Invented by Girolamo Cardano in the 16th century the Cardan gear is a way of converting rotary motion into straight line motion. Watch how the red dot on the inner purple gear exactly follows the vertical dotted line.
The outer gear has a diameter exactly twice as large as the inner gear. In the above example they have 40 and 20 teeth respectively.

Cardano also invented a type of universal joint and investigated the mathematics of probability. Understanding the mathematics of risk helped him make a living from gambling until eventually he could find no-one to gamble with and had to move onto new pastures...