# Crown wheel and spur pinion at right angles (face gear, 3 : 1)

> How does a crown wheel mesh with an ordinary spur pinion?

- Category: Mechanisms › Gears
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 26 (1868)
- Page: https://xemstudio.com/objects/crown-wheel-spur-pinion-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=crown-wheel-spur-pinion-mechanism · Plain text: https://xemstudio.com/objects/crown-wheel-spur-pinion-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

- Resize: multiply every length by one factor k and the motion stays identical: angles, ratios, timing and the formulas below do not change, because a mechanism's motion depends only on the ratios of its lengths. Here, scales with k: pinion axis height; stays the same: crown wheel, pinion, ratio; step to the nearest standard size (and redraw the hole or pocket it fits): shafts.
- Resize: Gears scale by the module m (pitch Ø = m·z, centre distance = m·(z₁ + z₂)/2): keep the tooth counts so the ratio stays, and choose a standard module (0.5, 0.8, 1, 1.25, 1.5, 2, 2.5, 3).
- Resize: fit clearances stay in mm (a slide fit is the same gap at any size); keep every printed wall and pin at least two nozzle widths; mass grows with k³ but part strength only with k², so at k = 2 parts are about 8× heavier and 4× stronger: check pins and thin links when scaling up.
- A crown wheel (face gear) carries its teeth on its face; an ordinary spur pinion whose axis lies in the wheel's pitch plane meshes with them and turns the motion through 90° — the clockmaker's contrate wheel, the mill's crown-and-trundle. Ratio = tooth ratio, 54 : 18 = 3 : 1.
- For a true involute pinion the crown teeth cannot be drawn directly: they are generated by the pinion itself. Here each tooth is the envelope of the catalog 18-tooth module 1.5 pinion's teeth as the pair turns at 3 : 1, computed slice by slice across the 7 mm face (r 37.5–44.5) and lofted; the pinion sits with its axis 13.5 mm (its pitch radius) above the wheel's pitch plane, centred on the face. Checked at seven positions through a tooth passage: no overlap beyond contact.
- Brown's No. 26 (crown wheel and spur gear at right angles; little used in his day). Drawn turned 5° (pinion) / 1.67° (wheel).
- Parts (each has its own page): crown-wheel-m1-5-54t-for-18t-pinion, spur-gears-module-1-5, linear-shafts-h6.
- Brown's movement No. 26 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| crown wheel | 54 T, module 1.5, face r 37.5–44.5 |
| pinion | 18 T spur (catalog) |
| ratio | 3 : 1 |
| shafts | 90°, intersecting |
| pinion axis height | 13.5 mm above the pitch plane |

## 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

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

Index: https://xemstudio.com/files/hardware/crown-wheel-spur-pinion-mechanism/index.json · license: https://xemstudio.com/files/hardware/crown-wheel-spur-pinion-mechanism/LICENSE.md

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

## Questions

**How does a crown wheel mesh with an ordinary spur pinion?**

A crown wheel (face gear) carries its teeth on its face; an ordinary spur pinion whose axis lies in the wheel's pitch plane meshes with them and turns the motion through 90° — the clockmaker's contrate wheel, the mill's crown-and-trundle. Ratio = tooth ratio, 54 : 18 = 3 : 1.

**Can any spur pinion run on a crown wheel?**

Only the pinion it was generated for (module, pressure angle, tooth count and root form): the crown tooth form is the envelope of that pinion's teeth.

**Why is a face gear's face width so short?**

The tooth form changes with radius: inside the nominal pitch radius the teeth are undercut, outside it they become pointed; only a few modules each way are usable (here 3 inside, 4 outside).

## Fits with

- [Crown wheel (face gear), module 1.5, 54 teeth, generated by an 18-tooth spur pinion](https://xemstudio.com/objects/crown-wheel-m1-5-54t-for-18t-pinion/)
- [Spur gears, module 1.5: 10 to 80 teeth (20° involute)](https://xemstudio.com/objects/spur-gears-module-1-5/)
- [Linear shafts Ø3 to Ø25 mm (h6), 100 to 1000 mm long](https://xemstudio.com/objects/linear-shafts-h6/)