Gears and gear ratios
What you’ll learn
- What gears do: change speed, torque and direction
- How to calculate a gear ratio
- Common gear types: spur, worm, rack and pinion, bevel
Speed versus torque
Torque is turning force: how hard something twists. Motors spin fast but weakly. Gears let you trade speed for torque.
- Small gear drives a big gear: the output turns slower but with more torque (good for lifting and pushing).
- Big gear drives a small gear: the output turns faster with less torque.
- Two meshing gears turn in opposite directions.
Gear ratio
Gear ratio = teeth on the driven (output) gear ÷ teeth on the driving (input) gear
A 12-tooth gear driving a 36-tooth gear: 36 ÷ 12 = 3:1.
- Output speed = input speed ÷ 3
- Output torque ≈ input torque × 3 (a little less in real life because of friction)
Compound gear trains put two gears on one shaft. Their ratios multiply: 3:1 then 3:1 gives 9:1. That’s how the small yellow “TT” gear motors in robot kits turn a fast motor into slow, strong wheel turns (around 48:1).
Gear types
| Type | What it does | Seen in |
|---|---|---|
| Spur | Straight teeth, parallel shafts | Gearboxes, LEGO |
| Worm | A screw driving a gear: huge ratio (one turn of the worm moves the gear one tooth) and usually can’t be driven backwards | Lifts, arm joints that must hold position |
| Rack and pinion | Turns rotation into straight-line motion | Steering, linear actuators |
| Bevel | Turns the motion through 90° | Hand drills, differentials |
Example: a lifting arm
A motor spins at 6,000 rpm but is too weak to lift an arm. A gearbox with stages of 5:1, 4:1 and 5:1 gives 5 × 4 × 5 = 100:1. Output: 60 rpm with about 100 times the torque (minus friction losses).
Example: a fast spinner
A 40-tooth gear drives an 8-tooth gear: ratio = 8 ÷ 40 = 1:5. The output spins five times faster but with one fifth of the torque, which is good for a fan, not for a robot climbing a ramp.
Example: LEGO gears
| Driver | Driven | Ratio | Effect |
|---|---|---|---|
| 8T | 24T | 3:1 | 3× slower, stronger |
| 24T | 8T | 1:3 | 3× faster, weaker |
| 8T | 40T | 5:1 | 5× slower, stronger |
| worm | 24T | 24:1 | Very slow, very strong, holds position |
Calculate the ratioEasy
A 10-tooth gear drives a 50-tooth gear. What’s the ratio, and is the output faster or slower? 50 ÷ 10 = 5:1. Five times slower, about five times more torque.
Compound trainMedium
Two stages: 12T → 36T, then 10T → 40T on the next shaft. What’s the overall ratio? If the motor turns at 1,200 rpm, how fast is the output? 3:1 × 4:1 = 12:1. 1,200 ÷ 12 = 100 rpm.
Design for a rampHard
Your robot can’t climb a ramp: the wheels stall. You can’t change the motor. What do you change, and what’s the downside? Use a higher gear ratio (e.g. 48:1 instead of 20:1) or smaller wheels. You gain torque, but the robot gets slower on flat ground.
Quick check
Finished this lesson?