# Bevel gears for shafts at an oblique angle (60°), 20 : 30

> How are gears made for shafts that meet at an angle other than 90°?

- Category: Mechanisms › Gears
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 42 (1868)
- Page: https://xemstudio.com/objects/oblique-bevel-gears-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=oblique-bevel-gears-mechanism · Plain text: https://xemstudio.com/objects/oblique-bevel-gears-mechanism/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/)

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

## Notes

- Bevel gears work for any shaft angle Σ: each pitch cone angle follows from tan δ₁ = sin Σ / (N₂/N₁ + cos Σ), and δ₁ + δ₂ = Σ. The cones still share an apex where the shafts meet.
- Here Σ = 60° with 20 and 30 teeth: δ = 23.41° and 36.59°, cone distance 37.75 mm, ratio 1.5 : 1; spherical-involute teeth, drawn turned 5°.
- Brown's No. 42 (gears transmitting rotary motion between shafts set obliquely).
- Parts (each has its own page): bevel-gear-m1-5-20t-for-30t-60deg, bevel-gear-m1-5-30t-for-20t-60deg, linear-shafts-h6.
- Brown's movement No. 42 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| module (large end) | 1.5 |
| teeth | 20 / 30 |
| shaft angle | 60° |
| pitch cones | 23.41° / 36.59° |
| ratio | 1.5 : 1 |

## 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. 42: figure, his text and an animation](https://507movements.com/mm_042.html) — web — Publisher's page; dimensions are facts

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

Index: https://xemstudio.com/files/hardware/oblique-bevel-gears-mechanism/index.json · license: https://xemstudio.com/files/hardware/oblique-bevel-gears-mechanism/LICENSE.md

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

## Questions

**How are gears made for shafts that meet at an angle other than 90°?**

Bevel gears work for any shaft angle Σ: each pitch cone angle follows from tan δ₁ = sin Σ / (N₂/N₁ + cos Σ), and δ₁ + δ₂ = Σ. The cones still share an apex where the shafts meet.

## Fits with

- [Bevel pinion, module 1.5, 20 teeth for a 30-tooth wheel at 60° shaft angle, spherical involute](https://xemstudio.com/objects/bevel-gear-m1-5-20t-for-30t-60deg/)
- [Bevel wheel, module 1.5, 30 teeth for a 20-tooth pinion at 60° shaft angle, spherical involute](https://xemstudio.com/objects/bevel-gear-m1-5-30t-for-20t-60deg/)
- [Linear shafts Ø3 to Ø25 mm (h6), 100 to 1000 mm long](https://xemstudio.com/objects/linear-shafts-h6/)