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