$3.$ Please use the schematic below to design a gear box and answer the questions. $(40$ points$)$

$1)$ Please demonstrate the failure mechanisms of gears. $(10$ points$)$

$2)$ The gear box below is to transmit the power through two pairs of gears$($spur gear and bevel gear$).$ Please demonstrate how we can determine the maximum transmittable power when everything is given for the gear box except the power. You don't need to write any equation, but clearly explain the procedures step$-$by$-$step to determine the maximum transmittable power by this gear box. $(30$ points$)$