Question $3(20$ marks$)$

A pair of spur gears has $10$ and $18$ teeth, a module of $12mm,20$ pressure angle, $12$ mm addendum, and $15$ mm dedendum. The pinion drives in a clockwise direction.

a$)$ Draw the base, pitch and addendum circles for both gears

Using theoretical approach, calculate:

b$)$ The length of path of contact.

c$)$ The contact ratio $($the average number of pairs of teeth in contact$).$

d$)$ The angles of approach and recess for pinion and gear.

e$)$ The number of teeth on the smallest pinion that will mesh with the gear without interference.