Mechanical
Planetary Gears
Sun, planets, ring — concentric gear system with high power density
A planetary (epicyclic) gear system uses a central sun gear, multiple planet gears mounted on a carrier, and a surrounding ring gear with internal teeth. Three coaxial input/output options enable many ratios in a compact footprint. Holding any one element and driving another yields a different ratio. Used in automatic transmissions, hub gears, wind turbines, robotics, and tool drivers. High torque capacity per volume, balanced loads, coaxial input and output.
- ComponentsSun, planets, carrier, ring
- CoaxialInput and output share central axis
- ModesHold ring, hold sun, hold carrier
- Power density2 to 5x equivalent parallel-shaft trains
- Load sharingMultiple planets share torque
- ApplicationsAutomatic transmissions, wind turbines, hubs
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Why planetary gears matter
- Power density. High torque in compact volume.
- Coaxial. Input and output on same shaft simplifies layout.
- Multiple ratios. Selectively hold elements for different ratios.
- Wind turbines. Step up rotor speed to generator.
- Automatic transmissions. Heart of multi-speed automatics.
- Robotics. Servo drives with low backlash.
- Differentials. Bevel epicyclic splits torque.
Common misconceptions
- Single ratio. Same gearset gives multiple ratios via held element.
- Sun is always input. Any element can be input or output.
- Three planets always. Number depends on load and balance — 3 to 5 typical.
- No backlash. Multiple meshes accumulate backlash; precision designs minimize.
- Planet count free. Tooth counts must satisfy assembly constraints (sun + ring even, etc).
- Same as differential. Differential is a specific bevel-gear epicyclic case.
Frequently asked questions
How does a planetary gearset work?
A central sun gear meshes with multiple (typically 3 to 5) planet gears that orbit it. A carrier holds the planets on bearings. A ring gear with internal teeth surrounds them, meshing with the planets externally. Three rotating elements share a common axis. Holding one element fixed and driving another determines the third's motion and the gear ratio.
What ratios can a planetary set produce?
Three primary modes. Hold ring, drive sun, output carrier: ratio = 1 + (ring teeth / sun teeth), large reduction with same direction. Hold sun, drive ring, output carrier: ratio = 1 + (sun/ring), modest ratio. Hold carrier, drive sun, output ring: ratio = -ring/sun, reversal. Combining sets in series multiplies ratios further.
Why such high power density?
Multiple planets share the load. Three planets each carry one-third of input torque, allowing smaller individual gears. Internal-tooth ring gear meshes with planets at favorable contact angles. Coaxial geometry packs efficiently. Compared to parallel-shaft trains of equivalent ratio, planetary sets occupy 30 to 50% of the volume for the same torque capacity.
How are automatic transmissions built?
Stacks of planetary sets with clutches and brakes selectively hold or release elements to engage gear ratios. A traditional 4-speed automatic uses two or three planetary sets and several clutches. Modern 8 to 10 speed transmissions use four or more sets in cleverly arranged kinematic schemes. Same gearset implements multiple ratios by reconfiguring which element is held.
What is the differential's relation?
Automotive differentials use bevel-gear epicyclic geometry to split drive torque between two output shafts at any speed ratio. Equal speeds: standard cruising. Different speeds (cornering): inner wheel slows, outer speeds up; differential allows this while maintaining torque. Limited-slip and locking differentials add friction or clutches to prevent excessive slip on low-traction surfaces.
Where else are planetaries used?
Wind turbine gearboxes step up rotor speed by ratios of 90 to 100, multiple planetary stages in series. Internal hub gears in bicycles. Wheel hubs in trucks and tractors. Robot servo drives. Power tool gearboxes. Watch movements (epicyclic moonphase). Aircraft auxiliary gearboxes. Helicopter main rotor gearboxes split torque from twin engines.
What is the formula for ratios?
Willis' equation. Let omega-s, omega-r, omega-c be sun, ring, carrier angular velocities; let N_s, N_r be sun, ring tooth counts. Then (omega-s minus omega-c) divided by (omega-r minus omega-c) equals minus N_r divided by N_s. Combined with one constraint (one element held), this solves for any ratio. Captures all configurations of a single planetary set.