Automated Generation of Kempe Linkageand Its Complexity

It is a famous result of Kempe that a lillkage can be designed togenerate any given plane algebraic curve. In this paper, Kempe's result is improvedto give a precise algorithm for generating Kempe linkage. We proved that for analgebraic plane curve of degree n, Kempe linkage uses at most O(n4) links. Effortsto implement a program which may generate Kempe linkage and simulation of thegeneration process of the plane curves are presellted in the paper.