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GATE 2016 ME (ME3) – Question 20

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

The number of degrees of freedom in a planar mechanism having n links and j simple hinge joints is

  1. $3(n-3)-2j$
  2. $3(n-1)-2j$
  3. $3n-2j$
  4. $2j-3n+4$

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Show answer and explanation

Correct answer: (B) $3(n-1)-2j$

Explanation

Each moving planar link contributes three degrees of freedom. A revolute joint removes two relative freedoms. With n links including ground and j such joints, mobility is **3(n−1)−2j, B**, provided the constraints are independent and there are no special geometric redundancies.