And Yet It Moves: Paradoxically Moving Linkages in Kinematics
Metric Geometry
2020-04-28 v1
Abstract
The configuration space of a mechanical linkage, consisting of rigid bodies moving in space constrained by joints, is defined by algebraic conditions. If these equations do not define a complete intersection, then the dimension of the configuration space is higher than expected. These linkages violate the Chebychev-Gr\"ubler-Kutzbach formula for the degree of freedom of mobility. Mathematicians developed a variety of methods to describe and understand this phenomenon. This paper explains some of them.
Keywords
Cite
@article{arxiv.2004.12635,
title = {And Yet It Moves: Paradoxically Moving Linkages in Kinematics},
author = {Josef Schicho},
journal= {arXiv preprint arXiv:2004.12635},
year = {2020}
}
Comments
29 pages, 15 figures