The exploded drawing in figures $($a$)-($c$)$ shows details of the Transmission $($d$)$ components.

Assume shaft diameter is $0\mathrm{.}5$ in$.$

The engine delivers a torque of $T_{in}=3000lb*$ in

to the transmission. The transmission is in low gear and has a ratio

of $R=2\mathrm{.}778,$ where $R=\frac{\text{T}\text{o}\text{u}\text{t}}{\text{T}\text{i}\text{n}}$ such that $T_{\text{o}\text{u}\text{t}}=8333lb*$ in

Gear diameters of A and C are $2\frac{1}{4}$ in$.$

Gear diameters of B and D are $3\frac{3}{4}$ in$.$

Hence the center$-$to$-$center distance between the shafts is

$\frac{2\frac{1}{4}+3\frac{3}{4}}{2}=3$ in

Input gear A rotates at engine speed and drives the countershaft

gear B$.$ Countershaft gear C meshes with the main shaft gear D$.$

The mainshaft is supported with bearings at I and II$.$

The countershaft is supported with bearings at III and IV$.$

Assume a pressure angle of $\frac{O}{?}=20.$

Note: The input and output torque shown is on the mainshaft.

$($b$)$ Mainshaft

Draw a stress element for the critical point.

Draw the Mohr's Circle for this stress element and determine the principal stresses and maximum

shear stress.

Design $(5$ points each$)$

Assume there are $4$ bolts that are required to hold the transmission gear box in place. Provide a

sketch showing the location of these bolts $($i$.$e$.$ vertical and horizontal dimensions with respect to a

reference point, e$.$g$.$ the center of one of the shafts$).$ With your selected positioning of the bolts,

determine the reaction forces at each bolt due to the torque, $T_{\text{b}\text{o}\text{x}}.$

Calculate the support reactions at I, II$,$ III, and IV$,$ and the torque, $T_{\text{o}\text{u}\text{t}},$ for $3$ different

combinations of gear dimensions for A$,$ B$,$ C$,$ and D$.$

Note: The combination you choose must maintain the shaft center$-$center spacing of $3$ in $.$

Hint: Creating an MSExcel sheet to do this will greatly simplify your work.