Mechanism creation in tensegrity structures by cellular morphogenesis

Abstract

Tensegrity structures are self-equilibrated statically and kinematically indeterminate structures. Cellular morphogenesis represents a generative process for the composition of complex tensegrity structures based on elementary cells. This article discusses the mechanism creation by the integration of mobility conditions in the generation of tensegrity structures using cellular morphogenesis. The creation of finite and infinitesimal mechanisms in tensegrity structures is described by the adhesion of cells sharing less than d nodes (d being the dimension of the workspace) and by the fusion of cells with the removal of two edges. Parametric descriptions of the infinitesimal displacements in the case of trivial and finite mechanisms are derived by the analysis of rigid assemblies corresponding to the rigid parts of the structure. In addition, an interpretation of the degeneracy of tensegrity structures in the case of self-stressable mechanisms is also presented. Analytical solutions of the degeneracy space for configurations resulting from adhesion and the fusion of two cells with the removal of two edges are described using symbolic calculations on the rigidity matrices of tensegrity structures. Although the study focuses on selected configurations and arrangements, the generalization of the ideas and findings included in this paper can lead to the generation of tensegrity structures with predefined static as well as kinematic properties, thus further enabling the application of tensegrity systems in science and engineering.