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## Elementary proofs of Kempe universality

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### Standard

In: Mathematical Proceedings of the Royal Irish Academy, Vol. 117A, No. 1, 01.05.2017, p. 23-37.

Research output: Contribution to journalJournal articlepeer-review

### Harvard

Power, SC 2017, 'Elementary proofs of Kempe universality', Mathematical Proceedings of the Royal Irish Academy, vol. 117A, no. 1, pp. 23-37. https://doi.org/10.3318/pria.2017.117.04

### APA

Power, S. C. (2017). Elementary proofs of Kempe universality. Mathematical Proceedings of the Royal Irish Academy, 117A(1), 23-37. https://doi.org/10.3318/pria.2017.117.04

### Vancouver

Power SC. Elementary proofs of Kempe universality. Mathematical Proceedings of the Royal Irish Academy. 2017 May 1;117A(1):23-37. https://doi.org/10.3318/pria.2017.117.04

### Author

Power, Stephen Charles. / Elementary proofs of Kempe universality. In: Mathematical Proceedings of the Royal Irish Academy. 2017 ; Vol. 117A, No. 1. pp. 23-37.

### Bibtex

@article{7ac06920a1b14833aa04b2bb0a5b08ca,
title = "Elementary proofs of Kempe universality",
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.",
keywords = "Kempe universality, linkages, infinite bar-joint frameworks",
author = "Power, {Stephen Charles}",
year = "2017",
month = may,
day = "1",
doi = "10.3318/pria.2017.117.04",
language = "English",
volume = "117A",
pages = "23--37",
journal = "Mathematical Proceedings of the Royal Irish Academy",
issn = "1393-7197",
number = "1",

}

### RIS

TY - JOUR

T1 - Elementary proofs of Kempe universality

AU - Power, Stephen Charles

PY - 2017/5/1

Y1 - 2017/5/1

N2 - 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.

AB - 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.

KW - Kempe universality, linkages, infinite bar-joint frameworks

U2 - 10.3318/pria.2017.117.04

DO - 10.3318/pria.2017.117.04

M3 - Journal article

VL - 117A

SP - 23

EP - 37

JO - Mathematical Proceedings of the Royal Irish Academy

JF - Mathematical Proceedings of the Royal Irish Academy

SN - 1393-7197

IS - 1

ER -