A gear train swaps rotational speed for torque in exact proportion to tooth count: two meshed gears turn at speeds inversely proportional to their number of teeth, because their pitch-circle edges must travel at the same linear (tangential) speed where the teeth engage. Torque scales the opposite way, so — ideally, with no friction — power in equals power out.
ω₂/ω₁ = N₁/N₂ (speed ratio, inverse to teeth)
T₂/T₁ = N₂/N₁ (torque ratio, direct to teeth)
P = T·ω (power is conserved end-to-end)
- Input speed — how fast the driver gear (N₁) is spun by the motor; every downstream gear's speed follows from the ratios above.
- Driver teeth N₁ / Driven teeth N₃ — the tooth counts of the first and last gear in the train set the overall reduction ratio N₃/N₁: fewer teeth on the driver and more on the driven gear means a bigger speed drop and a bigger torque gain.
- Idler gear — the middle gear meshes with both neighbours. It reverses direction twice (so input and output spin the same way) but its own tooth count cancels out of the overall ratio — a real mechanical-engineering fact this train is built to demonstrate.
- Load torque — the resisting torque applied at the output shaft; the diagram bar shows how much of the driver's available torque is consumed driving that load versus spare capacity.
Real-world relevance: this exact N₁/N₃ reduction is how a car's transmission, a power-drill gearbox, or a wind-turbine nacelle trades a fast, low-torque motor shaft for the slow, high-torque output a wheel or blade actually needs.