# Crank pin in a slotted yoke (Scotch yoke)

> How does a Scotch yoke turn rotation into pure harmonic motion?

- Category: Mechanisms › Linkages
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 93 (1868)
- Page: https://xemstudio.com/objects/scotch-yoke-crank-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=scotch-yoke-crank-mechanism · Plain text: https://xemstudio.com/objects/scotch-yoke-crank-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

- The crank pin runs in a slot across a sliding yoke, so the yoke moves exactly r·cos θ: simple harmonic motion with no connecting rod and no rod angularity — Brown's 'crank wrist in a slotted yoke'.
- Catalog Scotch-yoke parts, 30 mm stroke: crank pin at 15 mm carrying a 623 bearing in the 10 mm slot; drawn at 50°, the yoke 9.64 mm from centre. A guide block holds the rod straight.
- Brown's No. 93.
- Parts (each has its own page): scotch-yoke, ball-bearings-metric, scotch-yoke-rod-guide-8x8, dowel-pins-metric.
- Brown's movement No. 93 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| stroke | 30 mm |
| crank radius | 15 mm |
| slot | 10 mm (623 bearing) |
| motion | x = 15 cos θ |

## 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. 93: figure, his text and an animation](https://507movements.com/mm_093.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/scotch-yoke-crank-mechanism/index.json · license: https://xemstudio.com/files/hardware/scotch-yoke-crank-mechanism/LICENSE.md

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

## Questions

**How does a Scotch yoke turn rotation into pure harmonic motion?**

The crank pin runs in a slot across a sliding yoke, so the yoke moves exactly r·cos θ: simple harmonic motion with no connecting rod and no rod angularity — Brown's 'crank wrist in a slotted yoke'.

## Fits with

- [Scotch yoke: slotted yoke and crank disc, 20 and 30 mm stroke](https://xemstudio.com/objects/scotch-yoke/)
- [Ball bearings, 683 to 6210 and flanged F6xx (ISO 15)](https://xemstudio.com/objects/ball-bearings-metric/)
- [Rod guide 20 × 20 × 18 with an 8 × 8 slot](https://xemstudio.com/objects/scotch-yoke-rod-guide-8x8/)
- [Dowel pins, 2–6 mm (ISO 2338 / DIN 6325)](https://xemstudio.com/objects/dowel-pins-metric/)