# Crossed flat belt 12 × 1.5 for Ø40 and Ø80 pulleys at 160 mm (loop drawn on the pulleys)

> How long is a crossed belt?

- Category: Hardware › Mechanism parts
- Kind: Modern device
- Basis: Xem Studio design following Brown's figure (1868); true size, no printing allowance
- Page: https://xemstudio.com/objects/crossed-flat-belt-12x1-5-pulleys-40-80-c160/ · JSON: https://xemstudio.com/api/geometry?object=crossed-flat-belt-12x1-5-pulleys-40-80-c160 · Plain text: https://xemstudio.com/objects/crossed-flat-belt-12x1-5-pulleys-40-80-c160/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/)

## Overall (mm)

| length | width | height |
|---|---|---|
| 223.0 | 83.0 | 12.37 |

**Exact dimensions.** True size, with no printing tolerance added.

## Notes

- Flat belt 12 × 1.5 mm crossed between Ø40 and Ø80 pulleys 160 mm apart: inside length = 2√(C² − (R₁ + R₂)²) + (R₁ + R₂)(π + 2·asin((R₁ + R₂)/C)) = 531.27 mm.
- Each strand turns half a turn about its own length so the same face runs on both pulleys; the strands lie flat on each other where they cross (drawn 0.1 mm apart).
- Xem Studio design following Brown's figure; true size, no printing allowance (apply your own to the mating features).

## Sizes

| dimension | value |
|---|---|
| width × thickness | 12 × 1.5 mm |
| inside length | 531.27 mm |
| for | Ø40 + Ø80 at 160 mm, crossed |

## 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
- Xem Studio: [drawing](https://xemstudio.com/objects/crossed-belt-drive-mechanism/) — 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-flat-belt-12x1-5-pulleys-40-80-c160/index.json · license: https://xemstudio.com/files/hardware/crossed-flat-belt-12x1-5-pulleys-40-80-c160/LICENSE.md

- crossed-flat-belt-12x1-5-pulleys-40-80-c160: [STEP](https://xemstudio.com/files/hardware/crossed-flat-belt-12x1-5-pulleys-40-80-c160/crossed-flat-belt-12x1-5-pulleys-40-80-c160.step) · [STL](https://xemstudio.com/files/hardware/crossed-flat-belt-12x1-5-pulleys-40-80-c160/crossed-flat-belt-12x1-5-pulleys-40-80-c160.stl) — belt loop, centred on z = 10

## Questions

**How long is a crossed belt?**

Flat belt 12 × 1.5 mm crossed between Ø40 and Ø80 pulleys 160 mm apart: inside length = 2√(C² − (R₁ + R₂)²) + (R₁ + R₂)(π + 2·asin((R₁ + R₂)/C)) = 531.27 mm.

## Fits with

- [Crossed belt drive (driven pulley reversed), 2 : 1](https://xemstudio.com/objects/crossed-belt-drive-mechanism/)