Write a computer program that will analyze a spur gear or helical-mesh gear, accepting and ; compute , and ; and give advice as to the smallest tooth count that will allow a pinion to run with...

Write a computer program that will analyze a spur gear or helical-mesh gear, accepting

and
; compute

, and

; and give advice as to the smallest tooth count that will allow a pinion to run with itself without interference, run with its gear, and run with a rack. Also have it give the largest tooth count possible with the intended pinion.