# Crank, slotted arm and toothed sector driving a rack

> How does a crank in a slotted arm move a rack back and forth?

- Category: Mechanisms › Gears
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 131 (1868)
- Page: https://xemstudio.com/objects/crank-slotted-arm-sector-rack-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=crank-slotted-arm-sector-rack-mechanism · Plain text: https://xemstudio.com/objects/crank-slotted-arm-sector-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 crank pin, in a slide block, runs in the slot of an arm pivoted 70 mm from the crank centre: the arm rocks through ±9.9° (sin⁻¹ 12/70). A 60-tooth sector on the same pivot turns with the arm and drives a rack below: the rack moves R × angle = 30 mm × 0.346 rad = 10.4 mm total, each way, with the quick-return timing of the slotted lever.
- Drawn at crank angle 200°: arm at 9.71°, rack 5.08 mm from mid-stroke, teeth meshed on the sector's pitch circle.
- Brown's No. 131 (rectilinear motion of a rack from a crank by a slotted arm and toothed sector).
- Parts (each has its own page): slotted-arm-sector-gear-m1-60t-60deg-b5, gear-rack-m1-120-full-depth, crank-disc-36-pin-r12, slide-block-12x6, dowel-pins-metric.
- Brown's movement No. 131 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| crank radius | 12 mm |
| pivot distance | 70 mm |
| arm swing | ±9.9° |
| sector | 60 T, R30 |
| rack stroke | 10.4 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. 131: figure, his text and an animation](https://507movements.com/mm_131.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/crank-slotted-arm-sector-rack-mechanism/index.json · license: https://xemstudio.com/files/hardware/crank-slotted-arm-sector-rack-mechanism/LICENSE.md

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

## Questions

**How does a crank in a slotted arm move a rack back and forth?**

A crank pin, in a slide block, runs in the slot of an arm pivoted 70 mm from the crank centre: the arm rocks through ±9.9° (sin⁻¹ 12/70). A 60-tooth sector on the same pivot turns with the arm and drives a rack below: the rack moves R × angle = 30 mm × 0.346 rad = 10.4 mm total, each way, with the quick-return timing of the slotted lever.

## Fits with

- [Slotted arm with a 60° toothed sector (module 1, 60 T), Ø5 bore](https://xemstudio.com/objects/slotted-arm-sector-gear-m1-60t-60deg-b5/)
- [Gear rack, module 1, 120 mm, full-depth 20° teeth](https://xemstudio.com/objects/gear-rack-m1-120-full-depth/)
- [Crank disc Ø36 × 5, Ø5 bore, Ø3 pin hole at 12 mm](https://xemstudio.com/objects/crank-disc-36-pin-r12/)
- [Slide block 12 × 6.2 mm for a 6.4 mm slot](https://xemstudio.com/objects/slide-block-12x6/)
- [Dowel pins, 2–6 mm (ISO 2338 / DIN 6325)](https://xemstudio.com/objects/dowel-pins-metric/)