Question

The sun gear in the figure is driven clockwise at 100 rpm. The ring gear is held stationary. For the number of teeth shown on the gears, the arm rotates at

• A. 0 rpm
• B. 20 rpm
• C. 33.33 rpm
• D. 666.67 rpm

Answer 1

The correct option is B 20 rpm

Method - I:

Gear	1	2	3
No.of teeth	80	30	20(sun)
Speed of (RPM)	+N positive sign means clockwise	$\frac{+N\times 80}{30}$ clockwise for internal gear meshing	$\frac{-N\times 80\times 30}{30\times 20}$ anti-clockwise for external gear meshing
Speed after adding speed of arm +y (clockwise)	N+y	$\frac{+N\times 80}{30}+y$	$\frac{-N\times 80\times 30}{30\times 20}+y$

Given:
$N+y=0$

$y=-N$

Sun gear means "3"

$\frac{-N\times 80\times 30}{30\times 20}+y=0$

$-4N-N=100$

$-5N=100$

$N=-20$

$\therefore y=-N=+20\text{rpm}$

Method II:

Relative velocity method:

Given: $T_s=20,T_p=30,T_R=80$

$N_s=100\text{rpm}\left(CW\right),N_R=0,N_a=?$

$\frac{N_S-N_a}{N_R=N_a}=\frac{-T_R}{T_s}$

$\frac{100-N_a}{0-N_a}=\frac{-80}{20}$

$100-N_a=4N_a$

$5N_a=100$

$N_a=20\text{rpm (CW)}$