History of the Epitrochoid

Albrecht Duerer first described the epitrochoid in 1525. Duerer mentioned the curve in his book, "Instruction in Measurement with Compass and Straight Edge." He called the curve 'spider lines' because he thought the curve resembled an arachnid.

In his work with gear teeth, Ole Roemer studied the epitrochoid in 1674. Many other mathematicians have studied the curve, including Leibniz, Newton, La Hire, Desargues, and L'Hopital.

Uses of the Epitrochoid
The Wankel Rotary Engine
The Wankel Rotary Engine was developed in the 1920s by Felix Wankel. Initially developed as an air compressor, the engine is now used in automobiles. The rotor is an equilateral triangle with curved sides, and the bore is an epitrochoid curve. The measurements of all parts must be precise, because all epitrochoid curves would obviously not work as car engines.

The Spirograph
Almost everybody remembers drawing pictures with a Spirograph when they were young. The Spirograph is based on the roulette curves, the hypocycloid, the hypotrochoid, the epicycloid, and the epitrochoid. The intriguing pictures drawn with a spirograph can also be drawn with parametric equations on a coordinate grid.

Special Cases