

• A.

  Double crank mechanism
• B.

  Crank-rocker mechanism
• C.

  Double rocker mechanism
• D.

  Parallelogram mechanism

Explanation

and O₂O₄ is fixed link. It will act as a crank-rocker mechanism

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Question for GATE Past Year Questions: Kinematics of Mechanisms

Try yourself:An instantaneous configuration of a four-bar mechanism, whose plane is horizontal, is shown in the figure below. At this instant, the angular velocity and angular acceleration of link O₂A are ω = 8 rad/s and α = 0, respectively, and the driving torque (τ) is zero. The link O₂A is balanced so that its centre of mass falls at O₂.

At the instant considered, what is the magnitude of the angular velocity of O₄B?

[2005]

• A.

  1 rad/s
• B.

  3 rad/s
• C.

  8 rad/s
• D.

  64/3 rad/s

Explanation

∴ 

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Question for GATE Past Year Questions: Kinematics of Mechanisms

Try yourself:An instantaneous configuration of a four-bar mechanism, whose plane is horizontal, is shown in the figure below. At this instant, the angular velocity and angular acceleration of link O₂A are ω = 8 rad/s and α = 0, respectively, and the driving torque (τ) is zero. The link O₂A is balanced so that its centre of mass falls at O₂.

At the same instant, if the component of the force at Joint A along AB is 30N, then the magnitude of the Joint reaction at O₂

_[2005]

• A.

  is zero
• B.

  is 30 N
• C.

  is 78 N
• D.

  cannot be determined from the given data

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Question for GATE Past Year Questions: Kinematics of Mechanisms

Try yourself:The input link O₂P 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 ∠O₄O₂P = 180°, is

[2007]

• A.

  4
• B.

  2√2
• C.

  1
• D.

  1√2

Explanation

Now, 

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Question for GATE Past Year Questions: Kinematics of Mechanisms

Try yourself:A quick return mechanism is shown below. The crank OS is driven at 2 rev/s in counter clockwise direction.

If the quick return ratio is 1 : 2, then the length of the crank in mm is

[2007]

• A.

  250
• B.

  250√3
• C.

  500
• D.

  500√3

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Question for GATE Past Year Questions: Kinematics of Mechanisms

Try yourself:A quick return mechanism is shown below. The crank OS is driven at 2 rev/s in counter clockwise direction.

 The angular speed of PQ in rev/s when the block R attains maximum speed during forward stroke (stroke with slower speed) is (in rad/s)

[2007]

• A.

  1/3
• B.

  2/3
• C.

  2
• D.

  3

Explanation

Maximum speed during forward stroke occur when QR & QS are perpendicular.

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Question for GATE Past Year Questions: Kinematics of Mechanisms

Try yourself: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, P is 125 mm, then the distance d(in mm) between the crank centre to lever pivot centre point should be

[2009]

• A.

  144.3
• B.

  216.5
• C.

  240.0
• D.

  250.0

Explanation

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Question for GATE Past Year Questions: Kinematics of Mechanisms

Try yourself:For the four-bar 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

[2011]

• A.

  3
• B.

  3/2
• C.

  1
• D.

  2/3

Explanation

For the given configuration

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Question for GATE Past Year Questions: Kinematics of Mechanisms

Try yourself:Consider a slider crank mechanism with non zero masses and inertia. A constant torque t is applied on the crank as shown in the figure. Which of the following plots best resembles variation of crank angle θ versus time

[2015]

• A.

  
• B.

  
• C.

  
• D.

  

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Question for GATE Past Year Questions: Kinematics of Mechanisms

Try yourself:The crank of a slider-crank mechanism rotates counter-clock wise (CCW) with a constant angular velocity ω, as shown. Assume the length of the crank to be r.

Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where the crank is parallel to x-axis, is given by

[2019]

• A.

  –ω²r
• B.

  2ω²r
• C.

  ω²r
• D.

  –2ω²r

Explanation

Exactly analysis means exactdimensions have to be taken. No approximation is allowed. It means velocity diagram and acceleration diagram with exact geometry (dimensions) need to be drawn.

The velocity diagram of the above problem is as follows :

 perpendicular to OP
 in the direction of movement of slider..
Since, p, q are coinciding i.e. no relative motion between p and q

∴ There will be nor adial acc. of link PQ.
Only tangential acc.  will be there.
Also for link OP, α = 0 i.e. no tangential acceleration

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Question for GATE Past Year Questions: Kinematics of Mechanisms

Try yourself:The number of degrees of freedom of a five link plane mechanism with five revolute pairs as shown in the figure is

[1993]

• A.

  3
• B.

  4
• C.

  2
• D.

  1

Explanation

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Question for GATE Past Year Questions: Kinematics of Mechanisms

Try yourself:Match the following with respect to spatial mechanisms.

[2004]

• A.

  P-1 Q-3 R-1
• B.

  P-5 Q-4 R-3
• C.

  P-2 Q-3 R-1
• D.

  P-4 Q-5 R-3

Explanation

For revolute joint, degree of freedom = 1
For cylinderical joing, degree of freedom = 2
For spherical joint, degree of freedom = 3
Degree of constraints = 6 – Degree of freedom

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Question for GATE Past Year Questions: Kinematics of Mechanisms

Try yourself:A double parallelogram mechanism is shown in the figure. Note that PQ is a single link. The mobility of the mechanism is

[2011]

• A.

  -1
• B.

  0
• C.

  1
• D.

  2

Explanation

There is one link which is redundantin nature.
Therefore, DOF = 1.

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Question for GATE Past Year Questions: Kinematics of Mechanisms

Try yourself:The number of degrees of freedom of the linkage shown in the figure is

[2015]

• A.

  -3
• B.

  0
• C.

  1
• D.

  2

Explanation

Number of links, N = 6
Total number as binary joints, j = 7
F =  3 (N – 1) – 2j = 15 – 14 = 1.

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