Pulley systems
A pulley is a wheel with a rope over it. On its own that sounds like it could not possibly matter, and yet the right arrangement lets a small motor lift something it has no business lifting. The whole of it comes down to one question: how many pieces of rope are holding the load up?
Count the supporting ropes
Look at the load and count the rope segments running down to it. If the load hangs from two segments, each of them carries half the weight, so you only have to pull half as hard. Four segments, a quarter each.
effort = load ÷ number of supporting ropes
And the price, which is exactly as large as the saving:
rope you must pull = distance lifted × number of supporting ropes
Count the blue rope segments running down to the load. That number divides the force and multiplies the rope you have to pull.
The three arrangements
| Type | Supporting ropes | What it gives you |
|---|---|---|
| Fixed — the wheel is bolted to something solid | 1 | No force saved at all. What it changes is the direction you pull in — down instead of up, or round a corner — which is very often the whole reason it is there. |
| Movable — the wheel travels with the load | 2 | Half the force, twice the rope. The pull direction is unchanged. |
| Combined — fixed and movable together (a block and tackle) | 2, 4, 6… | Both at once: the force divided by the count and a convenient direction to pull in. |
A fixed pulley being “no help” is worth dwelling on, because it is where the counting rule proves itself. One rope, one whole load — and it is still the pulley you reach for most often, because pulling downwards with your weight behind it beats pulling upwards every time.
Nothing is gained
Multiply the two formulas together and the gain cancels the cost exactly: half the force over twice the distance is the same amount of work. A pulley system does not create effort out of nothing — it lets you spend the same effort in a form you can actually manage, a little at a time instead of all at once.
That is the same bargain gears and levers make, in three different shapes. Once you have seen it in one of them, the other two stop being new.
Building them out of LEGO
- Use a proper pulley wheel or a smooth free-spinning wheel on an axle. A rope dragged over a fixed beam is a friction brake with extra steps.
- String stretches, and stretch eats your lift. Braided cord is far better than the thin white string for anything carrying weight.
- Every extra wheel adds friction. A four-rope block and tackle does not quite give you the full quarter — measure what you actually get rather than trusting the arithmetic.
- Wind the rope onto a spool neatly. A rope that piles up on itself changes the effective spool radius as it winds, so the lift speed drifts through the run.
Why it matters
Cranes, lifts, sailing boats, gym machines and window blinds all count ropes for a living. The counterweight on a lift is a pulley system; so is the tackle a single person uses to raise an engine out of a car.
More mechanics tutorials
- Mechanisms without motors — How to investigate a build with no electronics in it, and where each idea lives.
- Gearing up and gearing down — Trade turns for force, or force for turns — you cannot have both.
- Changing the direction of a turn — Reverse a turn, restore it with an idler, or send it round a 90° corner.
- Levers — effort, load and pivot — Where the pivot sits decides the force you need and the distance you get.
- Elastic and stored energy — Stretch a band, store energy, let it go — and find where more stops helping.
- Scissor mechanisms — Crossed links that extend and retract, and why the last bit is the hardest.
- Oscillatory motion — Turning a rotation into a back-and-forth, and what sets the rhythm.
- Centre of gravity — Why a robot tips, and how to build one that does not.
- Biomimetic mechanisms — Linkages that copy how animals move — turning a rotation into a step.