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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


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