# Worm (involute helicoid, ZI), axial module 1.5, 1-start, pitch Ø16 × 40, Ø6 bore

> What are the dimensions of a module 1.5, 1-start worm?

- Category: Mechanisms › Gears
- Kind: Modern device
- Basis: Xem Studio design following Brown's figure (1868); true size, no printing allowance
- Page: https://xemstudio.com/objects/worm-zi-m1-5-1start-d16-l40-bore6/ · JSON: https://xemstudio.com/api/geometry?object=worm-zi-m1-5-1start-d16-l40-bore6 · Plain text: https://xemstudio.com/objects/worm-zi-m1-5-1start-d16-l40-bore6/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 |
|---|---|---|
| 19.0 | 19.0 | 40.0 |

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

## Notes

- Right-hand involute-helicoid (ZI) worm: axial module 1.5, 1 start, pitch Ø16, lead 4.71 mm, lead angle γ = atan(m z₁ / d₁) = 5.36°, normal module 1.49, normal pressure angle 20°; tip Ø19, root Ø12.25 (addendum m, dedendum 1.25 m), thread thickness πm/2 on the pitch cylinder.
- Every transverse section is an involute of the base cylinder Ø3.97 (rb = r₁ cos αt, tan αt = tan 20° / sin γ, αt = 75.62°), swept helically along the 40 mm length (8.49 turns): the flank is an exact involute helicoid, the surface of a helical gear with 1 tooth, so it meshes conjugately with any involute helical gear of normal module 1.49 on crossed axes.
- Xem Studio design following Brown's figure; true size, no printing allowance (apply your own to the mating features).

## Sizes

| dimension | value |
|---|---|
| axial module | 1.5 |
| starts | 1 |
| pitch Ø | 16 mm |
| lead | 4.71 mm |
| lead angle | 5.36° |
| normal module | 1.49 |
| tip / root Ø | 19 / 12.25 mm |
| length | 40 mm |
| bore | Ø6 |

## 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. 31: figure, his text and an animation](https://507movements.com/mm_031.html) — web — Publisher's page; dimensions are facts
- Xem Studio: [drawing](https://xemstudio.com/objects/worm-and-worm-wheel-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/worm-zi-m1-5-1start-d16-l40-bore6/index.json · license: https://xemstudio.com/files/hardware/worm-zi-m1-5-1start-d16-l40-bore6/LICENSE.md

- worm-zi-m1-5-1start-d16-l40-bore6: [STEP](https://xemstudio.com/files/hardware/worm-zi-m1-5-1start-d16-l40-bore6/worm-zi-m1-5-1start-d16-l40-bore6.step) · [STL](https://xemstudio.com/files/hardware/worm-zi-m1-5-1start-d16-l40-bore6/worm-zi-m1-5-1start-d16-l40-bore6.stl) — worm, axis Z, z 0..40, a thread centred on +X at z = 0

## Questions

**What are the dimensions of a module 1.5, 1-start worm?**

Right-hand involute-helicoid (ZI) worm: axial module 1.5, 1 start, pitch Ø16, lead 4.71 mm, lead angle γ = atan(m z₁ / d₁) = 5.36°, normal module 1.49, normal pressure angle 20°; tip Ø19, root Ø12.25 (addendum m, dedendum 1.25 m), thread thickness πm/2 on the pitch cylinder.

## Fits with

- [Worm and worm wheel, module 1.5, 1-start, 30 : 1](https://xemstudio.com/objects/worm-and-worm-wheel-mechanism/)