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
Instantaneous centers (I-centers) are points where two links have the same velocity at a given instant.
- is the fixed pivot for link 2, so .
- is the pin joint between links 1 and 2, so .
- is the pin joint between links 1 and 3, so .
- is the pin joint between links 3 and 4, so .
- is the point of rolling contact without slip between the disc (link 4) and ground (link 0), so .
- According to Kennedy's Theorem, the three I-centers for any three links must be collinear. For links 0, 2, and 1, must lie on the line joining and . For links 0, 4, and 3, must lie on the line joining and .
- The dashed lines in the figure show that is the intersection of lines and . This identifies as a higher-order I-center (specifically or depending on the full kinematic chain).
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