# Helical (oblique-toothed) gears on parallel shafts, 20 : 30, helix 20°

> Why are helical gears smoother than spur gears?

- Category: Mechanisms › Gears
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 40 (1868)
- Page: https://xemstudio.com/objects/helical-gears-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=helical-gears-mechanism · Plain text: https://xemstudio.com/objects/helical-gears-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 teeth are cut along a helix, so each tooth comes into mesh gradually from one end of the face to the other and more than one pair is always in contact: quieter, smoother and stronger than straight teeth, at the cost of an end thrust along the shafts.
- Normal module 1.5, helix 20° (right hand on the 20-tooth, left on the 30-tooth), 12 mm face: transverse module 1.6, centre distance 39.91 mm, transverse pressure angle 21.17°. Each transverse section is an exact involute spur mesh, twisted 15.68° over the face on the pinion.
- Brown's No. 40 (oblique-toothed gears, giving a more continuous bearing of the teeth).
- Parts (each has its own page): helical-gear-mn1-5-20t-beta20-rh-bore6, helical-gear-mn1-5-30t-beta20-lh-bore8, linear-shafts-h6.
- Brown's movement No. 40 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| normal module | 1.5 |
| teeth | 20 / 30 |
| helix | 20°, opposite hands |
| face | 12 mm |
| centre distance | 39.91 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. 40: figure, his text and an animation](https://507movements.com/mm_040.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/helical-gears-mechanism/index.json · license: https://xemstudio.com/files/hardware/helical-gears-mechanism/LICENSE.md

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

## Questions

**Why are helical gears smoother than spur gears?**

The teeth are cut along a helix, so each tooth comes into mesh gradually from one end of the face to the other and more than one pair is always in contact: quieter, smoother and stronger than straight teeth, at the cost of an end thrust along the shafts.

**What is the centre distance of helical gears?**

m_n (N₁ + N₂) / (2 cos β): 1.5 × 50 / (2 cos 20°) = 39.91 mm here.

## Fits with

- [Helical gear, normal module 1.5, 20 teeth, helix 20° right hand, face 12, Ø6 bore](https://xemstudio.com/objects/helical-gear-mn1-5-20t-beta20-rh-bore6/)
- [Helical gear, normal module 1.5, 30 teeth, helix 20° left hand, face 12, Ø8 bore](https://xemstudio.com/objects/helical-gear-mn1-5-30t-beta20-lh-bore8/)
- [Linear shafts Ø3 to Ø25 mm (h6), 100 to 1000 mm long](https://xemstudio.com/objects/linear-shafts-h6/)