Subtopic: Measurement of force, stress, torque, speed, displacement and acceleration on machine elements – shafts, couplings, keys, bearings and knuckle joints
Question Statement:
Two links OA and OB are connected by a pin joint at O such that ∠AOB is 144°. If the diameter of pin joint is d and the angular velocity of each link is ω, then the velocity of rubbing at the pin joint O when the links move in opposite directions is
Options:
(A) 0
(B) ωd
(C) 2/5 π ωd
(D) 1/2 ωd
Official Answer Key:
B
Step-by-Step Solution & Explanation
Velocity of rubbing at a pin joint = (sum of angular velocities of the two connected links) × pin radius, i.e. v = (ω₁+ω₂)(d/2). With ω₁=ω₂=ω rotating in opposite directions, the relative angular velocity is 2ω, so v = 2ω×(d/2) = ωd. The 144° included angle is extraneous data (does not affect rubbing velocity, which depends only on relative angular velocity and pin size) — a designed distractor.
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