# Mitre (bevel) gear, module 2, 20 teeth, Ø5 bore, spherical involute

> What are the dimensions of a module 2, 20-tooth bevel gear (mitre)?

- Category: Hardware › Mechanism parts
- Kind: Modern device
- Basis: Xem Studio design following Brown's figure (1868); true size, no printing allowance
- Page: https://xemstudio.com/objects/mitre-gear-m2-20t-bore5/ · JSON: https://xemstudio.com/api/geometry?object=mitre-gear-m2-20t-bore5 · Plain text: https://xemstudio.com/objects/mitre-gear-m2-20t-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/)
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## Overall (mm)

| length | width | height |
|---|---|---|
| 42.72 | 42.72 | 23.91 |

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

## Notes

- Straight bevel gear, module 2 at the large end, 20 teeth, for a 20-tooth mate at 90° shaft angle: pitch cone angle 45°, cone distance 28.28 mm, pitch Ø40, face width 9.4 mm, Ø5 bore, Ø28.47 hub.
- Teeth are exact spherical involutes (base cone sin γb = sin δ · cos 20°), converging to the pitch apex: each flank is a cone from the apex over the spherical involute, so two such gears roll with line contact at every position; ends are spheres centred on the apex (radii A0 and A0 − F). Addendum m, dedendum 1.25 m at the large end.
- 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 | 20 (mate 20) |
| shaft angle | 90° |
| pitch cone | 45° |
| cone distance A0 | 28.28 mm |
| face width | 9.4 mm |
| pitch Ø | 40 mm |
| tip Ø | 42.72 mm |
| bore | Ø5 |
| apex to back of hub | 36.28 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. 25: figure, his text and an animation](https://507movements.com/mm_025.html) — web — Publisher's page; dimensions are facts
- Xem Studio: [drawing](https://xemstudio.com/objects/mutilated-bevel-gear-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-m2-20t-bore5/index.json · license: https://xemstudio.com/files/hardware/mitre-gear-m2-20t-bore5/LICENSE.md

- mitre-gear-m2-20t-bore5: [STEP](https://xemstudio.com/files/hardware/mitre-gear-m2-20t-bore5/mitre-gear-m2-20t-bore5.step) · [STL](https://xemstudio.com/files/hardware/mitre-gear-m2-20t-bore5/mitre-gear-m2-20t-bore5.stl) — gear, pitch apex at the origin, axis +Z, a tooth on +X

## Questions

**What are the dimensions of a module 2, 20-tooth bevel gear (mitre)?**

Straight bevel gear, module 2 at the large end, 20 teeth, for a 20-tooth mate at 90° shaft angle: pitch cone angle 45°, cone distance 28.28 mm, pitch Ø40, face width 9.4 mm, Ø5 bore, Ø28.47 hub.

## Fits with

- [Mutilated bevel gear driving two bevel gears alternately, opposite ways](https://xemstudio.com/objects/mutilated-bevel-gear-mechanism/)