Question

The maximum length of arc of contact for two mating gears, in order to avoid interference, is

(a) (r + R) sin φ

(b) (r + R) cos φ

(c) (r + R) tan φ

(d) none of the mentioned

The question was asked in an interview for internship.

This is a very interesting question from Toothed Gearing in chapter Toothed Gearing & Gear Trains of Machine Kinematics

Answer 1

Right choice is (c) (r + R) tan φ

The best explanation: Interference may only be prevented, if the addendum circles of the two mating gears cut the

common tangent to the base circles between the points of tangency.

                       maximum length of arc of contact = (r + R) tan φ

where r = Pitch circle radius of pinion,

R = Pitch circle radius of driver, and

φ = Pressure angle.