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. A constant torque is applied on the crank as shown in the figure. Which of the following plots best resembles variation of crank angle, versus time
Correct answer
(D) [figure]
Solution
1.A constant torque is applied to the crank. The work done by the torque is .
2.This work increases the kinetic energy of the mechanism: .
3.The moment of inertia of a slider-crank mechanism varies periodically with the crank angle .
4.Consequently, the angular velocity will have a mean increasing trend (due to constant torque) but will fluctuate within each cycle due to the varying inertia.
5.The crank angle is the integral of . An increasing with periodic fluctuations results in a curve that is generally concave up (parabolic-like) with superimposed ripples. Option (D) correctly illustrates this behavior.
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