Gears: Trading Speed for Strength
A motor's speed is a currency, and the gearbox is the exchange booth: ten turns in, one turn out, tenfold the torque — minus a little friction, plus a little wobble called backlash.
Builds on: 1.1 DC Motors: Fast, Weak and Hungry
Same idea, other course:Vector: work and power, the currency itself
The exchange rate
Mesh a small gear with a big one and count teeth. A 10-tooth gear driving a 50-tooth gear must turn five times for one output turn — that is a gear ratio of 5:1. The output is five times slower and, in the ideal case, five times stronger:
This is why a bare DC motor — thousands of RPM, doorknob torque — becomes useful the moment a gearbox translates it: a 100:1 reduction turns 6000 RPM of whir into 60 RPM of confident shove. Power (speed × torque) is conserved through the box; only its shape changes. Nothing is free: each meshing stage eats a few percent to friction.
Backlash: the space between the teeth
Meshed teeth need a whisker of clearance to roll without jamming — and that whisker is backlash: reverse the input and the output stands still for a moment while the teeth cross the gap. For wheels, harmless. For a robot arm reversing direction at a target, it is a dead zone where the joint ignores you — and no controller downstream can fully undo a lie in the mechanism itself.
The fixes are mechanical and priced accordingly: tighter gears, split anti-backlash gears, belt drives (the belt’s tension takes up the slack), or the exotic gearboxes in industrial arm joints — engineered specifically to make the gap tiny.
Sizing a drivetrain, roughly
The bench-top recipe: find the torque the task needs (weight × lever arm, then double it for margin), find your motor’s comfortable torque, and gear down by the ratio between them. Speed is what remains — if the geared-down speed is too slow for the job, the motor is too small, and no ratio will save it.
Big, slow, gearless motors exist — and where budgets allow, they are glorious: zero backlash, perfect back-drivability, silent. Their price and weight are why the rest of the world runs on small fast motors plus gears. Every drivetrain is this same trade, settled at a different budget.
⚗️ Lab — The Exchange Booth
A motor, a two-gear train with an adjustable ratio, and a load to lift. Meters for speed, torque and what the friction fee cost you.
- Raise the ratio and watch the output slow while its torque multiplies — the load that stalled at 1:1 lifts easily at 20:1.
- Reverse the motor and watch the output hesitate — the backlash gap, in slow motion. Tighten it and see the dead zone shrink.
- Find the smallest ratio that lifts the heavy load. Note what happened to your lifting speed.
Work it by hand — 0 / 2
No multiple choice here: compute the value and type it. Suffixes like 2.5k or 20m are understood; answers within ±2% count.