How Gears Work
Geometry & Trigonometry
Understanding gear systems in bicycles, cars, and machinery
Introduction
Gears are fundamental components in countless machines - from bicycle gear systems to car transmissions to industrial equipment. When two gears mesh together, they transfer motion and force between rotating shafts. A key principle is that smaller gears rotate faster than larger ones when connected, while larger gears can multiply force. The relationship is inversely proportional: if one gear has twice as many teeth as another, it rotates at half the speed but with twice the torque. This exploration examines how gear ratios work, how compound gear systems multiply effects, and how engineers design gear systems for specific purposes.
Guiding Questions
- Count the teeth on two meshing gears. How do their rotation speeds relate?
- For a real bicycle, compute the distance travelled per pedal turn in each gear.
- Why do gear ratios on a cassette form a roughly geometric sequence? Check with real data.
- Design a gear range for a chosen rider and hill. Justify your ratios mathematically.