Universal (Hooke / Cardan) joint — dimension sheet
Source: Xem Studio, https://xemstudio.com/objects/universal-joint-mechanism/  (CC BY 4.0)
Basis: Xem Studio drawing; classic mechanism (Brown No. 50)
Catalog version: 2026-10-20

Sizes: see table below
- Two yokes at 90° on a cross: shafts at an angle β turn together, but the output speed swings: ω₂/ω₁ = cos β / (1 − sin²β·cos²θ), between cos β and 1/cos β twice per turn.
- Two joints in phase with equal angles (a double Cardan or a drive shaft with both yokes aligned) cancel the swing.
- Brown shows two forms (Nos. 50 and 51). The 5 mm printable joint is its own page.
- Parts (each has its own page): universal-joint-5mm, clevis-pins. Brown's movement No. 50 shows it (1868).

parameter  value
angle β (max, printable joint)  ≈30°
speed swing at 30°  0.866 – 1.155

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

Xem Studio scan: not needed; this is a published standard. The sheet is the geometry.
API: https://xemstudio.com/api/geometry?object=universal-joint-mechanism