Linking (n − 2)-dimensional panels inn-space II: (n − 2, 2)-frameworks and body and hinge structures (original) (raw)

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.

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1. Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, 0511, Singapore
   Tiong-Seng Tay

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Tay, TS. Linking (n − 2)-dimensional panels in_n_-space II: (n − 2, 2)-frameworks and body and hinge structures.Graphs and Combinatorics 5, 245–273 (1989). https://doi.org/10.1007/BF01788678

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• Received: 27 November 1985
• Revised: 10 August 1987
• Issue date: December 1989
• DOI: https://doi.org/10.1007/BF01788678

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