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Elementary proofs of Kempe universality

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>1/05/2017
<mark>Journal</mark>Mathematical Proceedings of the Royal Irish Academy
Issue number1
Volume117A
Number of pages15
Pages (from-to)23-37
Publication StatusPublished
<mark>Original language</mark>English

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.