page thirteen

The Engine

The Folly stood a building up but nothing in it moved. This room takes today's number and lays out a machine instead — a driving wheel, a train of gears cut with real involute teeth, sometimes a belt, and two or three mechanisms on the end that do something with all that turning. Then it runs. Every wheel is geared to every other wheel properly, so the last shaft turns at exactly the rate the tooth counts say it should. Take hold of it and turn it yourself.

Drag anywhere to turn the machine by hand. Click a wheel or a mechanism to read its numbers. Space bar starts and stops it.

Finish
Seed — Train — Parts —

Nothing in that table was chosen by a person. Tomorrow the whole machine is scrapped.

How the date becomes a machine

  1. 01

    Cut the teeth

    Every gear here is a real involute gear. One module — the tooth size — is chosen for the whole machine, and from it each wheel gets a pitch circle, an addendum, a dedendum and a base circle. The flank of every tooth is the curve you get by unwinding a taut string from that base circle, which is the shape that lets two wheels roll on each other at a constant speed instead of grinding.

  2. 02

    Lay out the train

    Three to five stages are set out one after another. Each new shaft is placed exactly the sum of the two pitch radii away from the last, at a direction chosen to keep it clear of everything already on the plate. Some shafts carry two wheels at once — a big one driven, a small one driving — which is how a train gets a serious reduction out of a small frame. Occasionally a stage is a belt instead, and if the belt is crossed the next shaft runs backwards.

  3. 03

    Mesh it honestly

    Teeth cannot simply be drawn on. Each wheel is given a phase worked out from its neighbour's phase, its own tooth count and the angle of the line between the two centres, so that a tooth on one wheel always arrives in a gap on the other. Turn the machine slowly and watch any mesh: nothing passes through anything.

  4. 04

    Put it to work

    The end of the train gets mechanisms, and each one solves its own kinematics every frame. The crank and slider uses the piston equation. The four-bar linkage is found by intersecting two circles, and the point traced by its coupler is a genuine coupler curve — that lopsided loop is not decoration. The Geneva wheel indexes on the real arctangent, dwelling while the pin is out of the slot. The cam is a profile in polar coordinates and the follower simply reads it off. The governor's balls fly out as the speed rises, because that is all a governor has ever done.

Same number, different work: the Folly designs the building this machine would live in, the Chronicle gives the country round it eight hundred years of history, the Atlas raises the ground, the Codex invents the alphabet the maker's plate would be cut in, the Orrery hangs a family of worlds round a new star, the Observatory scatters a night sky, the Menagerie breeds something to live under it, the Almanac files the day's news and the Chimes play it.