# Crossed belt drive (driven pulley reversed), 2 : 1

> Why does a crossed belt reverse the driven pulley?

- Category: Mechanisms › Belt and friction drives
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 2 (1868)
- Page: https://xemstudio.com/objects/crossed-belt-drive-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=crossed-belt-drive-mechanism · Plain text: https://xemstudio.com/objects/crossed-belt-drive-mechanism/sheet.txt
- License: dimension sheet CC BY 4.0 (Xem Studio); files Xem Studio Design License (free to use and sell from, not to redistribute as files: https://xemstudio.com/license/)
- 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

- Crossing the belt between two pulleys makes the driven pulley turn the opposite way to the driver; the ratio is still D₂/D₁ (80/40 = 2 : 1).
- Both pulleys get the same wrap, π + 2·asin((R₁ + R₂)/C) = 224.05° here, more than an open belt gives the small pulley, so a crossed belt grips better; the strands rub where they cross, so it suits slow, narrow belts.
- Drawn on the catalog flanged pulleys Ø40 and Ø80 (16 mm faces) at 160 mm centres with a 12 × 1.5 belt, inside length 531.27 mm. Brown's No. 2.
- Parts (each has its own page): flanged-flat-pulley-40, flanged-flat-pulley-80, crossed-flat-belt-12x1-5-pulleys-40-80-c160.
- Brown's movement No. 2 (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 | 160 mm |
| ratio | 2 : 1, reversed |
| wrap (both) | 224.05° |
| belt | 12 × 1.5, 531.27 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. 2: figure, his text and an animation](https://507movements.com/mm_002.html) — web — Publisher's page; dimensions are facts

## Free STEP/STL (1 parts, Xem Studio Design License, Xem Studio)

Index: https://xemstudio.com/files/hardware/crossed-belt-drive-mechanism/index.json · license: https://xemstudio.com/files/hardware/crossed-belt-drive-mechanism/LICENSE.md

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

## Questions

**Why does a crossed belt reverse the driven pulley?**

Crossing the belt between two pulleys makes the driven pulley turn the opposite way to the driver; the ratio is still D₂/D₁ (80/40 = 2 : 1).

**How long is a crossed belt?**

2√(C² − (R₁ + R₂)²) + (R₁ + R₂)(π + 2 asin((R₁ + R₂)/C)); it depends only on R₁ + R₂, so stepped pulleys with a constant diameter sum keep it tight.

## 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/)
- [Crossed flat belt 12 × 1.5 for Ø40 and Ø80 pulleys at 160 mm (loop drawn on the pulleys)](https://xemstudio.com/objects/crossed-flat-belt-12x1-5-pulleys-40-80-c160/)