Epicyclic (Planetary) Gearset

Coaxial gear reduction and power-splitting train of sun, planet, carrier, and ring gears offering multiple speed ratios.

Specifications & Metrics

type: Mechanical Power Transmission
governing equation: N_s ω_s + N_r ω_r = (N_s + N_r) ω_c (Willis kinematic equation)
primary function: Coaxial high-torque speed reduction, multi-ratio transmission, and two-input mechanical summing
key parameters: Sun tooth count (N_s), ring tooth count (N_r), planet count (n_p), assembly condition (N_s + N_r)/n_p = integer
originator: Antikythera Mechanism (~80 BCE), Agostino Ramelli (1588), William Murdoch (1781 sun-and-planet)

Used in antiquity in the Antikythera mechanism (~80 BCE) to model lunar anomalies and in Agostino Ramelli's 1588 bookwheel, a planetary gearset meshes a central sun gear and an internal-toothed outer ring gear with multiple planet gears mounted on a rotating carrier.
Governed by the kinematic equation N_s·ω_s + N_r·ω_r = (N_s + N_r)·ω_c, locking either the sun, the carrier, or the ring gear yields three distinct coaxial gear ratios without unmeshing teeth — the foundation of automotive automatic transmissions.
Because load is shared simultaneously across multiple planet pinions in a compact coaxial envelope, planetary gearboxes achieve high torque-to-weight density in geared turbofan aero-engines, wind turbines, and hybrid vehicle power-split transaxles.