# Rack and pinion, module 1 (20 T pinion, 120 mm rack)

> How far does a rack move per turn of the pinion?

- Category: Mechanisms › Gears
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 113 (1868)
- Page: https://xemstudio.com/objects/rack-and-pinion-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=rack-and-pinion-mechanism · Plain text: https://xemstudio.com/objects/rack-and-pinion-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 turning on a fixed axis drives a straight toothed rack: one turn moves the rack π·m·N = 62.83 mm for a 20-tooth module 1 pinion (its pitch circumference). Either part can drive.
- The rack is the basic rack of the involute system (straight 20° flanks), so it meshes with every module 1 gear; the pinion's axis sits exactly one pitch radius (10 mm) above the rack's pitch line.
- Brown's No. 113: circular motion to straight-line motion and back.
- Parts (each has its own page): spur-gears-module-1, gear-rack-m1-120-full-depth.
- Brown's movement No. 113 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| module | 1 |
| pinion | 20 T, pitch Ø20 |
| rack | 120 mm |
| travel per turn | 62.83 mm |
| pinion axis above pitch line | 10 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. 113: figure, his text and an animation](https://507movements.com/mm_113.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/rack-and-pinion-mechanism/index.json

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

## Questions

**How far does a rack move per turn of the pinion?**

A pinion turning on a fixed axis drives a straight toothed rack: one turn moves the rack π·m·N = 62.83 mm for a 20-tooth module 1 pinion (its pitch circumference). Either part can drive.

**How far does a rack move per pinion revolution?**

Pitch circumference: π × module × teeth (62.83 mm for module 1, 20 teeth).

## Fits with

- [Spur gears, module 1: 10 to 80 teeth (20° involute)](https://xemstudio.com/objects/spur-gears-module-1/)
- [Gear rack, module 1, 120 mm, full-depth 20° teeth](https://xemstudio.com/objects/gear-rack-m1-120-full-depth/)