# Elliptical gear, module 1.5, 31 teeth, eccentricity 0.5, bore at a focus

> How are elliptical gears made?

- Category: Mechanisms › Gears
- Kind: Modern device
- Basis: Xem Studio design following Brown's figure (1868); true size, no printing allowance
- Page: https://xemstudio.com/objects/elliptical-gear-m1-5-31t-e0-5-focus-bore/ · JSON: https://xemstudio.com/api/geometry?object=elliptical-gear-m1-5-31t-e0-5-focus-bore · Plain text: https://xemstudio.com/objects/elliptical-gear-m1-5-31t-e0-5-focus-bore/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/)

## Overall (mm)

| length | width | height |
|---|---|---|
| 52.67 | 46.09 | 12.0 |

**Exact dimensions.** True size, with no printing tolerance added.

## Notes

- Pitch curve an ellipse with semi-axes 24.89 × 21.55 mm (eccentricity 0.5, perimeter 31 × π × 1.5 = 146.08 mm), the Ø8 bore at a focus; teeth generated by a 20° basic rack rolled round the pitch curve without slip (addendum m, dedendum 1.25 m), so any two such gears mesh. Outline: every tooth flank and fillet is a spline fitted to the generated curve within 0.008 mm.
- 31 teeth (odd): a pair pivoted at their foci 49.77 mm apart (the major axis) meets tooth-to-space at both ends of the major axis. 12 mm face.
- Xem Studio design following Brown's figure; true size, no printing allowance (apply your own to the mating features).

## Sizes

| dimension | value |
|---|---|
| module | 1.5 |
| teeth | 31 |
| pitch ellipse | 49.77 × 43.11 mm |
| eccentricity | 0.5 |
| bore | Ø8 at a focus |
| face | 12 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. 33: figure, his text and an animation](https://507movements.com/mm_033.html) — web — Publisher's page; dimensions are facts
- Xem Studio: [drawing](https://xemstudio.com/objects/elliptical-gears-focus-mechanism/) — web — Publisher's page; dimensions are facts

## Free STEP/STL (1 parts, Xem Studio Design License, Xem Studio)

Index: https://xemstudio.com/files/hardware/elliptical-gear-m1-5-31t-e0-5-focus-bore/index.json · license: https://xemstudio.com/files/hardware/elliptical-gear-m1-5-31t-e0-5-focus-bore/LICENSE.md

- elliptical-gear-m1-5-31t-e0-5-focus-bore: [STEP](https://xemstudio.com/files/hardware/elliptical-gear-m1-5-31t-e0-5-focus-bore/elliptical-gear-m1-5-31t-e0-5-focus-bore.step) · [STL](https://xemstudio.com/files/hardware/elliptical-gear-m1-5-31t-e0-5-focus-bore/elliptical-gear-m1-5-31t-e0-5-focus-bore.stl) — gear, bore (focus) on the Z axis, near vertex on +X, z 0..12

## Questions

**How are elliptical gears made?**

Pitch curve an ellipse with semi-axes 24.89 × 21.55 mm (eccentricity 0.5, perimeter 31 × π × 1.5 = 146.08 mm), the Ø8 bore at a focus; teeth generated by a 20° basic rack rolled round the pitch curve without slip (addendum m, dedendum 1.25 m), so any two such gears mesh. Outline: every tooth flank and fillet is a spline fitted to the generated curve within 0.008 mm.

## Fits with

- [Elliptical gears turning about their foci (speed ratio 0.33 – 3)](https://xemstudio.com/objects/elliptical-gears-focus-mechanism/)