Motion polynomials and planar linkages

Abstract

We present the Mathematica package PlanarLinkages, which provides commands for constructing and visualizing planar linkages that draw a prescribed algebraic curve of genus 0, or more generally, that follow a prescribed rational motion. Since the implemented algorithms are heavily based on the concept of motion polynomials, the functionality of the package also includes basic arithmetic of motion polynomials and a factorization procedure.