Automated Generation of Kempe Linkage and its Complexity

Abstract. It is a famous result of Kempe that we may design a linkage to generate any given plane algebraic curve. In this paper, Kempe’s result is improved to give a precise algorithm for generating Kempe’s linkage.. We also proved that for an algebraic plane curve of degree n, Kempe’s linkage uses at most O(n 4) links. We also report our efforts to implement a program which may generate the Kempe’s linkage and simulate the generation process of the plane curves. 1