Levai's Gear Configuration 1

Gear Configuration 1

flickr:4962352050

Here,

f = 2
a = 1
l = 4

from which, we get

(1)
\begin{align} \frac {\omega_{4/1}}{\omega_{2/1}}& =\frac {\omega_4-\omega_1}{\omega_2-\omega_1}\\ \end{align}
(2)
\begin{split} \frac {\omega_{4/1}}{\omega_{2/1}}& =\left(\frac {-N_2}{N_3}\right)\left(\frac {N_3}{N_4}\right)\\ & =\left(\frac {-N_2}{N_4}\right)\\ \end{split}

therefore from (1) and the expression above, we get

(3)
\begin{align} \omega_4 & =\left(\frac {-N_2}{N_4}\right)\left(\omega_2 - \omega_1\right) + \omega_1\\ \end{align}

This is the angular velocity of the Ring gear in terms of the angular velocity of the Arm and the angular velocity of the Sun gear for the configuration shown.

How gears work