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)\begin{equation} N_3/N_4=1 \end{equation}

and

(4)\begin{equation} N_5/N_6=1 \end{equation}

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