Planar Linkages Following a Prescribed Motion
Symbolic Computation
2016-10-19 v2 Computational Geometry
Robotics
Algebraic Geometry
Rings and Algebras
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.
Keywords
Cite
@article{arxiv.1502.05623,
title = {Planar Linkages Following a Prescribed Motion},
author = {Matteo Gallet and Christoph Koutschan and Zijia Li and Georg Regensburger and Josef Schicho and Nelly Villamizar},
journal= {arXiv preprint arXiv:1502.05623},
year = {2016}
}
Comments
33 pages, 12 figures