GATE ME 2021 Set 2 — Question 25
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Theory of Machines & Vibrations → Mechanisms & Linkages → Velocity & Acceleration Analysis
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Question
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.
Correct answer
(D) All points P, Q, R, S, T and U are instantaneous centers of mechanism
Solution
Number the links: 1 = fixed link (ground), with pivot and the rolling surface; 2 = crank ; 3 = coupler ; 4 = disc. With links there are instantaneous centres.Primary (by inspection):
- (fixed pivot of the crank)
- (pin joint)
- (pin at the disc centre)
- (pure rolling contact: the contact point has zero relative velocity)
- lies on line (line ) and on line (line ); their intersection is .
- lies on line (line , the dashed ground line) and on line (line ); their intersection is .
- (A), (B) and (C) each omit at least one of these centres ( is a primary centre; and are the two secondary centres).
- (D) lists all six.
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