Semester 1 / Mechanics / Dynamics / Gears

Gears

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When 2 gears touch:

r1ω1=r2ω2r_1 \omega_1 = r_2 \omega_2

Pitch

Also known as module of the gear wheel. Denoted by mm.

d=mz=2rd = mz = 2r
Here:
dd
pitch circle diameter
mm
pitch of the gear
zz
no. of teeth in the gear
rr
radius of the gear

Epicyclic Gears

In below equations:

  • ωp\omega_p - Absolute angular speed of planet wheel PP

External

External epicyclic gears

ωp=(1+rSrP)ωL−(rSrP)ωS\omega_p=\Big(1+\frac{r_S}{r_P}\Big)\omega_L - \Big(\frac{r_S}{r_P}\Big)\omega_S

Internal

Internal epicyclic gears

ωp=(1−rArP)ωL+(rArP)ωA\omega_p=\Big(1-\frac{r_A}{r_P}\Big)\omega_L + \Big(\frac{r_A}{r_P}\Big)\omega_A
Written by November 3, 2026 1 min read
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