How do mechanical gears work?

The Law of Gears:
A primary requirement of gears is the constancy of angular velocities or proportionality of position transmission. High-speed gear trains also require transmission at constant angular velocities. Constant velocity is the 'conjugate action' of the gear tooth profile. A common normal to the tooth profiles at their point of contact must pass through a fixed point on the line of centers called the pitch point. Any two profiles engaging each other and satisfying the law of gearing are conjugate curves.