We study body-and-hinge and panel-and-hinge chains in Rd , 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.
extremal configuration, Morse-Bott function, Hessian matrix, hinge structure, maximum reach, revolute-jointed manipulator
Borcea, Ciprian and Streinu, Ileana, "Extremal Configurations of Hinge Structures" (2008). Computer Science: Faculty Publications, Smith College, Northampton, MA.