# Mutilated pinion and double rack (continuous rotation to reciprocation)

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

- Category: Mechanisms › Intermittent motion
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 114 (1868)
- Page: https://xemstudio.com/objects/mutilated-gear-double-rack-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=mutilated-gear-double-rack-mechanism · Plain text: https://xemstudio.com/objects/mutilated-gear-double-rack-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 pinion with teeth on half its rim turns continuously between two facing racks on one frame: for half a turn it drives the upper rack (frame moves one way 31.42 mm), for the other half the lower rack (frame comes back).
- The toothless half is cut to the root circle so it clears the other rack; the racks are spaced one pitch diameter apart (20 mm) with their teeth in phase, which keeps the hand-over clean (half a turn = 10 pitches each way).
- Brown's No. 114.
- Parts (each has its own page): mutilated-pinion-m1-20t-half, double-rack-frame-120.
- Brown's movement No. 114 (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 |
| rack spacing (pitch lines) | 20 mm |
| stroke | 31.42 mm each way |

## 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. 114: figure, his text and an animation](https://507movements.com/mm_114.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/mutilated-gear-double-rack-mechanism/index.json

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

## Questions

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

A pinion with teeth on half its rim turns continuously between two facing racks on one frame: for half a turn it drives the upper rack (frame moves one way 31.42 mm), for the other half the lower rack (frame comes back).

## Fits with

- [Mutilated pinion, module 1, 20 T with 10 teeth kept (half)](https://xemstudio.com/objects/mutilated-pinion-m1-20t-half/)
- [Double rack frame, module 1, racks 20 mm apart (120 × 44)](https://xemstudio.com/objects/double-rack-frame-120/)