⚙ Gearbox

How it works

Everything here is honest kinematics. When two gears mesh, the small one turns teeth-in ÷ teeth-out times as fast as the big one, and every mesh flips the direction of turn. Put a 12-tooth gear on a 36-tooth gear and it spins exactly three times as fast, the other way. An idler in between restores the direction without changing the ratio. The motor drives one gear; everything its teeth can reach is worked out from there, mesh by mesh.

Gears can also share a shaft. Tick with pinion and the bench places a pair: a big wheel with a small pinion keyed to the same arbor, one plane below its wheel — the way clock movements stack their plates. Gears in different planes never touch, so a wheel can pass over gears it doesn't drive, and trains can climb wheel → pinion → wheel with the ratios multiplying along the way.

Belts reach where teeth can't. Pick a pulley size and click a shaft to key a belt wheel onto it — or click empty bench for a loose pulley shaft — then arm the belt tool and click two pulleys: a strap spans them. The big pulley turns d-small ÷ d-big times as fast as the small one, and both turn the same way: a belt doesn't flip the direction the way meshed teeth do. Belts have no teeth to line up, so a strap can be re-timed anywhere — which is why a loop containing a belt never binds on tooth phase. It still has to agree on direction, though: one belt across the jammed triangle frees it, while a belt hung on a loop with an odd number of meshes fights itself just the same. The bench halts and tells you which.

Loops are worked out too, and they are strict: three gears closed back on themselves can only turn if their teeth line up all the way round. When they don't, the bench refuses to run and shows you the pair that collides — exactly what real gears would do.

Cams turn round motion into up-and-down. Pick a profile — the egg lobe of an engine's camshaft, the twelve-step snail a striking clock reads its hours from, the pinned drum of a music box — and click a shaft to key it on: it turns with its arbor, lobe and all. Arm the follower tool and click the cam wherever you like: the follower points at the cam's centre and rides the profile, lifted exactly as far as the shape under it is tall. The lift readout is not a decoration — the drawn outline and the number are one and the same function of the angle. A lobe sweeps its whole disc, so a cam needs a shaft whose neighbours keep clear of it; one disc per shaft (cam or belt wheel, not both); and a follower only ever reads — nothing it does feeds back into the shaft.

Linkages carry the round motion off into a straight line. Pick a crank size and click a gear: a pin keys onto the wheel's face and swings round with the arbor. Then arm the rod & slider tool, click the pin, and click where the block should sit: a rod joins pin to block, and the block slides in a straight guide bolted to the bench. When the guide lands near the crank's centre it snaps onto the centre line — the classic in-line figure, whose stroke is exactly twice the crank radius. Pull it aside and the guide stays offset: the two strokes stop being mirror images and the return becomes the quick one. The same slider-crank runs both ways in the world — in the engine the piston drives the crank, in the saw the crank drives the blade — but here the motor always turns the crank and the slider rides along, reading its geometry.

A ratchet lets a train turn one way only. Key a ratchet wheel onto a shaft — the ↻/↺ palette chooses which way it spins freely — and bolt a pawl to the plate so its tip rests on the ring. Drive the wheel the free way and it is an ordinary key, mesh for mesh; drive it the other way and the pawl holds it, so the shaft (and everything rigidly meshed with it) stands still while the part pushing it slips over the one-sided teeth — the slip is the click you feel in a socket wrench. Every shaft now has three rest states: turning, held by the pawl, or jammed. Held and jammed are different things — a hold is legal, the rest of the train keeps turning, and the bench says so in amber — but neither can show a torque, because a stopped shaft's twist isn't a kinematic answer. Flip the motor's direction and watch a ratcheted load hold on the back-stroke while everything before it runs on; a wheel with no pawl enforces nothing at all.

A Geneva drive turns a steady rotation into a stepping one. Pick a slot count, click the shaft that should carry the pin, then the shaft that should carry the wheel: a crank pin on the driver engages a radial slot and pushes the wheel one step per driver turn — the other way, as always — then a locking arc holds the wheel still while the pin swings clear. The wheel's average is exact and simple (one turn in, one slot out), but its instantaneous motion is not: it moves while the pin is in a slot and rests between. The bench keeps the two honest — the ratio chip reads the average, while the drawing takes its angle from the pin's actual place in the slot, so the wheel visibly stops and starts, and can never be shown turning smoothly through a rest it doesn't take.

