Kempe's Universality Theorem for Rational Space Curves
Computational Geometry
2018-07-31 v4 Robotics
Symbolic Computation
Algebraic Geometry
Rings and Algebras
Abstract
We prove that every bounded rational space curve of degree d and circularity c can be drawn by a linkage with 9/2 d - 6c + 1 revolute joints. Our proof is based on two ingredients. The first one is the factorization theory of motion polynomials. The second one is the construction of a motion polynomial of minimum degree with given orbit. Our proof also gives the explicity construction of the linkage.
Cite
@article{arxiv.1509.08690,
title = {Kempe's Universality Theorem for Rational Space Curves},
author = {Zijia Li and Josef Schicho and Hans-Peter Schröcker},
journal= {arXiv preprint arXiv:1509.08690},
year = {2018}
}
Comments
The final publication is available at Springer via http://dx.doi.org/10.1007/s10208-017-9348-x