# Spur gear pair, module 1, 20 : 40 teeth (2 : 1)

> How do two spur gears change speed and direction?

- Category: Mechanisms › Gears
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 24 (1868)
- Page: https://xemstudio.com/objects/spur-gear-pair-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=spur-gear-pair-mechanism · Plain text: https://xemstudio.com/objects/spur-gear-pair-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 involute spur gears on parallel shafts: the speed ratio is the inverse tooth ratio (20 : 40 → output at half speed, double torque) and the shafts turn in opposite directions.
- Module 1, 20° pressure angle, centre distance m(N₁ + N₂)/2 = 30 mm exactly; teeth meet on the pitch line with no backlash drawn.
- Brown's figure 24 is the plain spur pair, the base of every gear train in the book.
- Parts (each has its own page): spur-gears-module-1.
- Brown's movement No. 24 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| module | 1 |
| teeth | 20 / 40 |
| ratio | 2 : 1 |
| centre distance | 30 mm |
| face width | 8 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. 24: figure, his text and an animation](https://507movements.com/mm_024.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/spur-gear-pair-mechanism/index.json

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

## Questions

**How do two spur gears change speed and direction?**

Two involute spur gears on parallel shafts: the speed ratio is the inverse tooth ratio (20 : 40 → output at half speed, double torque) and the shafts turn in opposite directions.

**What is the centre distance of a 20 and 40 tooth module 1 pair?**

30 mm: m × (20 + 40) / 2.

## Fits with

- [Spur gears, module 1: 10 to 80 teeth (20° involute)](https://xemstudio.com/objects/spur-gears-module-1/)