# Mitre (bevel) gear, module 2, 24 teeth, Ø5 bore, spherical involute (spline flanks)

> What are the dimensions of a module 2, 24-tooth mitre gear?

- 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/mitre-gear-m2-24t-bore5/ · JSON: https://xemstudio.com/api/geometry?object=mitre-gear-m2-24t-bore5 · Plain text: https://xemstudio.com/objects/mitre-gear-m2-24t-bore5/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 |
|---|---|---|
| 50.74 | 50.74 | 26.9 |

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

## Notes

- Straight bevel gear for a 90° shaft angle with an equal mate (a mitre gear): module 2 at the large end, 24 teeth, pitch cone angle 45°, cone distance 33.94 mm, pitch Ø48, tip Ø50.74, face width 11.3 mm, Ø5 bore, Ø35.16 hub, 41.94 mm from the apex to the back of the hub.
- Teeth are exact spherical involutes (base cone sin γb = sin δ · cos 20°), converging to the pitch apex: each flank is one ruled face — a cone from the apex over the spherical involute — so two such gears roll with line contact at every position; ends are spheres about the apex (radii A0 and A0 − F). Addendum m, dedendum 1.25 m at the large end. Drawn with one spline per flank instead of a facetted polyline, so three of them fit an assembly STEP under 20 MB.
- Xem Studio design following Brown's figure; true size, no printing allowance (apply your own to the mating features).

## Sizes

| dimension | value |
|---|---|
| module (large end) | 2 |
| teeth | 24 |
| shaft angle | 90° (mate: same gear) |
| pitch cone | 45° |
| cone distance A0 | 33.94 mm |
| face width | 11.3 mm |
| pitch Ø | 48 mm |
| tip Ø | 50.74 mm |
| bore | Ø5 |
| apex to back of hub | 41.94 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. 7: figure, his text and an animation](https://507movements.com/mm_007.html) — web — Publisher's page; dimensions are facts
- Xem Studio: [drawing](https://xemstudio.com/objects/bevel-reversing-gear-fast-loose-pulleys-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/mitre-gear-m2-24t-bore5/index.json · license: https://xemstudio.com/files/hardware/mitre-gear-m2-24t-bore5/LICENSE.md

- mitre-gear-m2-24t-bore5: [STEP](https://xemstudio.com/files/hardware/mitre-gear-m2-24t-bore5/mitre-gear-m2-24t-bore5.step) · [STL](https://xemstudio.com/files/hardware/mitre-gear-m2-24t-bore5/mitre-gear-m2-24t-bore5.stl) — gear, pitch apex at the origin, axis +Z, a tooth on +X

## Questions

**What are the dimensions of a module 2, 24-tooth mitre gear?**

Straight bevel gear for a 90° shaft angle with an equal mate (a mitre gear): module 2 at the large end, 24 teeth, pitch cone angle 45°, cone distance 33.94 mm, pitch Ø48, tip Ø50.74, face width 11.3 mm, Ø5 bore, Ø35.16 hub, 41.94 mm from the apex to the back of the hub.

## Fits with

- [Fast and loose pulleys with bevel gears: start, stop or reverse an upright shaft](https://xemstudio.com/objects/bevel-reversing-gear-fast-loose-pulleys-mechanism/)
- [Rocking shaft driving an upright shaft continuously through two opposed ratchets and bevel gears](https://xemstudio.com/objects/opposed-ratchets-bevel-gears-rocking-mechanism/)