Parametric Representations of Polynomial Curves Using Linkages

This paper shows the construction of linkages that draw parts of three well-known curves characterized by distances from points and lines: the lemniscate of Bernoulli, the Peaucellier-Lipkin linkage for a straight line, and Yates’ parabola. Basic algebra, geometry and trigonometry are used to find parametric representations of the loci of points in the system of linkages.