Conoid (curved cone) pulleys: varied speed with a belt of constant length — dimension sheet
Source: Xem Studio, https://xemstudio.com/objects/conoid-pulleys-mechanism/  (sheet CC BY 4.0; files Xem Studio Design License, https://xemstudio.com/license/)
Basis: Xem Studio design following Brown No. 10 (1868)
Catalog version: 2026-10-20

Sizes: see table below
- Two straight cones head to tail keep r₁ + r₂ constant, which keeps a CROSSED belt the same length but not an open one: an open belt goes slack away from the middle. Curving the cones by the right amount makes the open-belt length exactly constant.
- Here Ø24–Ø56 × 64 conoids at 110 mm; at 20 mm along, Ø27.9 drives Ø51.9, ratio 0.54. The belt length 346.65 mm is the same at every position (straight cones of the same size lose -4.64 mm near the ends).
- Brown's No. 10 (cone pulleys of curved outline for gradually varying speed).
- Parts (each has its own page): conoid-pulley-24-56x64-bore8, flat-belt-10x1-5-conoid-pulleys-c110.
- Brown's movement No. 10 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

parameter  value
pulleys  2 × Ø24–Ø56 × 64 conoids, head to tail
centres  110 mm
ratio range  0.43 – 2.33 (approx.)
drawn at 20 mm  ratio 0.54
belt  10 × 1.5, 346.65 mm

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. 10: figure, his text and an animation — web — Publisher's page; dimensions are facts — https://507movements.com/mm_010.html

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