Levai's Gear Configuration 9
Gear Configuration 9
<Diagram (i) from p. 505>
Here,
f = 2
a = 1
l = 5
from which, we get
(1)\begin{align} \frac {\omega_{5/1}}{\omega_{2/1}}& =\frac {\omega_5-\omega_1}{\omega_2-\omega_1}\\ \end{align}
(2)
\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
(3)\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.
page revision: 1, last edited: 15 Sep 2010 01:24