Worm (involute helicoid, ZI), axial module 1.5, 1-start, pitch Ø16 × 40, Ø6 bore — dimension sheet
Source: Xem Studio, https://xemstudio.com/objects/worm-zi-m1-5-1start-d16-l40-bore6/  (sheet CC BY 4.0; files Xem Studio Design License, https://xemstudio.com/license/)
Basis: Xem Studio design following Brown's figure (1868); true size, no printing allowance
Catalog version: 2026-10-20

Overall (mm): length 19.0, width 19.0, height 40.0
- 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).

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

Files elsewhere (not hosted by Xem Studio; license as stated by the publisher):
- Henry T. Brown (1868, public domain): Five Hundred and Seven Mechanical Movements — scan on archive.org — web — Publisher's page; dimensions are facts — https://archive.org/details/fivehundredseven00browiala
- 507movements.com: Brown's movement No. 31: figure, his text and an animation — web — Publisher's page; dimensions are facts — https://507movements.com/mm_031.html
- Xem Studio: drawing — web — Publisher's page; dimensions are facts — https://xemstudio.com/objects/worm-and-worm-wheel-mechanism/

Free files (Xem Studio Design License, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/worm-zi-m1-5-1start-d16-l40-bore6/index.json
API: https://xemstudio.com/api/geometry?object=worm-zi-m1-5-1start-d16-l40-bore6