Find the ratios of sliding velocity to the rolling velocity at the instant

Question

A gear with 42 teeth and a pinion with 19 teeth are cut with involute teeth of pressure angle 20⁰ and module pitch 6 mm. The addendum of each wheel is 6 mm. Find:

1. The length of the Arc of contact.
2. The number of pairs of teeth in contact.
3. The angle turned through by the pinion, while any one pair of teeth is in contact.
4. The ratios of sliding velocity to the rolling velocity at the instant (a) the engagement commences, (b) the engagement terminates and (c) at the pitch point.                                                                                                            

 

Answer 1

Given a rack and pinion gear