Gears that mesh: module, teeth and backlash

The four gear shapes, and the three numbers that decide whether a printed pair actually turns.

Four shapes in the Mechanism group are involute gears — Spur gear, Ring gear, Rack and Worm — and they are the parts you place when you want *one* gear. They are not the same thing as the gear generators, which assemble a whole mechanism and space it for you.

Two numbers are the entire gear. Module is the size of one tooth and Teeth is how many there are, so the pitch diameter — the imaginary circle where two gears actually roll on each other — is just the two multiplied. Everything else is trim. This is also why you cannot make a gear "a bit bigger": scaling it changes the module, and a gear with a different module meshes with nothing.

Meshing is module plus pressure angle, and nothing else. Two gears run together when both match; the tooth counts are free and their ratio is the reduction. Get the module right and a 12-tooth pinion drives a 60-tooth wheel at 5:1 without another thought. Get it wrong by 0.1 and no amount of moving the parts will save it. The centre distance follows from the same numbers — module × (z₁ + z₂) ÷ 2 — which is why a pair placed by eye jams or slips even when both gears are perfect.

Backlash defaults to zero, and zero is for mathematics. It thins each tooth slightly so the flanks are not touching on both sides at once. A pair modelled at exactly nominal size overlaps its mating tooth by a measurable amount at the standard centre distance, and printed at that size it locks solid — before a printer has added its own tolerance on top. Around 0.15 mm is a sane starting point, and it is the first thing to raise when a printed pair turns stiffly. Print the fit test coupon once if you would rather know your printer’s number than guess it.

Very few teeth do not work, for two separate reasons. The field accepts 4, and it should not be read as an invitation. A 4- or 6-tooth pinion physically interferes with a larger gear at the standard centre distance — real gearing solves that with profile shift, which these shapes do not do — and at the default module and bore a 4-tooth gear comes out as four loose teeth with nothing joining them, because the shaft hole has eaten the middle of it. Below about 8 teeth, shrink the bore and expect to check the result.

Very small modules vanish. Under roughly module 0.3 the solid stops resolving and evaluates to nothing at all — an empty node that still sits in the tree. If a gear disappears when you make it finer, that is what happened; go coarser. The Tooth tip read-out is the early warning, since a tooth too fine to print is usually also too fine to build.

Reach for a generator when you want a mechanism. A gear train lays out a line of gears already spaced and phased, and the planetary, rack-and-pinion and worm-drive generators do the same for their arrangements. Place the primitives when you want a single gear you will position yourself.

1. Add a Spur gear from the Mechanism group and set Module and Teeth. Those two are its size: the pitch diameter is module × teeth, so the default 20-tooth module-2 gear measures 40 mm.
2. Add the gear it has to drive and give it the same Module and the same Pressure ∠. That is what makes two gears mesh; the tooth counts are free, and their ratio is the reduction.
3. Sit their centres module × (teeth + teeth) ÷ 2 apart — 20 teeth against 30 at module 2 is 50 mm. Measure it rather than eyeballing it.
4. Raise Backlash off zero before you print anything that has to turn.
5. Set Bore Ø to the shaft, Thickness to the face width, and reach for Helix ∠ or Cone angle if you want a helical or a bevel gear.
6. For an internal gear use Ring gear — Rim width is the meat outside its teeth. For rotary-to-linear use Rack, where Back height is the bar under the teeth. For a right-angle reduction use Worm: Starts is how many threads are wound around it, and the ratio is the wheel’s teeth ÷ starts.
7. Watch the Tooth tip read-out, and read what it means if it turns orange.