Question $6.[5$ Marks$]$

You are required to connect two parallel shafts with a par of gears. The shafts are a

distance a apart from each other.

Figure $6$: A pair of gears connecting two shafts

$($a$)$ Find a relation between the module $m,$ the number of teeth on the smaller

$($pinion$)$ gear $N_p,$ transmission ratio $TR$ and the distance between the shafts $a.$

$($b$)$ The desired transmission ratio is $TR=6$ and the shafts are $a=84mm$ apart.

You may select gears with a module of $1mm,2mm,3mm,$ or $5$ mm $.$ How many

teeth should be on the two gears? Which module would you select and why?