Saramsha

No. 018  ·  4 October 2026

One Tooth at a Time

A falling weight wants to spin this wheel as fast as gravity allows. The escapement won't let it — it releases exactly one tooth every time the pendulum crosses centre, no more, no matter how hard the weight pulls. Drag the bob to give it a push, then try to starve it or overdrive it.

working range too little swing — it will stall too much swing — it will trip

About this piece

A ratchet with a conscience

A clock needs a source of force — a falling weight, a wound spring — because friction is always trying to stop it, and something has to keep paying that debt. But a falling weight does not want to turn a gear train slowly and evenly. Left alone, it would unspool as fast as gravity and the gearing allowed, the way a fishing reel runs out when you drop the rod. That is strong and useless: strong, because weights can pull hard; useless, because "as fast as it can" is not a rate anything can call time.

The escapement's whole job is to stand between the weight and the gear train and refuse to let that happen. Once a minute, once a second, however often the pendulum demands it, the escapement lets exactly one tooth of the wheel go past — and then catches the next one, hard, and holds the entire train motionless until it is asked again. The wheel in the drawing above is not spinning. It is being allowed to advance, one notch at a time, by a part whose only opinion is the one the pendulum gives it.

Two machines, each running the other

What makes this clever rather than just restrictive is that the exchange runs both ways. Each time a tooth is released, the escape wheel gives the pallet a short shove on its way past — and the pallet is rigidly attached to the pendulum. That shove is a small, precisely timed push, delivered right as the pendulum crosses centre, exactly cancelling out whatever the air and the pivot took from it on the previous swing. The pendulum sets the rate; the escapement keeps the pendulum alive. Neither one works without the other, and the whole arrangement is self-correcting in a way that single motors never are: if the weight pulls harder, it does not make the pendulum swing faster — a pendulum's period depends on its length and on gravity, nothing else, to a very good approximation — it just makes each of those small pushes arrive with a bit more force behind it.

That "very good approximation" has a name — circular error — and it is the one place the drive genuinely does sneak back in. A pendulum's period is exactly length-and-gravity only in the limit of an infinitesimal swing; at a real amplitude A it runs slightly long, by a factor of about 1 + A²/16. Swing it twice as wide and the clock loses a few extra seconds a day. Every precision pendulum clock ever built — Graham's, Shortt's, the master clock that used to govern Greenwich time — was an exercise in keeping that amplitude as small and as constant as the escapement would allow, which is also exactly why the weight slider above has a narrow working band rather than one correct value: anywhere inside it, the clock is honest; where in it barely matters.

Starving it, and overdriving it

Drag the weight slider to the floor and the model above will run down exactly the way a real clock does when nobody has wound it: each swing collects a slightly weaker push than the one before, the amplitude bleeds away, and eventually it falls below the angle the pallets need to clear a tooth at all. The escapement jams against the wheel, the pendulum rocks a few more times on its own and stops, and the clock is stopped — not broken, just unpowered. It needs a push and more weight to start again, the same as the one on your desk would.

Push the slider the other way and a different failure shows up. More force means a bigger shove each swing, which means a wider arc, which (via circular error) means the clock already runs slow before anything dramatic happens — but past a certain amplitude the geometry simply fails: the pallet cannot stay in contact with a tooth long enough for the next one to arrive in position, and the wheel runs free for an instant before the next pallet can catch up. That is a trip: the escapement loses the beat, and in a real movement it is usually accompanied by an alarming clatter and a trip to the clockmaker, not a self-correction. The model asks you to hit reset, honestly, for the same reason.

A little history

The first mechanical escapement, the verge, predates the pendulum by three centuries — medieval tower clocks used it with a swinging bar called a foliot, and kept time to within about fifteen minutes a day, which was adequate when nobody owned a watch to check it against. Galileo noticed in 1602 that a pendulum's swing time barely depends on how far it swings, and spent decades trying to use that fact without ever finishing a working clock. Christiaan Huygens did, in 1656, marrying a pendulum to a verge escapement and improving clock accuracy roughly sixtyfold overnight. The deadbeat escapement shown schematically here — no recoil, the wheel held dead still between releases rather than nudged backwards — is George Graham's, from 1715, and it is still the design inside most pendulum clocks sold today.

The default length, 994 mm, is a genuine seconds pendulum — one whose half-swing takes exactly one second, so it ticks once a second and completes a full swing in two. In the 1790s it was briefly proposed as the basis for the metre itself, before the French Academy chose a fraction of the Earth's meridian instead. This page models a lightly damped pendulum with a fixed decay per swing and a fixed release amplitude, which is a schematic simplification of the geometry, not a literal simulation of pallet contact — the physics it demonstrates (fixed rate, a stall threshold, a trip threshold) is real; the exact numbers are chosen to be visible on a screen in a few seconds rather than measured off a real movement. ?l=994 and ?drv=30 set the length (mm) and weight (0–100) on load.