# Eccentric spur gear and pinion on a swinging arm (variable speed)

> How does an eccentric gear give a varying speed?

- Category: Mechanisms › Gears
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 222 (1868)
- Page: https://xemstudio.com/objects/eccentric-gear-and-pinion-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=eccentric-gear-and-pinion-mechanism · Plain text: https://xemstudio.com/objects/eccentric-gear-and-pinion-mechanism/sheet.txt
- License: dimension sheet CC BY 4.0 (Xem Studio); files Xem Studio Design License (free to use and sell from, not to redistribute as files: https://xemstudio.com/license/)
- 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 40-tooth gear turns on a shaft 5 mm off its centre; a 20-tooth pinion on a swinging arm follows it, held at the exact 30 mm centre distance by a link from the gear's centre stud. The pinion's speed varies each turn as its contact point moves nearer and farther from the shaft: between about 0.75 and 1.25 of the mean 2 : 1 ratio.
- Drawn at 60° of shaft rotation: gear centre at (2.5, 4.33), pinion at (27.9, 20.29), arm pivot at (50, 0). Module 1, teeth in mesh with no backlash drawn.
- Brown's No. 222 (eccentric wheel with a link in place of the groove of No. 221).
- Parts (each has its own page): eccentric-spur-gear-m1-40t-e5-b5, spur-gears-module-1, swing-arm-30-holes-3-and-6, dowel-pins-metric.
- Brown's movement No. 222 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| gear | 40 T, bore 5 mm off centre |
| pinion | 20 T on a 30 mm arm |
| link | 30 mm, centre to centre |
| speed swing | 0.75 – 1.25 × mean |

## 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. 222: figure, his text and an animation](https://507movements.com/mm_222.html) — web — Publisher's page; dimensions are facts

## Free STEP/STL (1 parts, Xem Studio Design License, Xem Studio)

Index: https://xemstudio.com/files/hardware/eccentric-gear-and-pinion-mechanism/index.json · license: https://xemstudio.com/files/hardware/eccentric-gear-and-pinion-mechanism/LICENSE.md

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

## Questions

**How does an eccentric gear give a varying speed?**

A 40-tooth gear turns on a shaft 5 mm off its centre; a 20-tooth pinion on a swinging arm follows it, held at the exact 30 mm centre distance by a link from the gear's centre stud. The pinion's speed varies each turn as its contact point moves nearer and farther from the shaft: between about 0.75 and 1.25 of the mean 2 : 1 ratio.

## Fits with

- [Eccentric spur gear, module 1, 40 T, Ø5 bore 5 mm off centre, Ø3 centre stud hole](https://xemstudio.com/objects/eccentric-spur-gear-m1-40t-e5-b5/)
- [Spur gears, module 1: 10 to 80 teeth (20° involute)](https://xemstudio.com/objects/spur-gears-module-1/)
- [Swing arm / link 30 mm, Ø3 hole one end, Ø6 the other](https://xemstudio.com/objects/swing-arm-30-holes-3-and-6/)
- [Dowel pins, 2–6 mm (ISO 2338 / DIN 6325)](https://xemstudio.com/objects/dowel-pins-metric/)