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In this paper, we define a general class of tensegrity structures consisting of both compression members (ie bars) and tensile members (ie cables). For a given number N of bars, we define the topological structure which is necessary to establish a tensegrity. Necessary and sufficient conditions for prestress mechanical equilibria of the tensegrity are then provided in terms of a nonlinear function of the position and orientation of the bars, and the initial lengths of the cables.doi:10.2514/2.5119 fatcat:zzlpmgvdkbenxi2lmbzzms7q2a