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¨ucker embedding. These results are valid in arbitrary dimension. The three dimensional case is also relevant in robotics.
Borcea, Ciprian and Streinu, Ileana, "Singularities of Hinge Structures" (2008). Faculty Publications. Paper 12.