Levai's Gear Configuration 12

# Gear Configuration 12

Here,

a = 1
f = 2
l = 6

from which, we get

(1)
\begin{align} \frac {\omega_{6/1}}{\omega_{2/1}}& =\frac {\omega_6-\omega_1}{\omega_2-\omega_1}\\ \end{align}
(2)
\begin{align} \frac {\omega_{6/1}}{\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_5}{N_6}\right)\\ \end{align}

and,

(3)
\begin{align} &\left(\frac {N_4}{N_5}\right)=1 \end{align}

so,

(4)
\begin{align} &\frac {\omega_{6/1}}{\omega_{2/1}}& =\left(\frac {N_2N_5}{N_4N_6}\right)\\ \end{split} \end{align}

Therefore,

(5)
\begin{align} \frac {\omega_6-\omega_1}{\omega_2-\omega_1}&=\left(\frac {N_2N_5}{N_4N_6}\right)\\ \end{align}

from (1) and the expression above, we get

(6)
\begin{align} \omega_6 & =\left(\frac {N_2N_5}{N_4N_6}\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.

page revision: 19, last edited: 17 Sep 2010 16:24