QUESTION $2[15$ Marks$]$

Figure Q$2$ shows the top half of a compound epicyclic gearset with input shaft I rotating at a constant speed of $800$ rpm in clockwise direction and providing input power of $6$ kW $.$ Calculate the following:$-$

$($i$)$ The speed and direction of output shaft O and gear X if Annulus wheel A$2$ is rotating at $3500$rpm in counter$-$clockwise direction.

$($ii$)$ The speed and direction of output shaft O and gear X if Annulus wheel A $2$ is held stationary.

$($iii$)$ The braking torque $($magnitude and direction$)$ that must be applied to Annulus wheel A$2$ to hold it stationary, and assuming gear transmission efficiency is $90\%.$

Number of teeth:

$S1=50,S2,=40$

$P1=25,P2,=40$

$x=50,O,=60$

Figure Q$2$

$N_o=-4037\mathrm{.}5rpm,N_x=4845rpm$

$N_o=-100rpm,N_x=120rpm$

$T_b=-587\mathrm{.}284Nm,$