Tp4
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Here,

f = 2
a = 1
l = 7

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)\\ & =\left(\frac {-N_2N_4N_6}{N_3N_5N_7}\right)\\ \end{split}

Note:

(3)
$$N_3/N_4=1$$

and

(4)
$$N_5/N_6=1$$

because they are axial gears

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

(5)
\begin{align} \omega_4 & =\left(\frac {-N_2N_4N_6}{N_3N_5N_7}\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: 18, last edited: 08 Sep 2010 19:22