A newly proposed numerically controlled milling machine is to operate from a helical$-$

gear speed reducer designed to provide $65$ horsepower at an output shaft speed of $1150$

rpm$.$ It has been suggested by engineering management that a $3450-$rpm electric motor be

used to drive the speed reducer. An in$-$house gearing consultant has suggested that a

normal diametral pitch of $12,$ a normal pressure angle of $20,$ a helix angle of $15,$ an AGMA

quality number of $10,$ and a safety factor of $1\mathrm{.}7$ would be an appropriate starting point for

the design. Design the gears.