GATE 2025 ME – Question 60

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

An offset slider-crank mechanism is shown in the figure below. The length of the stroke of the slider is ______ mm (rounded off to nearest integer).

An offset slider-crank mechanism. The crank is 30 mm long and the connecting rod is 50 mm. The slider moves along a line that is offset by 10 mm from the crank pivot.

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Correct answer: 62

Explanation

The slider is at its extreme positions when the crank and rod are in line. At the farthest position, the distance along the slider line is $\sqrt{(50 + 30)^2 - 10^2} = \sqrt{6300} = 79.37$ mm. At the nearest position it is $\sqrt{(50 - 30)^2 - 10^2} = \sqrt{300} = 17.32$ mm. The stroke is $79.37 - 17.32 = 62.05$, which is 62 mm.