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Crown wheel and spur pinion at right angles (face gear, 3 : 1)
How does a crown wheel mesh with an ordinary spur pinion? · Hardware · basis: Xem Studio design following Brown No. 26 (1868)
Also called: crown wheel and pinion, face gear, contrate wheel, crown gear drive, rueda de corona y piñón, Kronenrad und Ritzel
Exact dimensions. True size, with no printing tolerance added.
- sizes
- 5 in table
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.
Crown wheel and spur pinion at right angles size chart
| 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
Other publishers' files are linked, not hosted. "verify" = check the license at the link before commercial use.
| Henry T. Brown (1868, public domain) | Five Hundred and Seven Mechanical Movements — scan on archive.org | web | Publisher's page; dimensions are facts |
| 507movements.com | Brown's movement No. 26: figure, his text and an animation | web | Publisher's page; dimensions are facts |
Free files
★ Free files 1 parts. Xem Studio design: free to use, print and sell things from; not to be republished as files. Xem Studio Design License. index.json
| crown-wheel-spur-pinion-mechanism-assembly | Assembled mechanism, all parts placed at one pose (STEP keeps each part separate) | STEP · STL |
https://xemstudio.com/mcp to Claude, ChatGPT, Cursor or any MCP client (free, no account, one minute) and it can look up exact sizes, mating fits and free STEP/STL from every chat.Plain text: sheet.txt · JSON: /api/geometry?object=crown-wheel-spur-pinion-mechanism
Fits with
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).