English

Elementary proofs of Kempe universality

Metric Geometry 2017-04-27 v2

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 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.

Keywords

Cite

@article{arxiv.1511.09002,
  title  = {Elementary proofs of Kempe universality},
  author = {S. C. Power},
  journal= {arXiv preprint arXiv:1511.09002},
  year   = {2017}
}

Comments

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