Problem $\backslash$# $\backslash (2(2+2+2=6\backslash$mathrm$\{$pts$\})\backslash )$

Minimum number of teeth of pinion and gears needs to be selected in order to avoid interference problem in meshed gears. Consider two spur gears are designed with $\backslash (20^\{\backslash$circ$\}\backslash )$ pressure angle and are meshed together. Please determine:

a$.$ The minimum number of teeth on pinion when gear ratio is $\backslash (1$: $1\backslash )$

b$.$ The minimum number of teeth on pinion when gear ratio is $\backslash (3$: $1\backslash )$

c$.$ The minimum number of teeth on pinion when gear ratio is $\backslash (5$: $1\backslash$mid $\backslash )$