A motor applies an input torque $T_1=50ft*lbf$ to gear $1$ in the direction shown. Gear $1$ has $32$ teeth, Gear $2$ has $114$ teeth, Gear $3$ has $36$ teeth, and Gear $4$ has $96$ teeth. The pressure angle

for the gears is the same as angles $$ and $.$ Both shafts are composed of $1006$ HR steel with a machined surface.

Various locations on the shafts $1$ and $2$ are to be analyzed: the diameter reduction from $d_1$ to $d_3$ on shaft $1,$ keyseats and fillets at each gear listed, fillets at each bearing $("$brg$"),$ and at the ring groove

$($fillet radius of $0\mathrm{.}05$ in $,$ width of $0\mathrm{.}13$ in $,$ and shaft diameter of $0\mathrm{.}93$ in at the middle of the groove$).$ At each of these potentially critical locations, find the appropriate fatigue stress concentration factors, the

endurance limit$,$ the torque and bending moment carried, and the factors of safety against yield and against fatigue. The target reliability is $99\%$ for both shafts. $($Recommended assumptions listed below

tables.$)$