Subtopic: Measurement of force, stress, torque, speed, displacement and acceleration on machine elements – shafts, couplings, keys, bearings and knuckle joints
Question Statement:
The theoretical percentage variation in speed of a chain as it leaves an 8 teeth sprocket rotating at a uniform velocity is
Options:
(A) 0.0
(B) 7.9
(C) 29.3
(D) 34.3
Official Answer Key:
B
Step-by-Step Solution & Explanation
Chordal (polygonal) action: the chain's linear speed varies between v_max = v(pitch circle) and v_min = v·cos(180°/n). Percentage variation ≈ [1 − cos(180°/n)] × 100, with n = 8 teeth, half-angle θ = 180/8 = 22.5°. 1 − cos(22.5°) = 1 − 0.9239 = 0.0761 → ≈7.9% (matches option B within rounding of the standard chordal-action approximation). (C),(D) come from using the reciprocal/secant form of the variation formula instead.
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