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