Subtopic: Design and selection of machine elements – gears, pulleys, chains and sprockets and belts
Question Statement:
In a Cardan (Hooke's) universal joint connecting two shafts inclined at joint angle $\alpha$, the instantaneous speed ratio $\frac{\omega_2}{\omega_1}$ varies during each revolution between:
Options:
(A) $\cos\alpha$ and $\frac{1}{\cos\alpha}$
(B) $\sin\alpha$ and $\frac{1}{\sin\alpha}$
(C) $\tan\alpha$ and $\cot\alpha$
(D) $1 - \alpha$ and $1 + \alpha$
Answer Key:
A
Step-by-Step Solution & Explanation
Angular velocity ratio fluctuates cyclically twice per revolution: minimum ratio is $\cos\alpha$ and maximum ratio is $1 / \cos\alpha$.