GATE ME 2024 Set 1 — Question 54
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Theory of Machines & Vibrations → Mechanisms & Linkages → Velocity & Acceleration Analysis
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Question
At the instant when OP is vertical and AP is horizontal, the link OD is rotating counter clockwise at a constant rate rad/s. Pin P on link OD slides in the slot BC of link ABC which is hinged at A, and causes a clockwise rotation of the link ABC. The magnitude of angular velocity of link ABC for this instant is _________________ rad/s (rounded off to 2 decimal places).
Correct answer
11.3 to 12.7
Solution
1.Velocity of pin P on link OD: Since OP is vertical and OD rotates CCW at rad/s, the velocity of P is horizontal to the left: m/s.
2.Relative velocity relationship: Let be the point on link ABC coincident with pin P. The velocity of is related to by , where is along the slot BC.
3.Kinematic constraints:
- Since AP is horizontal and A is a fixed hinge, must be vertical (perpendicular to AP).
- The slot BC is at to the horizontal.
- Horizontal component: m/s.
- Vertical component: m/s.
6.The magnitude of the angular velocity of link ABC is 12.12 rad/s.
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