# Scott Russell straight-line linkage (half-scissor)

> How does the Scott Russell linkage make a straight line?

- Category: Mechanisms › Linkages
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 339 (1868)
- Page: https://xemstudio.com/objects/scott-russell-straight-line-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=scott-russell-straight-line-mechanism · Plain text: https://xemstudio.com/objects/scott-russell-straight-line-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 bar AB of length 2r has its midpoint C pinned to a radius link OC = r; end A slides on a straight guide through O. Because A, B and O always lie on a circle round C, B moves on the exact straight line through O at right angles to the guide.
- Here r = 40: bar 80 mm (centre-hole link), radius link 40 mm, A in a 6.2 mm slot; at 35° B is 45.89 mm up the perpendicular. A moves 80·cos φ, B 80·sin φ.
- Brown's No. 339 (bar on the rod, one end sliding in a fixed slot, radius bar to its middle).
- Parts (each has its own page): centre-hole-link-80, four-bar-links, slot-guide-plate-90, slide-block-12x6, dowel-pins-metric.
- Brown's movement No. 339 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| bar AB | 80 mm |
| radius OC | 40 mm |
| guide | 6.2 mm slot |
| path of B | exact straight line |

## 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. 339: figure, his text and an animation](https://507movements.com/mm_339.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/scott-russell-straight-line-mechanism/index.json

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

## Questions

**How does the Scott Russell linkage make a straight line?**

A bar AB of length 2r has its midpoint C pinned to a radius link OC = r; end A slides on a straight guide through O. Because A, B and O always lie on a circle round C, B moves on the exact straight line through O at right angles to the guide.

## Fits with

- [Centre-hole link, 80 mm (three Ø3 holes: −40, 0, +40)](https://xemstudio.com/objects/centre-hole-link-80/)
- [Four-bar links: flat links with 20 to 100 mm hole centres](https://xemstudio.com/objects/four-bar-links/)
- [Slot guide plate 90 × 30 × 5, 6.2 mm slot (74 long)](https://xemstudio.com/objects/slot-guide-plate-90/)
- [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/)