Extremal Configurations of Hinge Structures

Details Extremal Configurations of Hinge Structures Extremal Configurations of Hinge Structures

2008-12-07

arxiv.org/abs/0812.1375v1

Mathematics

Differential Geometry

Scientific paper

We study body-and-hinge and panel-and-hinge chains in R^d, with two marked points: one on the first body, the other on the last. For a general chain, the squared distance between the marked points gives a Morse-Bott function on a torus configuration space. Maximal configurations, when the distance between the two marked points reaches a global maximum, have particularly simple geometrical characterizations. The three-dimensional case is relevant for applications to robotics and molecular structures.

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