GATE ME 2021 Set 1 — Question 62
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Theory of Machines & Vibrations → Mechanisms & Linkages → Four-Bar & Slider-Crank
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Question
The Whitworth quick return mechanism is shown in the figure with link lengths as follows: , , , .
The quick return ratio for the mechanism is _______ (round off to one decimal place).
Correct answer
1.9 to 2.1
Solution
For a Whitworth quick return mechanism, the quick return ratio () is given by:where is the angle subtended by the return stroke at the center of rotation of the crank. From the geometry of the mechanism, the return stroke occurs when the crank is between the two positions where it is perpendicular to the line of stroke of the slider. However, for the Whitworth mechanism specifically, the return angle is determined by the positions where the crank is collinear with the fixed link .
In the limiting positions, .
Therefore, .
The quick return ratio is:
In the limiting positions, .
Therefore, .
The quick return ratio is:
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