Question

In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, while the sun gear rotates counterclockwise at 100 rpm. Let the number of teeth on the sun planet and outer gears to be 50, 25 and 100, respectively. The ratio of magnitude of angular velocity of the planet gear to the angular velocity of the carrier arm is

Answer 1

We take convention clockwise (+ve)
$N_D=0$
$N_S=-100$
$T_S=50$,
$T_P=25$,
$T_D=100$
$\frac{N_p}{N_{ARM}}=?$

Motions	Arm	s(50)	P(25)	D(100)
1.Arm fixed let sun rotates by +,r.p.m clockwise	0	+x	$\frac{-x\times 50}{25}$	$-x\times \left(\frac{50}{25}\right)\times \left(\frac{25}{100}\right)$
2. Amr free	y	(y+x)	(y-2x)	$(y-\frac{x}{2})$

y + x = -100 ...(i)
$y-\frac{x}{2}=0$ ...(ii)
By Equation (i) - Equation (ii),
$\frac{3x}{2}=-100=x=\frac{-200}{3}$
$y=-100-x=-100+\frac{100}{3}=\frac{-100}{3}$
$N_P=y-2x=\frac{-100}{3}+\frac{400}{3}=\frac{300}{3}=100$
$N_{ARM}=y=\frac{-100}{3}$
$\frac{N_P}{N_{ARM}}=\frac{100}{\frac{-100}{3}}=-3$
$\left|\begin{array}{c}\frac{N_P}{N_{ARM}}\end{array}\right|=3$