ncgears

ncgears generates noncircular gear pairs from a transmission law or a pitch-curve shape.

The generator creates 2D outlines, verifies the assembled pair for interference and contact-motion error, and exports CSV, SVG, DXF, JSON, PNG, and animated GIF files. It supports closed gears, finite open segments, nonconvex pitch curves, unequal ratios, and involute-rack or cycloidal-rack tooth families. The complete application and geometry pipeline are implemented in Python; Shapely/GEOS provides robust floating-point polygon operations.

Project status: alpha. Generated geometry should be reviewed for the intended material, manufacturing process, load, speed, and tolerances.

Install

pip install ncgears

PNG and animated GIF previews are optional:

pip install "ncgears[plot]"

Command line

Most functionality is available in the CLI:

ncgears "phi - 0.08*sin(2*phi)" --teeth 24 --module 1.5 \
  --name two_lobe --dxf two_lobe.dxf --render --gif

ncgears "1 + 0.08*cos(2*phi)" --centrode --teeth 20 \
  --name centrode_two_lobe

Run ncgears --help for all commonly used options.

Basic python usage

Describe the desired relationship between the drive angle phi and the driven angle. Here the driven gear speeds up and slows down twice per revolution while returning to the same 1:1 average ratio:

import ncgears

pair = ncgears.generate(
    "phi - 0.08*sin(2*phi)",
    teeth=24,
    module=1.5,
    name="two_lobe",
)

print(pair.summary())
pair.export_dxf("two_lobe.dxf")
pair.export_svg("two_lobe.svg")

module and all exported coordinates use millimetres. The returned GearPair also provides:

pair.drive_outline           # (N, 2) NumPy array
pair.driven_outline          # centered on its own shaft
pair.placed_driven_outline   # translated into assembled position
pair.center_distance
pair.drive_teeth
pair.driven_teeth
pair.ratio
pair.maximum_transmission_error
pair.metadata                # complete verification report
pair.directory               # CSV and JSON source files
pair.render()                # pair.png; requires ncgears[plot]
pair.render_gif()            # pair.gif; follows the generated motion law

The output directory defaults to out/<name>/. Each successful generation contains drive.csv, driven.csv, metadata.json, and the sampled input.

Start from a pitch curve

If the drive gear's pitch radius is easier to describe than its motion law, use a centrode expression:

pair = ncgears.generate_from_centrode(
    "1 + 0.08*cos(2*phi)",
    teeth=20,
    module=1.0,
    name="centrode_two_lobe",
)

The radius may use arbitrary units; ncgears scales its arc length to the requested tooth count and module. By default it solves the center distance for one mate revolution. A specific ratio can be selected with target_cycle_delta. For example, a five-lobed 5:2 angular ratio uses:

import math

pair = ncgears.generate_from_centrode(
    "1 + 0.05*cos(5*phi)",
    teeth=100,
    target_cycle_delta=5 * math.pi,
    profile="cycloidal",
    name="five_to_two",
)

Closed and open designs

Closed gears require a smooth, strictly increasing motion whose cycle advance produces an integer mate tooth count. A simple 2:1 pair is:

pair = ncgears.generate("2*phi", teeth=20)  # 20 drive teeth, 10 driven teeth

Finite, non-repeating motion can be generated as an open segment:

pair = ncgears.generate(
    "1.8*phi + 0.03*sin(phi)",
    open_=True,
    drive_end=2.4,
    teeth=12,
    name="finite_segment",
)

What is verified

The Python engine uses swept rack-cutter solids and Shapely/GEOS regularized polygon operations. A successful result includes checks for:

• simple, hub-connected gear bodies
• sampled whole-cycle solid interference
• contact motion recovered from the finished outlines
• sweep resolution, root radius, tip thickness, and centrode curvature
• sliding-velocity and undercut diagnostics

metadata.json records geometry_backend: "shapely-geos", double-precision construction, worker limit, cutter-pose count, and the maximum sweep step. Independent involute gear sweeps and verification phases use a bounded thread pool of at most eight workers; the dependent cycloidal master/mate sweeps remain sequential. Floating-point Boolean error is normally far below the error from discretizing cutter motion; increase samples_per_radian when a design operates close to its tolerances.

These geometry checks are not load-rating or manufacturing certification.

Development

python -m pip install -e ".[dev]"
python -m pytest
ruff check ncgears tests
python -m build

The GitHub Actions workflow tests Python 3.10–3.13, builds a platform-independent ncgears wheel, and smoke-tests the installed wheel. Shapely supplies its GEOS runtime through its own platform wheels.

Method and prior work

The pitch-curve equations follow Uwe Bäsel, "Determining the geometry of noncircular gears for given transmission function". Tooth geometry is constructed by sweeping a parameterized rack cutter rather than assembling only locally convex branches. The silhouette-fitting problem addressed by Xu et al., "Computational Design and Optimization of Non-Circular Gears", is complementary: a fitted transmission derivative or polar centrode can be passed into ncgears.

Contributions and reproducible test cases are welcome through the issue tracker.

Project context

This project contains entirely AI generated code. This project has been my personal benchmark for determining how capable coding models are for over a year. Models have saturated this benchmark, so I'm releasing the project as an alpha.

License

ncgears is distributed under the Apache License 2.0.