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

Q1: The figure shows a wheel rolling without slipping on a horizontal plane with angular velocity ω1. A rigid bar PQ is pinned to the wheel at P while the end Q slides on the floor.
What is the angular velocity ω1 of the bar PQ? [GATE ME 2023]
GATE Past Year Questions: Dynamics of Machines | Theory of Machines (TOM) - Mechanical Engineering(a) ω2 =2ω1
(b) ω2 = ω1
(c) ω2 = 0.5ω1
(d) ω2 = 0.25ω1
Ans: (d)
GATE Past Year Questions: Dynamics of Machines | Theory of Machines (TOM) - Mechanical EngineeringAs Disc (Link 2) roll without slipping on Link 1 (surface) so their I-centre of rotation lies on point of contact to avoid relative motion in between them. So I12 lies on point of contact.
Link 2 and 3 have instantaneous center of rotation at I13 due to fixed surface of Link 1.
As per point Plies on link 2 and 3 both so, point PP has same velocity for Link 2 and 3 both.
As per Kennedy's theorem, if three plane bodies have relative motion among themselves, their I-centre must lie on a straight line. So, I23 must be on line joining I13 and I12 at point P.
By similar △PI12 B and ΔPl13 A, we have
GATE Past Year Questions: Dynamics of Machines | Theory of Machines (TOM) - Mechanical Engineering
or, I12 l13 = 0.25I23 l13 ...(i) 
Velocity of point P is same w.r.t. all instantaneous rotation so,
ω1 × I12I23 = ω2 × I23l13
By equation (i), we get
ω2 = 0.25ω1

Q1: The Whitworth quick return mechanism is shown in the figure with link lengths as follows: OP = 300 mm, OA = 150 mm, AR = 160 mm, RS = 450 mm.
GATE Past Year Questions: Dynamics of Machines | Theory of Machines (TOM) - Mechanical Engineering

The quick return ratio for the mechanism is ________(round off to one decimal place).  [GATE ME 2021 SET-1]
Ans: 1.9 to 2.1
GATE Past Year Questions: Dynamics of Machines | Theory of Machines (TOM) - Mechanical EngineeringGATE Past Year Questions: Dynamics of Machines | Theory of Machines (TOM) - Mechanical EngineeringGATE Past Year Questions: Dynamics of Machines | Theory of Machines (TOM) - Mechanical Engineering
⇒ α/2 = 60º
α = 120º
β = (360º - 120º) = 240º
GATE Past Year Questions: Dynamics of Machines | Theory of Machines (TOM) - Mechanical Engineering

Q1: The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular velocity ω, as shown. Assume the length of the crank to be r.
GATE Past Year Questions: Dynamics of Machines | Theory of Machines (TOM) - Mechanical EngineeringUsing 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 [GATE ME 2019 SET-2]
(a) −ω2r
(b) 2ω2r
(c) ω2r
(d) −2ω2r
Ans: (c)
GATE Past Year Questions: Dynamics of Machines | Theory of Machines (TOM) - Mechanical Engineeringsince the velocity of the point A and B are parallel ωAB = 0
GATE Past Year Questions: Dynamics of Machines | Theory of Machines (TOM) - Mechanical Engineering
ω2r + α = 0
α = -ω2r
aB = -α = -(-ω2r) = ω2r

Question: 499319]

Question for GATE Past Year Questions: Dynamics of Machines
Try yourself:Consider the triangular 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 is 75°, the ratio of connecting rod length to crank radius to

[1998]

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Question for GATE Past Year Questions: Dynamics of Machines
Try yourself:For a mechanism shown below, the mechanical advantage for the given configuration is
GATE Past Year Questions: Dynamics of Machines | Theory of Machines (TOM) - Mechanical Engineering

[2004]

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Question for GATE Past Year Questions: Dynamics of Machines
Try yourself:For a four bar linkage in toggle position, the value of mechanical advantage is

[2006]

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FAQs on GATE Past Year Questions: Dynamics of Machines - Theory of Machines (TOM) - Mechanical Engineering

1. What are the key topics covered in the Dynamics of Machines for GATE Mechanical Engineering?
Ans.The key topics include kinematics of machines, dynamics of rigid bodies, analysis of mechanisms, vibrations, and motion analysis. It also covers concepts like cams, gears, linkages, and the study of forces and torques in machines.
2. How can I prepare effectively for the Dynamics of Machines section in the GATE exam?
Ans.Effective preparation can be achieved by studying standard textbooks, solving previous years' GATE questions, and practicing numerical problems. It is also helpful to create a study schedule, focus on understanding concepts, and take mock tests to assess your knowledge.
3. What are some common types of questions asked in the Dynamics of Machines section of GATE?
Ans.Common types of questions include numerical problems related to the calculation of velocities and accelerations in mechanisms, questions on the stability of systems, and theoretical questions about machine components like gears and cams.
4. Which textbooks are recommended for studying Dynamics of Machines for GATE preparation?
Ans.Recommended textbooks include "Theory of Machines" by S.S. Rattan, "Mechanics of Machines" by G. K. Groover, and "Machine Design" by J. E. Shigley. These books provide comprehensive coverage of the subject and include solved problems for practice.
5. How important is the Dynamics of Machines section for scoring well in GATE Mechanical Engineering?
Ans.The Dynamics of Machines section is important as it covers fundamental concepts that are essential for understanding mechanical systems. A good score in this section can significantly contribute to the overall GATE score, making it crucial for candidates aiming for higher ranks.
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