GATE 2022 ME (ME2) – Question 52

Theory of Machines · Displacement, velocity and acceleration analysis of plane mechanisms · 2 marks · Numerical answer

In the configuration of the planar four-bar mechanism at a certain instant as shown in the figure, the angular velocity of the 2 cm long link is $\omega_2=5$ rad/s. Given the dimensions as shown, the magnitude of the angular velocity $\omega_4$ of the 4 cm long link is given by ______ rad/s (round off to 2 decimal places).

fixed pivots 10 cm apart; 2 cm input crank points right along the base, a 5 cm coupler joins it to the 4 cm output crank.

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Show answer and explanation

Correct answer: 1.24 to 1.26

Explanation

The input joint has vertical speed $5\times2=10$ cm/s. Projecting the relative joint velocities along the 5 cm coupler cancels the coupler rotation and gives $|\omega_4|(10-2)=10$, hence $|\omega_4|=1.25$ rad/s.