# Universal (Hooke / Cardan) joint

> Why does a universal joint not turn at constant speed?

- Category: Mechanisms › Couplings & joints
- Kind: Hardware
- Basis: Xem Studio drawing; classic mechanism (Brown No. 50)
- Page: https://xemstudio.com/objects/universal-joint-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=universal-joint-mechanism · Plain text: https://xemstudio.com/objects/universal-joint-mechanism/sheet.txt
- License: dimension sheet CC BY 4.0 (Xem Studio); linked files under their publishers' licenses
- 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

- 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).

## Sizes

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

## 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

## Questions

**Why does a universal joint not turn at constant speed?**

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.

## Fits with

- [Universal joint for Ø5 shafts: Ø14 yokes and 8 mm cross spider](https://xemstudio.com/objects/universal-joint-5mm/)
- [Clevis pins ISO 2341 B, Ø3 to Ø8](https://xemstudio.com/objects/clevis-pins/)