The whole face
A black disc on a pedestal, 14 brass gears around a 36-tooth sun, an orange disc behind the open middle. The sizes are not styling — they are what keeps the chain in mesh.
Bigger, further out, still in mesh
Two mirrored arms of 7 gears wind out from a 36-tooth sun. Scroll to follow one of them.
One arm, 7 gears
From the hub outwards the tooth counts run 14, 15, 18, 20, 22, 23, 26, and the centres move from 37.5 mm to 73.5 mm. Each gear is about a tenth bigger than the one before it, and sits about a tenth further out.
You see straight through it
The sun sits inside a black bezel with the orange disc behind it. A 14 mm bore runs right through the piece, so whatever is behind it shows in the middle.
One tooth size, everywhere
Module 1.5 mm on all 15 gears — the fixed tooth size the spiral is built around. 312 teeth in total, cut 5 mm thick, and in a low light the tips are the first thing you see.
Edge on, it is a plate
The gears stand off the front of the disc, each on its own short shaft with a cap over it. Sideways on, the whole vortex is about one gear thick, on a stem and an oval foot.
Where it stands
7.4 × 4.1 × 8.4 in on the foot and 10.4 oz of PLA: tall enough to read from across the room, thin enough to keep to the back of a shelf.
Why a spiral of gears can mesh at all
One tooth size across the whole disc, so growth and spacing have to be the same number.
Two gears mesh when the distance between their centres equals the sum of their pitch radii. Fix the tooth size — module 1.5 mm, the same on every gear here — and that becomes a rule about growth: a gear sitting a tenth further out has to be about a tenth bigger, or the teeth miss.
Seven gears keep to it. Their centres fall on one logarithmic spiral to within 0.03 mm, gaining 11.9% of their radius at every step — a rate that would multiply it 3.6 times in a full turn, if the disc were wide enough to take one. Measured off the shipped geometry, every centre distance lands within 0.1 mm of the textbook figure for a 1.5 mm module.
| Teeth | Pitch circle | From the hub |
|---|---|---|
| 14 | 21.0 mm | 37.5 mm |
| 15 | 22.5 mm | 41.9 mm |
| 18 | 27.0 mm | 47.0 mm |
| 20 | 30.0 mm | 52.8 mm |
| 22 | 33.0 mm | 59.2 mm |
| 23 | 34.5 mm | 66.0 mm |
| 26 | 39.0 mm | 73.5 mm |
The gaps are drawn in
Every gear has its own shaft, its own cap and its own set of clearances.
Each gear sits on a short shaft standing off the back plate, with a cap pressed over the end of it — that black cylinder at the centre of every gear. The gaps around that shaft are what a printed gear needs to turn without binding, and what an FDM printer needs if the parts are not to come out fused to each other.
Those are the numbers in the model as it shipped, measured rather than quoted. It is a prototype design: the fits are drawn and checked in the geometry, not proven in plastic.
- 0.7 mmwider than the shaft it turns on, across each bore
- 0.3 mmbetween the back of the gear and the plate
- 0.4 mmbetween the front of the gear and its cap
- 0.22 mmthat every tooth tip stops short of the textbook tip circle
The piece
Seven gears, each about a tenth bigger than the last, and the teeth still meet at the rim.
| Overall | 7.4 × 4.1 × 8.4 indisc upright on its foot |
|---|---|
| Weight | 10.4 oz |
| Material | PLA |
| Print time | 16 h 41 min |
| Gears | 15a 36-tooth sun and two arms of 7 |
| Teeth | 312module 1.5 mm, cut 5 mm thick |
| Bodies | 4415 gears, 14 hub caps, and the disc, bezel, axle, stem and foot that carry them |
| Colours | #060708 black, #B87524 brass, #FF3803 core |