# Elliptic trammel (trammel of Archimedes, ellipsograph)

> How does an elliptic trammel draw an ellipse?

- Category: Mechanisms › Linkages
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 152 (1868)
- Page: https://xemstudio.com/objects/elliptic-trammel-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=elliptic-trammel-mechanism · Plain text: https://xemstudio.com/objects/elliptic-trammel-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

- Two blocks slide in crossed grooves and carry a bar; a point on the bar a distance a from one block and b from the other draws an ellipse with semi-axes a and b.
- Here the blocks are 40 mm apart on an 80 mm centre-hole link and the pen hole is 40 mm beyond: semi-axes 80 and 40 mm. At 50° the pen is at (51.42, 30.64); x²/80² + y²/40² = 1.
- Brown's No. 152 (ellipsograph: traverse bar with two studs sliding in grooves of a cross).
- Parts (each has its own page): trammel-cross-plate-140, slide-block-12x6, centre-hole-link-80, dowel-pins-metric.
- Brown's movement No. 152 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| semi-axis a | 80 mm |
| semi-axis b | 40 mm |
| blocks | 2 × 12 × 6.2 × 5 |
| grooves | 6.2 × 5 deep, crossed |

## 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. 152: figure, his text and an animation](https://507movements.com/mm_152.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/elliptic-trammel-mechanism/index.json

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

## Questions

**How does an elliptic trammel draw an ellipse?**

Two blocks slide in crossed grooves and carry a bar; a point on the bar a distance a from one block and b from the other draws an ellipse with semi-axes a and b.

**Which point draws a circle?**

The midpoint between the two blocks (a = b) draws a circle of radius half their spacing.

## Fits with

- [Trammel cross plate 140 × 140 × 8 with crossed 6.2 mm grooves](https://xemstudio.com/objects/trammel-cross-plate-140/)
- [Slide block 12 × 6.2 mm for a 6.4 mm slot](https://xemstudio.com/objects/slide-block-12x6/)
- [Centre-hole link, 80 mm (three Ø3 holes: −40, 0, +40)](https://xemstudio.com/objects/centre-hole-link-80/)
- [Dowel pins, 2–6 mm (ISO 2338 / DIN 6325)](https://xemstudio.com/objects/dowel-pins-metric/)