Levai's Gear Configuration 6

Here,

*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}

to relate the angular velocities of gears 6 and 2, use the relationship between angular velocity and the number of teeth for each gear.

(2)\begin{split} \frac {\omega_{6/1}}{\omega_{2/1}}& =\left(\frac {-N_2}{N_4}\right)\left(\frac {N_5}{N_6}\right)\\ & =\left(\frac {-N_2*N_5}{N_4*N_6}\right)\\ \end{split}

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

(3)\begin{align} \omega_6 & =\left(\frac {-N_2*N_5}{N_4*N_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: 7, last edited: 24 Sep 2010 17:10