# Sun-and-planet gear (Watt's crank substitute), 30 : 30

> How does a sun-and-planet gear replace a crank?

- Category: Mechanisms › Gears
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 39 (1868)
- Page: https://xemstudio.com/objects/sun-and-planet-gear-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=sun-and-planet-gear-mechanism · Plain text: https://xemstudio.com/objects/sun-and-planet-gear-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 planet gear fixed to the end of a rocking rod is held in mesh with a sun gear on the output shaft by a free arm: each to-and-fro cycle of the rod carries the planet once round the sun.
- With equal gears the sun makes two turns per cycle (1 + N_planet/N_sun), which is why it was used: twice the shaft speed of a plain crank.
- Brown's No. 39 is the arrangement used by Watt as a substitute for the crank. Module 1, 30 + 30 teeth, centre distance 30 mm.
- Parts (each has its own page): spur-gears-module-1, sun-and-planet-arm-30, sun-and-planet-rod-100, linear-shafts-h6.
- Brown's movement No. 39 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| sun / planet | 30 T / 30 T, module 1 |
| arm centres | 30 mm |
| sun turns per rod cycle | 2 |
| rod | 100 mm |

## 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. 39: figure, his text and an animation](https://507movements.com/mm_039.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/sun-and-planet-gear-mechanism/index.json

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

## Questions

**How does a sun-and-planet gear replace a crank?**

A planet gear fixed to the end of a rocking rod is held in mesh with a sun gear on the output shaft by a free arm: each to-and-fro cycle of the rod carries the planet once round the sun.

## Fits with

- [Spur gears, module 1: 10 to 80 teeth (20° involute)](https://xemstudio.com/objects/spur-gears-module-1/)
- [Sun-and-planet arm, 30 mm centres, Ø10 holes](https://xemstudio.com/objects/sun-and-planet-arm-30/)
- [Sun-and-planet rod, 100 mm, with Ø10 × 13 planet boss](https://xemstudio.com/objects/sun-and-planet-rod-100/)
- [Linear shafts Ø3 to Ø25 mm (h6), 100 to 1000 mm long](https://xemstudio.com/objects/linear-shafts-h6/)