Problem $1(4$ points$)$: The speeds for a reduction spur gear pair are $2000$ rpm and $320$ rpm $,$ respectively. The pressure angle is designed to be $20.$ The gears have a $m=5m\frac{m}{?}$ teeth module and their center distance is $400$ mm $.$ For both the gears, using full depth teeth $($full$-$depth teeth means a standard working depth $(h_w)$ of $2m).$

a$.$ What is the pinion speed? What is the gear speed? Obtain the transmission ratio.

b$.$ Determine the circular pitch, number of teeth on the gear and the pinion, base pitch, angular pitch $($angular pitch $=\frac{2}{N}),$ addendum, dedendum, face width, backlash, radii of the addendum circle, radii of the dedendum circle, and base circles. For backlash information, consult Lec. $20$ notes $(10/14).$ For addendum and dedendum information, you will use Lec. $21$ notes $(10/16)$

c$.$ If center distance was decreased by $5$ mm but reduction ratio was kept the same as before, and base circle radii was fixed as before, determine all the parameters in part $($a$)$ again.