Planetary stage in motion
- Sun · fixed
- Planets
- Ring · fixed
- Carrier · fixed
↻ 200ring rpm in
→
↻ 132carrier rpm out
→
×1.52torque
Interactive Gear Guide
How a planetary gearbox works
One sun, a ring, and a set of planets on a rotating carrier. Change the teeth, the planet count and which member is held fixed — and watch the whole stage respond live.
Playground
Design a planetary stage
A planetary (epicyclic) stage packs a big reduction into a small, coaxial package by splitting the load across several planet gears. Pick the sun and planet teeth — the ring size follows automatically — then choose which member is fixed.
Overall ratio i1.52 : 1i = 1 + Zₛ/Zᵣ
Ring teeth Zᵣ50Zₛ + 2 Zₚ
Output speed↻ 132 rpmsame direction as input
Torque multiplier×1.52at output, before losses
Planet spin↻ 417 rpmabout its own pin
Pitch dia. dₛ / dₚ / dᵣ104 / 48 / 200 mmm · Z
Center distance a76 mmm (Zₛ + Zₚ) / 2
Assembly check✗ won't assemble(Zₛ + Zᵣ) / N = 25.33 — not an integer — change teeth or N
Neighbor clearance✓ gap 76 mmbetween planet tips
Load sharetorque per sun–planet mesh
Estimates for a standard single-stage epicyclic with involute teeth, module m. Real designs add profile shift, tolerances and bearing details — talk to our engineers for a manufacturing spec.
Start with the basicsHow a gear pair works — the interactive gear guide →
Reference
The planetary gearbox, explained
The four members, the one equation that governs them, and the design rules that decide whether a stage can even be assembled.
Sun gear Zₛ
The external gear at the center of the stage. Usually the high-speed input — it sees the most load cycles, so it gets the hardest tooth surface.
Planet gears Zₚ
Identical gears (usually 3–5) that mesh with the sun on the inside and the ring on the outside, each spinning on a carrier pin.
Ring gear (annulus) Zᵣ
The internal gear that encloses the stage. Its size is fixed by the others:
Zᵣ = Zₛ + 2 Zₚ
Carrier
The frame that holds the planet pins. When the planets orbit, the carrier turns — it is the slow, high-torque member of the stage.
The Willis equation
One relation ties all three speeds together — every configuration below is just this equation with one member held at zero.
(ωₛ − ωc) / (ωᵣ − ωc) = −Zᵣ / Zₛ
Ring fixed most common
Sun drives, carrier is the output. The workhorse reduction — typically 3:1 to 10:1 per stage, same direction of rotation.
i = 1 + Zᵣ / Zₛ
Sun fixed
Ring drives, carrier is the output. A mild reduction used in hub drives and some winches.
i = 1 + Zₛ / Zᵣ
Carrier fixed star gear
Sun drives, ring is the output, and the direction reverses. With no orbiting planets there are no centrifugal loads — good at very high speeds.
i = −Zᵣ / Zₛ
Assembly condition
Planets are spaced evenly, so the teeth must line up at every position. A stage can only be built if:
(Zₛ + Zᵣ) / N = integer
Try breaking it in the playground — the planets fall out of mesh with the ring.
Load sharing
Torque splits across N sun–planet meshes, so each tooth carries roughly T/N. That is why a planetary stage is several times smaller than a parallel-shaft gearbox of the same rating.
Multi-stage stacking
Input and output are coaxial, so stages bolt end-to-end and their ratios multiply — two 5:1 stages give 25:1 in one compact housing.
iₜₒₜ = i₁ × i₂
Where you meet them
Anywhere torque is huge and space is not.
- Slew drives & cranes
- Cement & ball mill drives
- Mixers, agitators, extruders
- Winches and hoists
- Wind-turbine gearboxes
Need a planetary gear — or a whole stage?
We cut suns, planets and internal ring gears, and refurbish complete planetary drives for cement, mining, sugar and steel plants across Egypt.