# Offset cranks with slotted arm (variable-speed coupling, Whitworth principle)

> How do two offset cranks give a varying speed?

- Category: Mechanisms › Linkages
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 220 (1868)
- Page: https://xemstudio.com/objects/offset-slotted-crank-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=offset-slotted-crank-mechanism · Plain text: https://xemstudio.com/objects/offset-slotted-crank-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

- Two parallel shafts 5 mm apart: a crank pin on the first slides in a slot on the second. The driven arm runs fast when the pin is nearest its shaft and slow when farthest: speed ratio swings between r/(r − e) and r/(r + e) = 1.71 and 0.71 here.
- Whitworth's quick return uses exactly this pair (the driven crank then works a slider), with the pin radius larger than the offset so both turn fully round.
- Brown's No. 220.
- Parts (each has its own page): crank-disc-36-pin-r12, slotted-crank-arm-30, dowel-pins-metric.
- Brown's movement No. 220 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| shaft offset e | 5 mm |
| pin radius r | 12 mm |
| speed range | 0.71 – 1.71 × input |

## 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. 220: figure, his text and an animation](https://507movements.com/mm_220.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/offset-slotted-crank-mechanism/index.json

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

## Questions

**How do two offset cranks give a varying speed?**

Two parallel shafts 5 mm apart: a crank pin on the first slides in a slot on the second. The driven arm runs fast when the pin is nearest its shaft and slow when farthest: speed ratio swings between r/(r − e) and r/(r + e) = 1.71 and 0.71 here.

## Fits with

- [Crank disc Ø36 × 5, Ø5 bore, Ø3 pin hole at 12 mm](https://xemstudio.com/objects/crank-disc-36-pin-r12/)
- [Slotted crank arm, Ø5 hub, 3 mm slot from 6 to 19 mm](https://xemstudio.com/objects/slotted-crank-arm-30/)
- [Dowel pins, 2–6 mm (ISO 2338 / DIN 6325)](https://xemstudio.com/objects/dowel-pins-metric/)