# Mutilated spur gear moving a rack, a spring bringing it back

> How does a part-toothed gear and a spring make a rack go back and forth?

- Category: Mechanisms › Intermittent motion
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 81 (1868)
- Page: https://xemstudio.com/objects/mutilated-gear-spring-rack-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=mutilated-gear-spring-rack-mechanism · Plain text: https://xemstudio.com/objects/mutilated-gear-spring-rack-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 spur gear with teeth on half its rim turns continuously above a rack: while its teeth are in mesh it drives the rack one way and compresses a spring; when the toothless half comes round the spring pushes the rack back.
- Catalog parts: the module 1, 20-tooth mutilated pinion (10 teeth) and the 120 mm full-depth rack; stroke = 10 × π = 31.42 mm. The rack slides on a base against a side rail; an Ø8 spring between the rack's end and the base's end wall returns it. Drawn in mesh.
- Brown's No. 81 (mutilated spur gear giving alternate rectilinear motion to a rack rod, a spring returning it).
- Parts (each has its own page): mutilated-pinion-m1-20t-half, gear-rack-m1-120-full-depth, compression-spring-od8-wire1-l30, rack-guide-base-170-spring-seat, dowel-pins-metric.
- Brown's movement No. 81 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| pinion | module 1, 10 of 20 teeth |
| stroke | 31.42 mm |
| spring | OD8 × Ø1 wire |

## 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. 81: figure, his text and an animation](https://507movements.com/mm_081.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/mutilated-gear-spring-rack-mechanism/index.json · license: https://xemstudio.com/files/hardware/mutilated-gear-spring-rack-mechanism/LICENSE.md

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

## Questions

**How does a part-toothed gear and a spring make a rack go back and forth?**

A spur gear with teeth on half its rim turns continuously above a rack: while its teeth are in mesh it drives the rack one way and compresses a spring; when the toothless half comes round the spring pushes the rack back.

## Fits with

- [Mutilated pinion, module 1, 20 T with 10 teeth kept (half)](https://xemstudio.com/objects/mutilated-pinion-m1-20t-half/)
- [Gear rack, module 1, 120 mm, full-depth 20° teeth](https://xemstudio.com/objects/gear-rack-m1-120-full-depth/)
- [Compression spring OD8, wire Ø1, free length drawn 30 mm, 8 coils](https://xemstudio.com/objects/compression-spring-od8-wire1-l30/)
- [Rack guide base 170 × 20 with side rail and spring seat](https://xemstudio.com/objects/rack-guide-base-170-spring-seat/)
- [Dowel pins, 2–6 mm (ISO 2338 / DIN 6325)](https://xemstudio.com/objects/dowel-pins-metric/)