A gear reduction uses a countershaft shown in the figure. Gear A receives power from another gear with the transmitted load force $\backslash ($ F$\_\{$A$\}\backslash )$ applied at the $\backslash (20^\{\backslash$circ$\}\backslash )$ pressure angle as shown below. The power is transmitted through the shaft and delivered through gear $\backslash ($ B $\backslash )$ through a transmitted load $\backslash ($ F$\_\{$B$\}\backslash )$ at the pressure angle shown below. The transmitted steady torque is $2819$ lbf in$.$ Show a preliminary design of the shaft by performing the following task.

a$)$ Sketch a general shaft layout including means to locate the components.

b$)$ Determine critical diameter of the shaft based on infinite fatigue life with a design factor of $1\mathrm{.}5.$ Check for yielding.

c$)$ Make any other dimensional decision necessary to specify all diameters.