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GATE 2021 ME (ME2) – Question 25

Theory of Machines · Displacement, velocity and acceleration analysis of plane mechanisms · 1 mark · Multiple choice

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.

Four-link mechanism with a disc rolling without slip and six labelled candidate instantaneous centres P–U. See the attached source image.
  1. Only P,Q,S
  2. Only P,Q,S,T
  3. Only P,Q,R,S,U
  4. All P,Q,R,S,T,U

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Correct answer: (D) All P,Q,R,S,T,U

Explanation

The pin joints give I₁₂=P,I₂₃=Q,I₃₄=S. Rolling without slip gives I₁₄=T at the ground contact.

By Kennedy’s theorem, I₁₃ lies on PQ and ST, intersecting at U. I₂₄ lies on PT and QS, intersecting at R. All six points are centres: **D**.