Problem $13\mathrm{.}020-$ Compound reverted gear train

A compound reverted gear train is to be designed as a speed increaser to

provide a total increase of speed of exactly $56$ to $1.$ With a $20$ pressure angle,

specify appropriate numbers of teeth to minimize the gearbox size while

avoiding the interference problem in the teeth. Assume all gears will have the

same diametral pitch. The $1$st stage has the largest speed ratio.

The number of teeth in gear $2$ is

The number of teeth in gear $3$ is

The number of teeth in gear $4$ is

The number of teeth in gear $5$ is