Gear Train

Trade speed for torque: a small gear driving a big one turns slower but stronger. Chain several pairs on shared shafts for big reductions, and watch the train turn.

Machine elementsGearsTorque

Inputs

Input examples

Write each gear pair as driver:driven teeth, separated by commas. Every driven gear shares its shaft with the next driver (a compound train).

Gear pairs (driver:driven teeth)

Input speed

Input torque

Efficiency per gear pair (%) — spur gears: 97–99%

Speed or Strength

Where two gears mesh, their teeth move at the same speed. A gear with three times as many teeth therefore turns three times slower — and, because the power stays (almost) the same, with three times the torque. Every meshing pair also reverses the direction of rotation.

For large reductions, gears are stacked: the big gear of one pair sits on the same shaft as the small gear of the next, and the ratios multiply. A winch, a clock or a car gearbox works this way. Each mesh loses a little power to friction, typically 1–3%.

ratioteeth driven / driver

× itorque up, speed down

pairsratios multiply

each meshreverses direction

The Gear Train

turning

the line on each gear shows its turning; the input turns at a fixed, slow display speed

Result

Enter the values above

Key Relations

Gear Ratio

Multiply driven over driver teeth for every pair in the train.

Example:

Speed and Torque

Power is speed times torque; it is kept apart from the losses, η per pair.

Example:

Power

With n in rpm and T in N·m this gives watts.

Sources & Verification

References

R. G. Budynas & J. K. Nisbett, Shigley’s Mechanical Engineering Design, 10th ed., McGraw-Hill, 2015 — Ch. 13 (Gears—General).