Levai's Gear Configuration 2

Know:

(1)\begin{align} \frac {\omega_{l/a}}{\omega_{f/a}}& =\frac {\omega_l-\omega_a}{\omega_f-\omega_a}\\ \end{align}

Here,

*f = 2*

*a = 1*

*l = 5*

from which, we get

(2)\begin{align} \frac {\omega_{5/1}}{\omega_{2/1}}& =\frac {\omega_5-\omega_1}{\omega_2-\omega_1}\\ \end{align}

to relate the angular velocities of gears 5 and 2, use the relationship between angular velocity and the number of teeth for each gear.

(3)\begin{split} \frac {\omega_{5/1}}{\omega_{2/1}}& =\left(\frac {-N_2}{N_3}\right)\left(\frac {N_4}{N_5}\right)\\ & =\left(\frac {-N_2*N_4}{N_3*N_5}\right)\\ \end{split}

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

(4)\begin{align} \omega_5 & =\left(\frac {-N_2*N_4}{N_3*N_5}\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: 11, last edited: 13 Oct 2010 02:53