Example 1

Example 1

flickr:4971323071

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)\\ & =(\frac {-N_2}{N_4})\\ \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.