# Pinion between a fixed and a free rack (travel doubler)

> How does a pinion between two racks double a stroke?

- Category: Mechanisms › Gears
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 118 (1868)
- Page: https://xemstudio.com/objects/pinion-between-racks-doubler-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=pinion-between-racks-doubler-mechanism · Plain text: https://xemstudio.com/objects/pinion-between-racks-doubler-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 pinion turns on an axle carried by a rod. Below it is a fixed rack, above it a rack free to slide. Moving the axle a distance d rolls the pinion on the fixed rack, and its top, moving at twice the axle's speed, carries the free rack 2d: the stroke is doubled with no gearing ratio.
- Module 1, 20-tooth pinion, racks with pitch lines 20 mm apart (one pitch diameter); drawn with the axle 6.28 mm (two pitches) along and the free rack 12.57 mm along. The free rack's own guide is not drawn.
- Brown's No. 118 (pinion on the connecting rod between a fixed and a movable rack).
- Parts (each has its own page): gear-rack-m1-120-full-depth, spur-gears-module-1, pinion-carrier-rod-100-bore6, dowel-pins-metric.
- Brown's movement No. 118 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| pinion | 20 T, module 1 |
| racks | 2 × 120 mm, pitch lines 20 mm apart |
| ratio | free rack = 2 × axle travel |
| 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. 118: figure, his text and an animation](https://507movements.com/mm_118.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/pinion-between-racks-doubler-mechanism/index.json · license: https://xemstudio.com/files/hardware/pinion-between-racks-doubler-mechanism/LICENSE.md

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

## Questions

**How does a pinion between two racks double a stroke?**

A pinion turns on an axle carried by a rod. Below it is a fixed rack, above it a rack free to slide. Moving the axle a distance d rolls the pinion on the fixed rack, and its top, moving at twice the axle's speed, carries the free rack 2d: the stroke is doubled with no gearing ratio.

## Fits with

- [Gear rack, module 1, 120 mm, full-depth 20° teeth](https://xemstudio.com/objects/gear-rack-m1-120-full-depth/)
- [Spur gears, module 1: 10 to 80 teeth (20° involute)](https://xemstudio.com/objects/spur-gears-module-1/)
- [Pinion carrier rod, 100 mm, Ø6 axle hole and Ø3 end hole](https://xemstudio.com/objects/pinion-carrier-rod-100-bore6/)
- [Dowel pins, 2–6 mm (ISO 2338 / DIN 6325)](https://xemstudio.com/objects/dowel-pins-metric/)