Planar linkages following a prescribed motion

Gallet, Matteo; Koutschan, Christoph; Li, Zijia; Regensburger, Georg; Schicho, Josef; Villamizar, Nelly

doi:10.1090/mcom/3120

Planar linkages following a prescribed motion
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by Matteo Gallet, Christoph Koutschan, Zijia Li, Georg Regensburger, Josef Schicho and Nelly Villamizar;

Math. Comp. 86 (2017), 473-506

DOI: https://doi.org/10.1090/mcom/3120

Published electronically: April 13, 2016

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Abstract:

Designing mechanical devices, called linkages, that draw a given plane curve has been a topic that interested engineers and mathematicians for hundreds of years, and recently also computer scientists. Already in 1876, Kempe proposed a procedure for solving the problem in full generality, but his constructions tend to be extremely complicated. We provide a novel algorithm that produces much simpler linkages, but works only for parametric curves. Our approach is to transform the problem into a factorization task over some noncommutative algebra. We show how to compute such a factorization, and how to use it to construct a linkage tracing a given curve.

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