Giambattista Suardi's Machine for Drawing Plane Curves and other Instruments for Cycloids

Giambattista Suardi's “Geometric Pen” was an instrument based on wires and gears that can be used to draw a variety of curves generated by combining different rotary motions. Suardi described his machine in 1752 and explained that its mechanism was inspired by Ptolemaic theory. The instrument allowed him to draw many curves based on the combination of three basic parameters: the angular velocity of the wheels, the ratio of their radii or their number of teeth, and the possible directions of the motions. This article describes some of the complex mechanical artifices that Suardi used to draw curves, as well as correlations between Suardi's machine and some later instruments. His machine was probably a precursor of the “Spirograph,” a geometric drawing device that produces mathematical roulette curves as hypotrochoids and epitrochoids. The well-known toy version was developed by British engineer Denys Fisher, who exhibited his Spirograph at the Nuremberg International Toy Fair in 1965. The invention is often attributed to Abdank-Abakanowicz, the inventor and designer of integraphs, a mechanical device for plotting logarithmic spirals; I show here where the error comes from