Chris Collins

Tools · bricks

Technic gearing

Plan gear trains with LEGO Technic-compatible gears — which pairs mesh on the stud grid (in line, on 3-4-5 diagonals, at 90° through bevels, worm and rack), the ratio, speed, torque and direction of every axle from a motor preset, an animated drawing to scale, and a solver that finds trains for a target ratio.

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How to use it

A planner for gear trains built from LEGO Technic-compatible gears. Technic gears are module 1 mm and the holes in a beam are 8 mm apart, so a gear’s pitch radius is its tooth count ÷ 16 in studs, and two gears mesh where their axles are (z₁ + z₂) ÷ 16 studs apart. An 8 and a 24 sit 2 studs apart on one beam; a 16 and a 24 want 2.5 — a half stud in line, or exactly 1.5 across and 2 up on a 3-4-5 triangle.

How to use it

  1. Gear train. Load an example or build the stages: each stage is a driver and the gear it drives, and the driven gear shares its axle with the next stage’s driver. For each stage choose how it meshes (parallel axles, bevels at 90°, a worm, or a rack) and, for parallel axles, which grid position — in line, or one of the diagonals that fit. Pick a motor: the cards give the ratio, the output speed with no load, the output torque at stall and at the motor’s maximum-power point, the gear efficiency and the power. The axle table gives every axle’s speed, direction and torque.

  2. The drawing shows the train to scale on the stud grid, gears turning at a speed you set, with the beams that hold whole-stud spacings (solid), and dashed where the spacing needs a half-stud offset. Stages through 90° (bevels, knob wheels) are drawn unfolded into the same plane and marked ⟂; a worm is drawn side-on, as its axle lies in the plane of the wheel. ⛶ Full screen gives the drawing the whole window.

  3. Spacing. Pick any two gears to see every way they mesh: the in-line centre distance and whether it is a whole or half stud, the diagonal positions within the tolerance (with the error in mm), the offsets for crossing axles through bevels, and worm and rack distances. A table shows the centre distance of every pair of spur and double-bevel gears at a glance.

  4. Ratio finder. Type a target such as 24, 1:3 (three times faster) or 60/8, the most stages and a tolerance, tick the gears you have, and the solver lists the trains that reach it — fewest stages first, then the closest ratio, then the cleanest spacing. Build loads one into the gear train.

  5. Catalogue lists the gears with part numbers, teeth and pitch radius; Explainer covers speed for torque, why worms lock (with a calculator for the friction), and backlash.

Method and assumptions

  • Pitch radius = z × 1 mm ÷ 2 ÷ 8 mm = z ÷ 16 studs, for every toothed gear (spur, clutch, double bevel, turntable rings). The worm’s pitch radius is taken as ½ stud (8 mm pitch diameter), so a worm and a 24 have axles 2 studs apart, a worm and an 8 one stud.

  • Fits. A spacing is "whole" or "half" when it is within the in-line tolerance (0.04 stud, about 0.3 mm) of a whole or half number of studs. Diagonals are searched on the half-stud grid with their own tolerance (0.06 stud, about 0.5 mm, by default — Technic gears run with a little slack, but more than about 0.1 stud skips under load).

  • Bevels at 90° on crossing axles: each gear’s centre sits about the other’s pitch radius plus a quarter stud from the crossing, so a 12 and a 20 double bevel sit 1½ and 1 stud from it. Every double-bevel and bevel tooth count is 4 more than a multiple of 8 (12, 20, 28, 36), which is why they all land on half studs. This is an approximation to check on the bench.

  • Efficiency per mesh is a rough figure for LEGO plastic gears including the axle friction: 92 % for parallel axles, 88 % for bevels at 90°, 75 % for knob wheels, 90 % for a rack. The worm is worked out from its lead angle (atan(1/8) ≈ 7.1° for module 1 on an 8 mm worm) and a friction coefficient μ (0.25 by default): η = tan λ ÷ tan(λ + φ) ≈ 32 %, and the worm self-locks when the friction angle φ = atan μ exceeds λ, that is for μ above about 0.125.

  • Motors are approximate figures at 9 V — no-load speed, stall torque and a rough peak efficiency — rounded from published bench tests (Philippe Hurbain’s LEGO motor comparison at philohome.com). Real motors vary from one to the next and with the battery; treat the outputs as estimates. The maximum-power point is taken at half the no-load speed and half the stall torque.

  • Direction: each parallel mesh reverses the rotation; a 90° stage turns the axis (the sense then depends on which side the gears sit); a worm’s wheel turns one way or the other depending on which side of the worm it is.

  • Ratio finder: one stage option per distinct ratio among the ticked gears (worms can only drive), combined up to the stage limit with pruning; trains are ordered with the speed-reducing stages towards the output, where the torque is.

  • Part numbers are from the usual parts catalogues; the ones marked * in the catalogue (the differentials and the 28-tooth single bevel) are not confirmed — check them on BrickLink or Rebrickable before ordering.

LEGO® and Technic are trademarks of the LEGO Group, which does not sponsor, authorise or endorse this site. This tool describes LEGO Technic-compatible parts and uses no LEGO logos.

Sharing

Share link copies a URL that opens this tool exactly as you have it set up — the stages, motor, tolerances, the spacing pair and the ratio-finder settings. Opening a link replaces your own saved settings for the tool; a Restore my settings button brings them back.

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