Mathematica package PlanarLinkages.m. 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.
References in zbMATH (referenced in 1 article )
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- Gallet, Matteo; Koutschan, Christoph; Li, Zijia; Regensburger, Georg; Schicho, Josef; Villamizar, Nelly: Planar linkages following a prescribed motion (2017)