GATE ME 2015 Set 1 — Question 24
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Theory of Machines & Vibrations → Mechanisms & Linkages → Dynamic Analysis of Linkages
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Question
Consider a slider crank mechanism with nonzero masses and inertia. The crank, pinned to the frame, drives a connecting rod attached to a slider of mass moving on a horizontal guide; the crank angle is measured from the line of stroke. A constant torque is applied on the crank, starting from rest.
Which of the following plots best resembles variation of crank angle, versus time
Correct answer
(D) [figure]
Solution
The constant torque does work on the mechanism, so the kinetic energy (and hence the crank speed ) keeps increasing on average: must rise faster and faster, starting from rest.However, the equivalent inertia of a slider-crank referred to the crank, , varies periodically with (the slider speed relative to the crank speed changes over each revolution). So within every revolution the angular velocity fluctuates about its rising mean.
- (A) Straight line: constant speed — ignores the acceleration due to the unbalanced torque ✗
- (B) Oscillation: the crank never completes revolutions — wrong for a constant driving torque with no resistance ✗
- (C) Smooth parabola: correct only for constant inertia (pure rotor), not a slider crank ✗
- (D) Increasing curve with periodic ripples: rising mean speed plus fluctuation from the varying inertia ✓
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