Gears

When 2 gears touch:

$$r_1 \omega_1 = r_2 \omega_2$$

Pitch

Aka. module of the gear wheel. Denoted by $m$. $$

$$d = mz = 2r$$

Here:

• $d$ - pitch circle diameter
• $m$ - pitch of the gear
• $z$ - no. of teeth in the gear
• $r$ - radius of the gear

Epicyclic gears

In below equations:

• $\omega_p$ - Absolute angular speed of planet wheel $P$

External

$$\omega_p=\Big(1+\frac{r_S}{r_P}\Big)\omega_L - \Big(\frac{r_S}{r_P}\Big)\omega_S$$

Internal

$$\omega_p=\Big(1-\frac{r_A}{r_P}\Big)\omega_L + \Big(\frac{r_A}{r_P}\Big)\omega_A$$