Tp15

# Austin's Test Page

## Gear Configuration 1

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Here,

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