Then there is the part that makes a clock a clock. Every machine above takes its pace from the motor; an escapement takes it from a pendulum instead. Key an escape wheel onto any toothed shaft, set the pendulum's period, and from that moment the wheel — and the whole rigid train it belongs to — turns at exactly one tooth per beat, while the motor's speed stops setting anything: the train obeys the pendulum and the motor turns at whatever rate the ratios demand. A 30-tooth escape wheel on a seconds pendulum (T = 2 s) turns exactly twice a minute, and that single rate is what the whole going train is built around. That pendulum's rod works out to about 0.994 m — a metre, near enough that the seconds pendulum was once offered as the definition of the metre itself. It is the one component on the bench that imposes a speed instead of deriving one — the difference between gears that turn and a machine that keeps time. Arm the little sound button and you can hear each tooth released, and the anchor pulses a ring on every beat whether or not the sound is on — both read from the wheel's actual turn, so pause the motor or jam the train and the clock falls silent with it. A small wall clock appears in the corner whenever an escapement is present, its hands reading the time the train keeps — the same actual-turn number, so the clock stops when the machine does. Beside it hangs a bell: at every whole hour, a hammer rings the number the hands read (twelve at noon), so the clock tells its own time out loud — and a clock that has drifted rings its own wrong hour. Press set clock and it is set to the time of day; from then on a second line under it reads the drift \u2014 the time the world has moved on minus the time the machine has kept. Run the train and it holds true; pause or jam it and the wall clock visibly falls behind, second by second. Once set, a faint dashed green needle also marks where the world is on the same dial \u2014 the angle between it and the solid minute hand is the drift itself. Behind the face, three small gears — the motion work — drive the hour hand from the minute hand at exactly twelve to one; the drawn movement and the drawn hands come from the same angle, so they cannot disagree. Press the movement to open that train out on the bench — every wheel named, its teeth counted, still turning at the rate it really turns. Beside the clock a small recorder keeps that drift's history on a strip of paper: a flat line while the clock holds true, a stair climbing away the moment it stops, so the error has a past and not only a present. And a clock needs power: hang the going weight on the drive and it runs on a cord \u2014 the block sinks as the seconds pass, and when the cord is spent the drive stops and the clock runs down, silent and falling behind until you wind it back up.

Speed is only half of every trade; the other half is twist. A slow shaft doesn't just turn slower — with an ideal, friction-free train it turns harder, in exact inverse proportion: gear a 72-tooth wheel onto the motor's 24 and it turns a third as fast with three times the torque. The bench shows that half too: every driven gear carries a small gold chip reading its torque as a multiple of the motor twist you set in the toolbar, and the selected gear's line spells the trade out — the same number the ratio quotes, pointed the other way. The exchange rate is exact because the bench is ideal: real trains spend a share of it on friction, and nothing here models that loss.

The shelf holds finished machines to take apart. The puzzles panel holds fourteen small challenges that walk the whole bench instead: double a speed, undo a flip with an idler, free a jammed triangle, move a rotation with straps alone, gear a motor down by exactly sixty to one the way a clock does, give the bench its first up-and-down with a cam and a follower, build a two-cylinder engine from two opposed crank pins, gear the motor down until a shaft carries three times its twist and let a crank pin spend that twist on a push, give a load a one-way ratchet so it drives forward and holds on the back-stroke, combine both for a winch that winds forward and holds the load, hand a driven train\u2019s pace to a pendulum escapement so the motor stops setting the speed, reverse a turn with a crossed strap at half speed, set a belt-driven drum\u2019s ratchet the way the cross turned it so it winds forward and backs the load, and \u2014 the last one \u2014 step a wheel one notch per motor turn through a real mesh and hold it still between notches. Each puzzle checks itself as you build, each one opens when the one before it is solved, and solved puzzles stay solved in your browser.

A bench is also portable. Press share and the whole machine — gears, pinions, pulleys, belts, the motor and its speed — is packed into the link itself. Anyone who opens it builds exactly what you built, straight in their own browser: no account, nothing uploaded, the link simply carries the drawing. If you want to keep more than one, name a bench and save current files it on your own shelf \u2014 also kept in this browser only, never sent anywhere, so it is waiting when you come back. And when a machine is worth showing, press picture to download it as a PNG: the bench exactly as it stands, on a captioned poster, drawn from the same canvas — so the picture can't show a machine the bench isn't.

Honest limits: speeds, directions and torque ratios are exact — torque is the ideal, friction-free trade, the chain of teeth and diameters taken at face value, with no friction, no wear and no notion of the strength of real teeth (a stalled, jammed train shows no torque at all, because a kinematic answer isn't one). The teeth are drawn simplified rather than as true involute curves. Belts are ideal: no slip, no stretch, no minimum-wrap check, and a strap is drawn straight between its pulleys — the bench does refuse a belt whose path would rub a part in the same plane. Belt wheels ride in their arbor's plane; a loose pulley shaft sits in the bench's base plane, and a belt can't jump planes. A ratchet is an ideal one-way coupling at the wheel's teeth: the bench shows the hold and the slip, not the pawl's shape or the strength of the teeth, and a saw wheel with no pawl enforces nothing. An escapement is modelled as a speed governor, not the full lock/drop/impulse physics of a real pallet: one tooth is released per beat, the pendulum's period is the exact quantity, and its on-screen swing is drawn wide only for legibility. The going weight is a model, not a wound barrel: it carries a few minutes of running on the bench rather than the day or more a real barrel holds, and its cord is drawn as a fraction of what is left, not in metres. Cams and their followers are radial and ideal: the follower points at the cam's centre, tracks the profile up and down, and only reads it — no offset followers, no springs, nothing feeds back into the shaft; at most four followers to a cam. Linkages are ideal joints: the rod is rigid and weightless, the guide frictionless, and the slider only ever reads its crank — a piston here can't drive the shaft the way a real power stroke does. At most three crank pins to a shaft, one rod to a pin, and the block's whole travel must stay on the plate; the guide may share its arbor's ground (that is the in-line figure), but other same-plane parts must keep clear of the block's path and the rod's sweep. Pinions are drawn on top of their own wheel so you can see them; in a real movement they hide beneath it. Planes move in whole steps, one mesh apart. One motor per bench. Your bench and your puzzle progress save themselves in your browser — nothing is sent anywhere; a share link carries the machine itself, and opening one simply rebuilds it on the spot.