# Scotch yoke: crank pin in a slotted crosshead on pillar guides

> What motion does a Scotch yoke give?

- Category: Mechanisms › Linkages
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 331 (1868)
- Page: https://xemstudio.com/objects/scotch-yoke-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=scotch-yoke-mechanism · Plain text: https://xemstudio.com/objects/scotch-yoke-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 slides in a slot across a crosshead that can only move along two guide pillars: the crosshead position is exactly y = r·sin θ — pure simple harmonic motion, stroke 2r = 24 mm, with no connecting rod.
- Drawn at θ = 40° with the catalog Ø36 crank disc (pin at 12 mm), a Ø3 pin in the 3 mm slot (contact on both faces) and two Ø5 × 100 linear shafts as the guides.
- Brown's No. 331 (crank wrist in a slotted cross-head between pillar guides, as in Nos. 93 and 279).
- Parts (each has its own page): crank-disc-36-pin-r12, scotch-yoke-crosshead-48x14-b5, linear-shafts-h6, dowel-pins-metric.
- Brown's movement No. 331 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| crank radius r | 12 mm |
| stroke | 24 mm |
| motion | y = r sin θ (simple harmonic) |
| guides | 2 × Ø5 shafts, 36 mm apart |

## 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. 331: figure, his text and an animation](https://507movements.com/mm_331.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-mechanism/index.json · license: https://xemstudio.com/files/hardware/scotch-yoke-mechanism/LICENSE.md

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

## Questions

**What motion does a Scotch yoke give?**

A crank pin slides in a slot across a crosshead that can only move along two guide pillars: the crosshead position is exactly y = r·sin θ — pure simple harmonic motion, stroke 2r = 24 mm, with no connecting rod.

**How is a Scotch yoke different from a slider-crank?**

There is no connecting rod: the pin drives the slot directly, so the motion is an exact sine, not the rod-ratio-distorted motion of a slider-crank.

## Fits with

- [Crank disc Ø36 × 5, Ø5 bore, Ø3 pin hole at 12 mm](https://xemstudio.com/objects/crank-disc-36-pin-r12/)
- [Scotch-yoke crosshead 48 × 14 × 8, 3 mm slot, two Ø5 guide bores](https://xemstudio.com/objects/scotch-yoke-crosshead-48x14-b5/)
- [Linear shafts Ø3 to Ø25 mm (h6), 100 to 1000 mm long](https://xemstudio.com/objects/linear-shafts-h6/)
- [Dowel pins, 2–6 mm (ISO 2338 / DIN 6325)](https://xemstudio.com/objects/dowel-pins-metric/)