Problem $1.$ Design a compound speed reducer gear train with a gear ratio of $140$ and diametral pitch of $16$ using the steel or cast iron gears available in the Boston Gear catalog given below. $(25$ points$)$

a$)$ Draw a schematic figure of the gear train.

b$)$ Specify diameters, $\backslash ($ d $\backslash )$ and tooth numbers, $\backslash ($ N $\backslash )$ for all gears.

c$)$ If the input velocity is $3600$ rpm $,$ find the velocity of each gear and identify their horsepower capacity using the given data.