Question $3[20$ marks$]$

$($a$)$ For the gear syatem in Figure Q$3-1,$ compute the rotational speed and torque for gear C $,$ provided that gear A revolvea at $60$ revolutions per minute in the clockwise direction, and with a torque of $120$ Nm $.$ The gear profles for A$,$ B$1,$ B$2,$ and C have $30,12,24,$ and $10$ teeth respectively. Note that $\backslash ($ B $1\backslash )$ and B$2$ are attached and rotate together as a single unit.

Fgure $(13-1$ A $3$ component gear system

$($b$)$ Figure Q$3-2$ shows an eplcyclic gear train with the following properties: The camer arm A is attached to the input shaft and the planetary gears, and rotates clockwise at $120$ revolutions per minute. The central sun gear B is fixed and has $24$ teeth. The triplet of planetary gears C $,$ each have $12$ teeth. Ring gear $\backslash ($ D $\backslash )$ is attached to the output shaft and has $48$ internal teeth. Determine the rotational speed and direction of rotation for the output shatt.