Peaucellier cell | Peaucellier's linkage

A linkage with six rods which draws the inverse of a given curve. When a pencil is placed at P, the inverse is drawn at P' (or vice versa). If a seventh rod (dashed) is added (with an additional pivot), P is kept on a circle and the locus traced out by P' is a straight line. It therefore converts circular motion to linear motion without sliding, and was discovered in 1864. Another linkage which performs this feat using hinged squares had been published by Sarrus in 1853 but ignored. Coxeter shows that O P×O P' = O A^2 - P A^2.