Question

When the addenda on pinion and wheel is such that the path of approach and path of recess are half of their maximum possible values, then the length of the path of contact is given by

(a) (r + R) sin φ/2

(b) (r + R) cos φ/2

(c) (r + R) tan φ/2

(d) (r + R) cot φ/2

I had been asked this question at a job interview.

This interesting question is from Toothed Gearing topic in portion Toothed Gearing & Gear Trains of Machine Kinematics

Answer 1

Right choice is (a) (r + R) sin φ/2

To explain: In case the addenda on pinion and wheel is such that the path of approach and path of recess are half of their maximum possible values, then

Path of approach, KP = 1/2 MP.