# Crown wheel (face gear), module 1.5, 54 teeth, generated by an 18-tooth spur pinion

> How are the teeth of a crown wheel shaped?

- 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/crown-wheel-m1-5-54t-for-18t-pinion/ · JSON: https://xemstudio.com/api/geometry?object=crown-wheel-m1-5-54t-for-18t-pinion · Plain text: https://xemstudio.com/objects/crown-wheel-m1-5-54t-for-18t-pinion/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 |
|---|---|---|
| 89.0 | 89.15 | 9.63 |

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

## Notes

- Face gear: 54 teeth standing on the face of a Ø89 disc (Ø8 bore), from radius 37.5 to 44.5 mm, each tooth the envelope of the module 1.5, 18-tooth involute spur pinion it runs with (the catalog gear, its own root form included): the pinion's axis lies in the wheel's pitch plane, 13.5 mm (its pitch radius) above the tooth-root plane's offset, and the pair turns at 3 : 1 while the pinion's teeth sweep the spaces — computed in 7 planes across the face at 0.25° steps and lofted through them (spline fit within 0.008 mm).
- Tooth top at +1.5 mm above the pitch plane, space bottom at −1.875 mm (0.25 m clearance under the pinion's tip); the toothed band is a 54-gon, so every tooth ends flat at its own inner and outer radius. The tooth form changes across the face: wider and undercut toward the centre, pointed toward the rim — which is why a face gear's face width is short (here 7 mm, from 3 modules inside the nominal pitch radius 40.5 to 4 outside).
- 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 | 54 |
| pinion | 18 T spur (catalog gear-m1-5-18t), axis in the pitch plane |
| face | r 37.5 → 44.5 mm (7 mm) |
| tooth top / root | +1.5 / −1.875 mm from the pitch plane |
| disc | Ø89 × 6 under the teeth, Ø8 bore |
| ratio | 3 : 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. 26: figure, his text and an animation](https://507movements.com/mm_026.html) — web — Publisher's page; dimensions are facts
- Xem Studio: [drawing](https://xemstudio.com/objects/crown-wheel-spur-pinion-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/crown-wheel-m1-5-54t-for-18t-pinion/index.json · license: https://xemstudio.com/files/hardware/crown-wheel-m1-5-54t-for-18t-pinion/LICENSE.md

- crown-wheel-m1-5-54t-for-18t-pinion: [STEP](https://xemstudio.com/files/hardware/crown-wheel-m1-5-54t-for-18t-pinion/crown-wheel-m1-5-54t-for-18t-pinion.step) · [STL](https://xemstudio.com/files/hardware/crown-wheel-m1-5-54t-for-18t-pinion/crown-wheel-m1-5-54t-for-18t-pinion.stl) — crown wheel, axis Z, pitch plane z = 0, a space centred on +X

## Questions

**How are the teeth of a crown wheel shaped?**

Face gear: 54 teeth standing on the face of a Ø89 disc (Ø8 bore), from radius 37.5 to 44.5 mm, each tooth the envelope of the module 1.5, 18-tooth involute spur pinion it runs with (the catalog gear, its own root form included): the pinion's axis lies in the wheel's pitch plane, 13.5 mm (its pitch radius) above the tooth-root plane's offset, and the pair turns at 3 : 1 while the pinion's teeth sweep the spaces — computed in 7 planes across the face at 0.25° steps and lofted through them (spline fit within 0.008 mm).

## Fits with

- [Crown wheel and spur pinion at right angles (face gear, 3 : 1)](https://xemstudio.com/objects/crown-wheel-spur-pinion-mechanism/)