# V-groove pulleys and round band, 1 : 1

> Why does a round band grip better in a V groove?

- Category: Mechanisms › Belt and friction drives
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 258 (1868)
- Page: https://xemstudio.com/objects/v-groove-pulleys-round-band-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=v-groove-pulleys-round-band-mechanism · Plain text: https://xemstudio.com/objects/v-groove-pulleys-round-band-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

- The band wedges between the two 40° flanks: the radial belt pull is multiplied by 1/sin 20° = 2.92 as normal force on the flanks, so it grips about three times as hard as on a flat face for the same tension.
- Two equal pulleys 100 mm apart on Ø8 shafts and a Ø5 endless band, drawn seated in both grooves (band centre radius 19.31 mm).
- Brown's No. 258.
- Parts (each has its own page): v-groove-pulley-45-40deg-band5-bore8, round-band-5-c100-pulleys-45v, linear-shafts-h6.
- Brown's movement No. 258 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| pulleys | 2 × Ø45 × 10 |
| band | Ø5 round |
| centre distance | 100 mm |
| ratio | 1 : 1 |

## 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. 258: figure, his text and an animation](https://507movements.com/mm_258.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/v-groove-pulleys-round-band-mechanism/index.json · license: https://xemstudio.com/files/hardware/v-groove-pulleys-round-band-mechanism/LICENSE.md

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

## Questions

**Why does a round band grip better in a V groove?**

The band wedges between the two 40° flanks: the radial belt pull is multiplied by 1/sin 20° = 2.92 as normal force on the flanks, so it grips about three times as hard as on a flat face for the same tension.

## Fits with

- [V-groove pulley Ø45 × 10, 40° groove, for a Ø5 round band, Ø8 bore](https://xemstudio.com/objects/v-groove-pulley-45-40deg-band5-bore8/)
- [Round band Ø5, endless, 321.33 mm centreline, on two pulleys 100 mm apart](https://xemstudio.com/objects/round-band-5-c100-pulleys-45v/)
- [Linear shafts Ø3 to Ø25 mm (h6), 100 to 1000 mm long](https://xemstudio.com/objects/linear-shafts-h6/)