Crown wheel and spur pinion at right angles (face gear, 3 : 1) — dimension sheet
Source: Xem Studio, https://xemstudio.com/objects/crown-wheel-spur-pinion-mechanism/  (sheet CC BY 4.0; files Xem Studio Design License, https://xemstudio.com/license/)
Basis: Xem Studio design following Brown No. 26 (1868)
Catalog version: 2026-10-20

Sizes: see table below
- 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.

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

Files elsewhere (not hosted by Xem Studio; license as stated by the publisher):
- Henry T. Brown (1868, public domain): Five Hundred and Seven Mechanical Movements — scan on archive.org — web — Publisher's page; dimensions are facts — https://archive.org/details/fivehundredseven00browiala
- 507movements.com: Brown's movement No. 26: figure, his text and an animation — web — Publisher's page; dimensions are facts — https://507movements.com/mm_026.html

Free files (Xem Studio Design License, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/crown-wheel-spur-pinion-mechanism/index.json
API: https://xemstudio.com/api/geometry?object=crown-wheel-spur-pinion-mechanism