$13-4$ A $21-$tooth spur pinion mates with a $28-$tooth gear. The diametral pitch is $3$ teeth$/$in and the pressure angle is $20.$ Make a drawing of the gears showing one tooth on each gear. Find and tabulate the following results: the addendum, dedendum, clearance, circular pitch, tooth thickness, and base$-$circle diameters; the lengths of the arc of approach, recess, and action; and the base pitch and contact ratio.

Solve Problem $13-4$ in the textbook. In this Problem, leave out the following two parts:

$(1)$ the length of the arc of approach

$(2)$ the length of the arc of recess.

Instead, find the lengths CP and PD as defined in the diagram below. The length of action will be equal to length of CP $+$ length PD$.$

Length of the tooth actic