The ✨ GEN's → Gear tool builds mathematically correct involute gears from a few numbers — no CAD. Spur gears cut flat on a 2-wire machine; helical and bevel gears use a 4-wire morph. Great for big demonstrator gears, kinetic sculptures, props and working foam mechanisms.
Gear basics in 30 seconds
A gear is defined by three numbers:
- Teeth (z) — how many teeth around the gear.
- Module (m) — tooth size, in mm. Bigger module = bigger, chunkier teeth. (Imperial uses "diametral pitch" instead; module is the metric version.)
- Pressure angle — the slope of the tooth flank. 20° is the modern standard; 14.5° is older/finer; 25° is stronger.
From those, every diameter follows: pitch Ø = m × z (the working diameter where teeth mesh), outer Ø = m × (z + 2), root Ø ≈ m × (z − 2.5). The tooth flank is a curve called an involute — the shape a string traces as it unwinds off a circle — which is what lets gears roll against each other smoothly at constant speed.
The golden rule: when do two gears mesh?
Two gears run together only if they share the same module and the same pressure angle. The number of teeth can differ (that's your gear ratio). The distance between their shafts is centre distance = (z₁ + z₂) × m ÷ 2. So a 20-tooth and a 40-tooth gear at module 8 mesh at (20+40)×8÷2 = 240 mm centres and give a 2:1 reduction.
Spur gears (2-wire)
The classic flat gear: the tooth profile is cut straight through the foam. It loads as a 2-axis cut, centred in a material block 90% of your cutter. Pick the foam thickness to suit.
Helical gears (4-wire)
A helical gear has teeth that twist along the thickness, so they engage gradually — quieter and smoother than spur gears. cncfoam.com makes one with a 4-wire morph: the left wire cuts the gear at 0° and the right wire cuts the same gear rotated by the twist angle, and the ruled surface between them forms the slanted teeth. Keep the twist modest (well under one tooth pitch) for clean teeth.
Bevel gears (4-wire)
A bevel gear carries its teeth on a cone, so a pair can transmit motion around a corner (typically 90°). Here the 4-wire morph tapers the gear: the left wire cuts the full-size gear and the right wire cuts a scaled-down copy, producing a truncated cone of teeth. The taper % sets how much smaller the back face is. It's an approximation of a true spherical-involute bevel, but reads correctly and meshes for demonstration and light-duty use.
Bore, spokes & lightening holes
Add a centre bore for a shaft, and choose a web style: solid, spokes (a hub, a rim and arms between them), or lightening holes (a ring of round holes). Because a hot wire is a continuous loop, it can't drop into an enclosed hole — so every interior hole is auto-slit to the nearest edge with a hairline cut, exactly as you would do by hand. The slits are routed through tooth valleys where possible. If you'd rather have clean closed holes, drill or pierce them on another tool after cutting.
Tips
- Avoid too few teeth. Below ~17 teeth at 20°, the involute starts to undercut near the root and the teeth weaken. Use more teeth or a higher pressure angle for small gears.
- Mind the kerf. The wire removes its own width, so set the kerf to keep teeth from coming out thin — especially at small module.
- Match your set. Decide one module + pressure angle for a whole gear train, then only vary the teeth.
- Foam choice. Denser XPS holds tooth detail better than coarse EPS at small sizes.
Related
See Morphing two profiles for how the 4-wire morph behind helical/bevel works, the Object bar to rescale the finished gear, and Kerf & cut quality for getting tooth thickness right.