Tp5

# Gear Configuration 12

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*f = 2*

*a = 1*

*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{split} \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)\\ & =\left(\frac {-N_2N_5}{N_4N_6}\right)\\ \end{split}

Therefore,

(3)\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

(4)\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: 6, last edited: 08 Sep 2010 19:20