$1($a$)$ A helical gear is mounted on a simple supported shaft as shown in Figure $1.$ Only bearing B takes thrust load. A flexible coupling $($not shown in Figure $1)$ for transmitting torque is attached to the right end of the shaft. The left end of the shaft is free standing.

$($i$)$ Draw load, shear force and bending moment diagrams for the shaft in both the horizontal and vertical planes. Indicate the axial forces loading in the diagrams.

$(7$ marks$)$

$($ii$)$ Design the shaft with constant diameter operating at $100$ rpm $,$ assuming that the shaft is machined from SAE $1137$ OQT $400$ and that $\backslash (\backslash$mathrm$\{$Kf$\}=2\mathrm{.}0\backslash )$ is applied to the gear. State all other assumptions made in calculations.

$(4$ marks$)$

$($iii$)$ Design the two bearings for the system if a design life of $10,000$ hour is desired. State all assumptions made.

$(5$ marks$)$