Elementary proofs of Kempe universality

Power, Stephen Charles (2017) Elementary proofs of Kempe universality. Mathematical Proceedings of the Royal Irish Academy, 117A (1). pp. 23-37. ISSN 1393-7197

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Abstract

An elementary proof is given to show that a parametrised algebraic curve in the plane may be traced out, in the sense of A. B. Kempe, by a finite pinned linkage. Additionally it is shown that any parametrised continuous curve $\gamma:[0,1]\to \bR^2$ may be traced out by an infinite linkage where the valencies of the joints is uniformly bounded. We also discuss related Kempe universality theorems and give a novel correction of Kempe's original argument.