Elementary proofs of Kempe universality
arXiv:1511.09002
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 γ: [0,1] to R^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.
11 figures. New Abstract, some reordering of commentary, an improved separation translator component and minor corrections. This preprint accepted for publication in the Mathematical Proceedings of the Royal Irish Academy