And Yet It Moves: Paradoxically Moving Linkages in Kinematics

2020/04/27 by Schicho, Josef · 1 citation
#53A17 #70B10 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2004.12635

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-Grübler-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.

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• Hypo-paradoxical Linkages: Linkages That Should Move-But Don't

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