Linking (n - 2)-dimensional panels in n-space II: (n - 2, 2)-frameworks and body and hinge structures

Abstract

An (n - 1, 2)-framework in n-space is a structure consisting of a finite set of (n - 2)-dimensional panels and a set of rigid bars each joining a pair of panels using ball joints. A body and hinge (or (n + 1, n - 1)-) framework in n-space consists of a finite set of n-dimensional bodies articulated by a set of (n - 2)-dimensional hinges, i.e., joints in 2-space, line hinges in 3-space, plane-hinges in 4-space, etc. In this paper we characterize the graphs of all rigid (n - 1, 2)- and (n + 1, n - 1)-frameworks in n-space. Rigidity here is statical rigidity or equivalently infinitesimal rigidity. © 1989 Springer-Verlag.