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arXiv:1511.09002math.MG

Elementary proofs of Kempe universality

S. C. Power

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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 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.

arXiv 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
Journal reference
DOI
Subjects
math.MGMetric Geometry

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Discussed in comments1 thread

  1. Animation of the Cubic of Stationary Curvature of a Fourbar Linkage 1 comment

    • Anyone have recommendations for learning about mechanical linkages (books/MOOC/other)? Recently I've been intrigued by things like straight line linkages: https://en.wikipedia.org/wiki/Peaucellier%E2%80%93Lipkin_lin... ...and the Chebyshev "paradoxical" linkage…

      GregBuchholzView on HNParent context

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