Planar linkages following a prescribed motion
Matteo Gallet,Christoph Koutschan,Zijia Li,Georg Regensburger,Josef Schicho,Nelly Villamizar +5 more
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TLDR
A novel algorithm is provided that produces much simpler linkages, but works only for parametric curves, and shows how to compute such a factorization, and how to use it to construct a linkage tracing a given curve.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.read more
Citations
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Journal ArticleDOI
Factorization of Motion Polynomials
TL;DR: The existence of a factorization of a monic, bounded motion polynomials, possibly after multiplication with a real polynomial, is considered and an affirmative answer for "bounded" motion polyno- mials is given.
Journal ArticleDOI
Factorization results for left polynomials in some associative real algebras: State of the art, applications, and open questions
TL;DR: In this article, the existence of factorizations with linear factors for polynomials over real involutive algebras is discussed. But they do not consider factorizations for non-division rings.
Journal ArticleDOI
Kempe’s Universality Theorem for Rational Space Curves
TL;DR: It is proved that every bounded rational space curve of degree d and circularity c can be drawn by a linkage with respect to revolute joints by means of the factorization theory of motion polynomials.
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Factorization Results for Left Polynomials in Some Associative Real Algebras: State of the Art, Applications, and Open Questions
TL;DR: The current state of the art of factorizations with linear factors for generic polynomials over division rings is explained, some new results are presented and examples and counter examples are provided.
Journal ArticleDOI
Reasoning about linkages with dynamic geometry
TL;DR: An on-going work on the crossroad of mechanical linkages, dynamic geometry and automated reasoning exemplifies how some automated reasoning tools based on symbolic computation and recently implemented in GeoGebra, can be used for linkage exploration.
References
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