Tp15

# Austin's Test Page

## Gear Configuration 1

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*f = 2*

*l = 7*

*a = 1*

from which, we get

(1)\begin{align} \frac {\omega_{7/1}}{\omega_{2/1}}& =\frac {\omega_7-\omega_1}{\omega_2-\omega_1}\\ \end{align}

(2)
\begin{split} \frac {\omega_{7/1}}{\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_6}{N_7}\right)\\ \end{split}

Gears 3 & 4 as well as 5 & 6 are on the same shaft, therefore their ratio is 1, giving us

(3)\begin{split} \frac {\omega_{7/1}}{\omega_{2/1}} =\left(\frac {-N_2 N_4 N_6}{N_3 N_5 N_7}\right)\\ \end{split}

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

(4)\begin{align} \omega_7 & = \omega_1 + \left(\frac{-N_2 N_4 N_6}{N_3 N_5 N_7}\right)\left(\omega_2 - \omega_1\right)\\ \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: 9, last edited: 09 Sep 2010 02:39