Gearing up and gearing down
Two meshed gears are a bargain. Whatever one of them gains in turns it loses in force, and whatever it loses in turns it gains in force. There is no arrangement of gears that gives you more of both, and no amount of building will find one.
The ratio is the teeth
Count the teeth on the gear you are turning (the driver) and the teeth on the one being turned (the follower). That is the whole calculation:
turns out = turns in × driver teeth ÷ follower teeth
An 8-tooth gear driving a 24 gives ⅓ of a turn out for every turn in — and three times the turning force. Turn the pair round and you get three turns out and a third of the force. Count the turns yourself below.
The number of teeth is the whole story. 8 teeth driving 24 means 8 ÷ 24 of a turn out for every turn in — and the force changes by exactly the opposite amount.
Gearing down, gearing up
| Arrangement | Turns | Force | What it is for |
|---|---|---|---|
| Gearing down — small driving large | fewer | more | winches, lifts, robot arms, anything that has to move a weight |
| Gearing up — large driving small | more | less | fans, spinners, launchers, wheels on a light fast robot |
| 1 : 1 — same size | same | same | moving the drive to a different axle, or fixing a direction |
The names are worth getting right because they are backwards from what people expect: gearing down makes the output slower, not smaller, and it is the setting that makes a weak motor able to lift things.
Gear trains
Put several pairs in a row and the ratios multiply. Two 1:3 reductions in series give 1:9 — which is how a Medium Motor ends up able to raise something it could never shift directly. This is also how a gearbox with a sensible number of parts reaches a ratio that a single pair never could: a 40-tooth gear driven by an 8 is 1:5, and doing it twice is 1:25.
Only the first and last gear affect the ratio. Anything in the middle passes the motion along and changes nothing but the direction — which is a whole idea of its own, in Changing the direction of a turn.
What it costs
Every mesh loses a little to friction, so a long train is less efficient than a short one. Gearing down far enough to lift a heavy load also makes the mechanism slow, and slow is not always acceptable. And a gear train that is geared down hard is very hard to turn backwards by hand, which is either a useful brake or a nuisance depending on what you are building.
Why it matters
A bicycle is the same idea with a chain instead of teeth in mesh: the low gear that gets you up a hill is turning the back wheel slowly and pushing hard, and the high gear you use going downhill does the opposite. Cars, drills, cranes and clocks are all making the same trade.
More mechanics tutorials
- Mechanisms without motors — How to investigate a build with no electronics in it, and where each idea lives.
- Changing the direction of a turn — Reverse a turn, restore it with an idler, or send it round a 90° corner.
- Pulley systems — Fixed, movable and combined — how rope pulled trades against force needed.
- 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.