GATE ME 2022 Set 1 — Question 38
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Theory of Machines & Vibrations → Mechanisms & Linkages → Four-Bar & Slider-Crank
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Question
A planar four-bar linkage mechanism with 3 revolute kinematic pairs and 1 prismatic kinematic pair is shown in the figure, where and . The T-shaped link CDEF is constructed such that the slider B can cross the point D, and CE is sufficiently long. For the given lengths as shown, the mechanism is
Correct answer
(A) a Grashof chain with links AG, AB, and CDEF completely rotatable about the ground link FG
Solution
The given mechanism is an inversion of a slider-crank mechanism (specifically a Whitworth quick-return mechanism type) where the slider path (link ) rotates about a fixed pivot .
Since both the input link and the output link can rotate fully, and the coupler also performs a complete rotation relative to the ground in such a double-crank configuration, the mechanism is a Grashof chain where all moving links are completely rotatable about the ground link .
1.Identify the links and fixed pivots:
- Fixed pivots: and . The distance between them is cm.
- Crank: cm.
- Connecting rod (coupler): cm.
- Rotating slider path: Link pivoting at .
- For the driving link to perform a complete rotation about , the distance between the fixed pivots must be less than the crank length . Here, , so can rotate fully.
- For the link to perform a complete rotation about , the fixed pivot must lie within the workspace of the slider . The distance of from () varies between cm and cm. Since the distance cm lies within this range (), the pivot is inside the workspace, allowing to rotate fully.
Since both the input link and the output link can rotate fully, and the coupler also performs a complete rotation relative to the ground in such a double-crank configuration, the mechanism is a Grashof chain where all moving links are completely rotatable about the ground link .
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