# Conoid (curved cone) pulley Ø24–Ø56 × 64, profile for constant open-belt length at 110 mm

> Why are some speed cones curved?

- 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/conoid-pulley-24-56x64-bore8/ · JSON: https://xemstudio.com/api/geometry?object=conoid-pulley-24-56x64-bore8 · Plain text: https://xemstudio.com/objects/conoid-pulley-24-56x64-bore8/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 |
|---|---|---|
| 71.26 | 71.26 | 64.0 |

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

## Notes

- A pair of these, mounted head to tail 110 mm apart, keeps an open belt at exactly the same length wherever it runs: the generatrix is r(z) = (s + 2g)/2 with g = (z − 32)/4 and s chosen so 2√(C² − d²) + πs + 2d·asin(d/C) stays 2C + 40π (d = −2g).
- The curve bulges up to 8.37 mm outside a straight cone near the ends; a flat belt touches it on its centre line.
- Xem Studio design following Brown's figure; true size, no printing allowance (apply your own to the mating features).

## Sizes

| dimension | value |
|---|---|
| diameters | Ø24 → Ø56 |
| length | 64 mm |
| profile | exact constant-belt-length curve for C = 110 |
| bore | Ø8 |

## 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. 10: figure, his text and an animation](https://507movements.com/mm_010.html) — web — Publisher's page; dimensions are facts
- Xem Studio: [drawing](https://xemstudio.com/objects/conoid-pulleys-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/conoid-pulley-24-56x64-bore8/index.json · license: https://xemstudio.com/files/hardware/conoid-pulley-24-56x64-bore8/LICENSE.md

- conoid-pulley-24-56x64-bore8: [STEP](https://xemstudio.com/files/hardware/conoid-pulley-24-56x64-bore8/conoid-pulley-24-56x64-bore8.step) · [STL](https://xemstudio.com/files/hardware/conoid-pulley-24-56x64-bore8/conoid-pulley-24-56x64-bore8.stl) — pulley, axis Z, small end at z = 0

## Questions

**Why are some speed cones curved?**

A pair of these, mounted head to tail 110 mm apart, keeps an open belt at exactly the same length wherever it runs: the generatrix is r(z) = (s + 2g)/2 with g = (z − 32)/4 and s chosen so 2√(C² − d²) + πs + 2d·asin(d/C) stays 2C + 40π (d = −2g).

## Fits with

- [Conoid (curved cone) pulleys: varied speed with a belt of constant length](https://xemstudio.com/objects/conoid-pulleys-mechanism/)