Wormgear

Worm gears for build123d, with real DIN-3975 engineering behind the geometry.

from wormgear import WormGear, WormWheel

worm  = WormGear(module=2.0, num_starts=1, length=40)   # is a build123d Part
wheel = WormWheel(module=2.0, num_teeth=30)             # is a build123d Part

worm.export_step("worm.step")
wheel.export_step("wheel.step")

Or for a guaranteed-matched pair in one line:

from wormgear import make_pair

worm, wheel = make_pair(module=2.0, ratio=30, length=40)

That's the whole API for most users. Both classes subclass build123d.BasePartObject, so you can show(), export_step(), or compose them into assemblies directly.

Why use this

Wormgear supplements the excellent build123d gear ecosystem (bd_warehouse for spur gears and other parts, py_gearworks for spur / helical / bevel / cycloid / inside-ring) with specialist support for worm gears, which neither of those libraries currently covers.

What it does:

• Implements real DIN-3975 derivation. Lead angle, pitch diameter, addendum/dedendum, throat radius for globoid worms — all standards-compliant rather than approximate.
• Calculates load-capacity-relevant fields per DIN-3996 (efficiency estimate, self-locking detection, recommended materials).
• Generates exact geometry. No "good enough after manufacturing" approximations — the STEP file is exactly what your CNC will cut or your printer will print.
• Two tooth profiles: ZA (straight flanks, CNC-friendly), ZK (slightly convex, 3D-print-friendly).

Install

pip install wormgear

Requires Python 3.12+. build123d (and its OpenCascade backend) installs automatically.

Beyond the basics

Engineering analysis

from wormgear import make_pair, check_mesh

worm, wheel = make_pair(module=2.0, ratio=30, length=40)

# Kinematic mesh validation (independent of how the gears were built)
report = check_mesh(worm._params, wheel._params, worm._assembly_params)
print(f"ok: {report.ok}, ratio: {report.ratio}, "
      f"centre distance: {report.centre_distance_mm:.2f} mm")

For full DIN-3975 design analysis (efficiency, self-locking, undercut, etc.):

from wormgear.calculator import design_from_module, validate_design

design = design_from_module(module=2.0, ratio=30)
result = validate_design(design)
print(f"efficiency: {design.assembly.efficiency_percent:.1f}%, "
      f"self-locking: {design.assembly.self_locking}")
for msg in result.warnings:
    print(f"warning: {msg.message}")

Validate a built model against the calculation

Once you've built (or imported) a 3D model, you can confirm it actually realises the engineering calculation — the measured tip/root diameters and length match the computed spec, and the pair meshes without interference:

from wormgear import make_pair, check_pair_geometry

worm, wheel = make_pair(module=2.0, ratio=30, length=40)

# Per-part, against the spec each was built from:
print(worm.validate())     # tip + root diameter, length, lead, ZA flank angle
print(wheel.validate())    # tip diameter (+ root for non-throated wheels)

# Whole pair, including a mesh-interference check (on by default):
from wormgear.calculator import design_from_module
design = design_from_module(module=2.0, ratio=30)
report = check_pair_geometry(worm, wheel, design, worm_length=40)
print("pass" if report.ok else "FAIL")

This verifies that the geometry realises the calculation — and, separately, the calculator's own numbers are cross-checked against an independent textbook example and calculator. It does not claim full DIN-3975 certification: each report lists what it does not cover (multi-start lead, wheel flank profile, throat diameter), so a green result is never mistaken for a guarantee. Tolerances default to a few hundredths of a millimetre — far below typical machining tolerances — and are adjustable per call.

See docs/VALIDATION.md for exactly what is and isn't checked, the calculation cross-validation, and a note on profile-shift behaviour.

Features (bores, keyways, set screws)

from wormgear import WormGear
from wormgear.core import BoreFeature, KeywayFeature

worm = WormGear(
    module=2.0, num_starts=1, length=40,
    bore=BoreFeature(diameter=8.0),
    keyway=KeywayFeature(),  # auto-sized DIN-6885 keyway
)

Web calculator

Don't want to write any code? wormgear.studio is the browser-based version of the calculator. It produces a JSON file you can load:

from wormgear import WormGear, WormWheel
from wormgear.io import load_design_json

design = load_design_json("my-design.json")
worm  = WormGear.from_design(design, length=40)
wheel = WormWheel.from_design(design)

CLI

For shell-driven workflows (CAM pipelines, batch generation):

wormgear design.json -o out/
wormgear design.json --profile ZK --globoid --worm-bore 8

See wormgear --help for the full set of options. (wormgear-geometry is kept as a backwards-compatible alias.)

Advanced: virtual hobbing

For high-precision conjugate contact (e.g. high-load applications or contact-stress analysis), wormgear.advanced.virtual_hobbing kinematically simulates the hobbing manufacturing process — slower than throated=True, but produces sub-tenth-percent-accurate tooth flanks:

from wormgear import WormGear, WormWheel
from wormgear.advanced import virtual_hobbing

worm = WormGear(module=2.0, num_starts=1, length=40)
wheel = WormWheel(module=2.0, num_teeth=30)
precise_wheel = virtual_hobbing(worm, wheel, steps=72)

Most users want plain WormWheel(throated=True) — reach for this when you specifically need kinematic accuracy.

Known limitations

• Even-numbered multi-start worm STL is slightly non-watertight. For num_starts ∈ {2, 4, 6, ...} the two opposing thread surfaces meet at a single shared vertex on the symmetry plane (a real OCC topology with is_valid=True, but degenerate for tessellation). The exported STL has ~6 open edges out of ~10,000 — about 0.06 % of the mesh. STEP output is unaffected and round-trips perfectly. Most STL slicers (Cura, PrusaSlicer) tolerate the open edges and slice normally; strict mesh-repair tools may flag them, and the workaround is a "make watertight" pass in Blender or Meshmixer. 1-start and odd-numbered multi-start worms are clean. See #223 for the diagnostic and attempted fixes.

• Profile shift adjusts tooth proportions, not centre distance. profile_shift is applied to the wheel and grows/shrinks the tooth (tip/root) per the standard DIN formulas, but it does not move the centre distance (which stays m·(q + z₂)/2). This is the "addendum modification at fixed centre distance" use; the "profile shift to achieve a non-standard centre distance" use (a = m·(q + z₂ + 2x)/2) is not implemented. See docs/VALIDATION.md and #245.

Related libraries

Wormgear is one library in the build123d gear ecosystem:

• bd_warehouse — spur gears, fasteners, bearings, threads, sprockets
• py_gearworks — spur, helical, bevel, cycloid, and inside-ring gears

Use them together: spur / helical gears from bd_warehouse or py_gearworks for parallel-shaft stages, wormgear for perpendicular reduction stages.

Documentation

• Architecture — system design
• Geometry — technical specification
• Engineering Context — DIN-3975/DIN-3996 background
• Validation & Accuracy — what is and isn't checked, calculation cross-validation, profile-shift behaviour

Background

Created for custom worm gear design in luthier (violin making) applications, where standard gears don't fit unusual envelope constraints. Extended to support CNC machining and 3D printing for makers and engineers.

License

MIT

Author

Paul Fremantle (@pzfreo)

How this was built

This project was coded entirely by AI under human direction. The design decisions, engineering requirements, and review were directed by a human; the implementation was written by AI.