Problem $3(4$ points$)$: A parallel$-$shaft gearset consists of an $18-$tooth helical pinion driving a $32-$tooth gear. The pinion has a left$-$hand helix angle of $25,$ a normal pressure angle of $20,$ a normal module of $3$ mm $.$ Using suitable formulae from lecture notes, find:

$($a$)$ The normal, transverse, and axial circular pitches

$($b$)$ The transverse module and the transverse pressure angle

$($c$)$ The pitch diameters of the two gears, base circle diameters of the two gears

$($d$)$ The addendum and dedendum of the two gears. How would you calculate contact ratio?