Problem $3(5$ points$)$: The geartrain system has an input power of $1$ kW $,$ with the input motor$-$driven shaft spinning at $1500$ rpm CW $.$ The gears have a module of $2\mathrm{.}5$ mm and pressure angle of $22\mathrm{.}5.$ Use full depth teeth if required.

a$.$ Determine the reduction ratio for the geartrain if gear $1$ is the input and gear $4$ is the output.

b$.$ Determine input torque, angular speeds, pitch circle and base circle radii of all the gears. Obtain center distance between gears $3$ and $4.$

c$.$ Draw FBDs of all the gears, showing the torques $($in their proper sense$),$ and transmitted and radial forces between the respective meshing gear pairs. What is the net force along the line of action for each gear mesh? For each pair, show the direction of line of action clearly.

Problem $4(5$ points$)$: A $20$ pressure angle steel spur gear pinion has $20$ teeth and a module of $4$ mm and is to transmit $7\mathrm{.}5$ kW at a speed of $250$ rpm to a gear with $36$ teeth.

Find the pitch line velocity of the pinion and the transmitted load based on the input power specification.

Assume the gear is cut and milled. Calculate the dynamic or velocity factor. Also, determine the Lewis form factor.

Use the Lewis stress equation and find the appropriate face width if the maximum allowable bending stress is $20$ kpsi $.$

Obtain the maximum contact stress value if Poisson's ratio and elastic modulus for the gear and pinion are, respectively, $0\mathrm{.}2,$ and $200$ GPa.