Worm and worm wheel, module 1.5, 1-start, 30 : 1 — dimension sheet
Source: Xem Studio, https://xemstudio.com/objects/worm-and-worm-wheel-mechanism/  (sheet CC BY 4.0; files Xem Studio Design License, https://xemstudio.com/license/)
Basis: Xem Studio design following Brown No. 31 (1868)
Catalog version: 2026-10-20

Sizes: see table below
- Resize: multiply every length by one factor k and the motion stays identical: angles, ratios, timing and the formulas below do not change, because a mechanism's motion depends only on the ratios of its lengths. Here, scales with k: centre distance; stays the same: worm, wheel, ratio; step to the nearest standard size (and redraw the hole or pocket it fits): shafts.
- Resize: Gears scale by the module m (pitch Ø = m·z, centre distance = m·(z₁ + z₂)/2): keep the tooth counts so the ratio stays, and choose a standard module (0.5, 0.8, 1, 1.25, 1.5, 2, 2.5, 3).
- Resize: fit clearances stay in mm (a slide fit is the same gap at any size); keep every printed wall and pin at least two nozzle widths; mass grows with k³ but part strength only with k², so at k = 2 parts are about 8× heavier and 4× stronger: check pins and thin links when scaling up.
- An endless screw (the worm) on one shaft meshes with a toothed wheel on a shaft at right angles: each turn of the worm advances the wheel one tooth (one thread), so the ratio is the tooth count — 30 : 1 here — in a single, quiet stage. The same result as the face-spiral drive of Brown's No. 29, but simpler to make, so far more used.
- Worm: involute helicoid (ZI), axial module 1.5, single start, pitch Ø16, lead angle 5.36°. Wheel: 30-tooth involute helical gear with helix angle = lead angle, same hand — a non-throated worm wheel, so the pair is an exactly conjugate crossed-helical pair (point contact) at centre distance 30.5 mm. Checked at nine positions over 1.5 worm turns: no overlap beyond contact.
- With a lead angle of 5.36° (below ~6°) the drive is self-locking: the wheel cannot drive the worm. Brown's No. 31; drawn with the worm turned 30°.
- Parts (each has its own page): worm-zi-m1-5-1start-d16-l40-bore6, worm-wheel-helical-m1-5-30t-for-1start-d16, linear-shafts-h6.
- Brown's movement No. 31 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

parameter  value
worm  module 1.5, 1-start, pitch Ø16, lead angle 5.36°
wheel  30 T helical, helix 5.36°
ratio  30 : 1
centre distance  30.5 mm
shafts  90°, non-intersecting

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

Free files (Xem Studio Design License, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/worm-and-worm-wheel-mechanism/index.json
API: https://xemstudio.com/api/geometry?object=worm-and-worm-wheel-mechanism