# Epicyclic (planetary) gear train: sun 24, planets 18, ring 60

> How does a planetary gear train get its ratio?

- Category: Mechanisms › Gears
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 502 (1868)
- Page: https://xemstudio.com/objects/epicyclic-gear-train-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=epicyclic-gear-train-mechanism · Plain text: https://xemstudio.com/objects/epicyclic-gear-train-mechanism/sheet.txt
- License: dimension sheet CC BY 4.0 (Xem Studio); linked files under their publishers' licenses
- Use in every chat: add https://xemstudio.com/mcp as a connector (https://xemstudio.com/use-with-ai/)

**Exact dimensions.** True size, with no printing tolerance added.

## Notes

- A sun gear, three planets on a carrier and a ring gear: hold the ring and drive the sun, and the carrier turns at 1/(1 + N_ring/N_sun) = 24/84 of sun speed (3.5 : 1) in the same direction.
- Tooth counts satisfy N_ring = N_sun + 2·N_planet (60 = 24 + 36) and (N_sun + N_ring)/planets = 84/3 = 28 (whole), so three equally spaced planets mesh with both at once — checked here at the drawn pose.
- Hold the carrier instead and the ring turns backwards at 24/60; hold the sun and ring-to-carrier is 60/84. Brown's Nos. 502–507 are the epicyclic trains.
- Parts (each has its own page): internal-ring-gear-m1-60t, spur-gears-module-1, planet-carrier-3x-r21, dowel-pins-metric.
- Brown's movement No. 502 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| sun | 24 T (Ø8 bore) |
| planets | 3 × 18 T on Ø5 dowels |
| ring | 60 T internal |
| carrier radius | 21 mm |
| ratio, ring fixed | 3.5 : 1 sun to carrier |

## Where the files are

- Henry T. Brown (1868, public domain): [Five Hundred and Seven Mechanical Movements — scan on archive.org](https://archive.org/details/fivehundredseven00browiala) — web — Publisher's page; dimensions are facts
- 507movements.com: [Brown's movement No. 502: figure, his text and an animation](https://507movements.com/mm_502.html) — web — Publisher's page; dimensions are facts

## Free STEP/STL (1 parts, CC BY 4.0, Xem Studio)

Index: https://xemstudio.com/files/hardware/epicyclic-gear-train-mechanism/index.json

- epicyclic-gear-train-mechanism-assembly: [STEP](https://xemstudio.com/files/hardware/epicyclic-gear-train-mechanism/epicyclic-gear-train-mechanism-assembly.step) · [STL](https://xemstudio.com/files/hardware/epicyclic-gear-train-mechanism/epicyclic-gear-train-mechanism-assembly.stl) — Assembled mechanism, all parts placed at one pose (STEP keeps each part separate)

## Questions

**How does a planetary gear train get its ratio?**

A sun gear, three planets on a carrier and a ring gear: hold the ring and drive the sun, and the carrier turns at 1/(1 + N_ring/N_sun) = 24/84 of sun speed (3.5 : 1) in the same direction.

**What is the ratio of a planetary gear with the ring fixed?**

1 + N_ring/N_sun from sun to carrier: 1 + 60/24 = 3.5 here.

## Fits with

- [Internal (ring) gear, module 1, 60 teeth, Ø80](https://xemstudio.com/objects/internal-ring-gear-m1-60t/)
- [Spur gears, module 1: 10 to 80 teeth (20° involute)](https://xemstudio.com/objects/spur-gears-module-1/)
- [Planet carrier for three planets on a 21 mm radius (Ø52 × 5)](https://xemstudio.com/objects/planet-carrier-3x-r21/)
- [Dowel pins, 2–6 mm (ISO 2338 / DIN 6325)](https://xemstudio.com/objects/dowel-pins-metric/)