Singularities of Hinge Structures
Differential Geometry
2008-12-09 v1
Abstract
Motivated by the hinge structure present in protein chains and other molecular conformations, we study the singularities of certain maps associated to body-and-hinge and panel-and-hinge chains. These are sequentially articulated systems where two consecutive rigid pieces are connected by a hinge, that is, a codimension two axis. The singularities, or critical points, correspond to a dimensional drop in the linear span of the axes, regarded as points on a Grassmann variety in its Pl\"{u}cker embedding. These results are valid in arbitrary dimension. The three dimensional case is also relevant in robotics.
Cite
@article{arxiv.0812.1373,
title = {Singularities of Hinge Structures},
author = {Ciprian S. Borcea and Ileana Streinu},
journal= {arXiv preprint arXiv:0812.1373},
year = {2008}
}