Gear Ratio

Meshing teeth must pass the same point at the same rate, so a 20-tooth driver turning a 60-tooth gear gives GR = 3: the output turns a third as fast and, ideally, with three times the torque. Any ratio above 1 is a reduction (more torque, less speed); below 1 is an overdrive. The Antikythera mechanism, built around 100 BC and recovered from a Greek shipwreck in 1901, already used more than 30 bronze gears — including a 223-tooth wheel — to predict eclipses, an achievement not matched in Europe for another 1,400 years.

Because power is torque times angular speed and gears conserve power apart from a percent or two of tooth friction, whatever you gain in torque you lose in speed. Chain a second pair in series and the ratios multiply, which is how a three-stage industrial reducer reaches 100:1 in a compact housing. Watch the convention: automotive and bicycle literature sometimes quotes the reciprocal, so always state which count is the driver.