Levai's Gear Configuration 9

Gear Configuration 9

<Diagram (i) from p. 505>


f = 2
a = 1
l = 5

from which, we get

\begin{align} \frac {\omega_{5/1}}{\omega_{2/1}}& =\frac {\omega_5-\omega_1}{\omega_2-\omega_1}\\ \end{align}
\begin{split} \frac {\omega_{5/1}}{\omega_{2/1}}& =\left(\frac {-N_2}{N_3}\right)\left(\frac {-N_3}{N_4}\right)\left(\frac {N_4}{N_5}\right)\\ & =\left(\frac {N_2}{N_5}\right)\\ \end{split}

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

\begin{align} \omega_5 & =\left(\frac {N_2}{N_5}\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 velocities of the Arm and Sun gears for the configuration shown.