GATE ME 2019 Set 2 — Question 46
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Theory of Machines & Vibrations → Mechanisms & Linkages → Velocity & Acceleration Analysis
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Question
The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular velocity , as shown. Assume the length of the crank to be .
Using exact analysis, the acceleration of the slider in the -direction, at the instant shown, where the crank is parallel to -axis, is given by
Correct answer
(C) ω² r
Solution
Let the crank length be and the connecting rod length be . The slider moves vertically along a line with a horizontal offset from the crank center . From the diagram, the slider is on the -axis ().The vertical position of the slider is:Differentiating with respect to time (where ):Differentiating again to find acceleration :At the instant shown, the crank is parallel to the -axis, so . Substituting into the acceleration expression:Given , then :Thus, the acceleration of the slider in the -direction is .
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