$1.$ The figure depicts a two speed IH Cub Cadet creeper gearbox. Only one arm of the three$-$arm carrier is illustrated. Study the schematic and make sure you understand how this gearbox functions. $($a$)$ How many teeth does the sun gear have? $($b$)$ What is the reduction ratio $($out$/$in$)$ when the creeper mode is engaged? $($c$)$ The ring gear has a pitch diameter of $72$ mm$.$ The pressure angle of these teeth is $20.$ What are the contact force components acting on the sun gear teeth? Assume the tractor uses a Kohler K$301$ engine $(12$ hp at $3600$ rpm$).$