# Open flat belt and two pulleys (2 : 1)

> How do you work out a belt drive's ratio and length?

- Category: Mechanisms › Belt and friction drives
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 1 (1868)
- Page: https://xemstudio.com/objects/belt-and-pulleys-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=belt-and-pulleys-mechanism · Plain text: https://xemstudio.com/objects/belt-and-pulleys-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

- An open belt on two pulleys turns both shafts the same way; speed ratio = D₂/D₁ = 80/40 = 2 : 1 (less a little slip). Belt inside length here 471.36 mm for 140 mm centres.
- Wrap on the small pulley = 2·acos((R₂ − R₁)/C) = 163.6°: the smaller the wrap, the less torque before slipping.
- Brown's No. 1 (belt and pulleys); a crossed belt (No. 2) reverses the driven shaft.
- Parts (each has its own page): flanged-flat-pulley-40, flanged-flat-pulley-80, flat-belt-1-5x16-pulleys-40-80-140.
- Brown's movement No. 1 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| pulleys | Ø40 and Ø80, flanged |
| centres | 140 mm |
| ratio | 2 : 1 |
| belt | 16 × 1.5, 471.36 mm |

## 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
- 507movements.com: [Brown's movement No. 1: figure, his text and an animation](https://507movements.com/mm_001.html) — web — Publisher's page; dimensions are facts

## Free STEP/STL (1 parts, CC BY 4.0, Xem Studio)

Index: https://xemstudio.com/files/hardware/belt-and-pulleys-mechanism/index.json

- belt-and-pulleys-mechanism-assembly: [STEP](https://xemstudio.com/files/hardware/belt-and-pulleys-mechanism/belt-and-pulleys-mechanism-assembly.step) · [STL](https://xemstudio.com/files/hardware/belt-and-pulleys-mechanism/belt-and-pulleys-mechanism-assembly.stl) — Assembled mechanism, all parts placed at one pose (STEP keeps each part separate)

## Questions

**How do you work out a belt drive's ratio and length?**

An open belt on two pulleys turns both shafts the same way; speed ratio = D₂/D₁ = 80/40 = 2 : 1 (less a little slip). Belt inside length here 471.36 mm for 140 mm centres.

## Fits with

- [Flanged flat-belt pulley Ø40, 16 mm face, Ø8 bore](https://xemstudio.com/objects/flanged-flat-pulley-40/)
- [Flanged flat-belt pulley Ø80, 16 mm face, Ø8 bore](https://xemstudio.com/objects/flanged-flat-pulley-80/)
- [Flat belt 16 × 1.5 for Ø40 and Ø80 pulleys at 140 mm (loop drawn on the pulleys)](https://xemstudio.com/objects/flat-belt-1-5x16-pulleys-40-80-140/)