Mechanism creation in tensegrity structures by cellular morphogenesis
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O R I G I NA L PA P E R
Omar Aloui · Landolf Rhode-Barbarigos
Mechanism creation in tensegrity structures by cellular morphogenesis
Received: 20 March 2020 / Revised: 12 August 2020 / Accepted: 15 August 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
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.
1 Introduction Structures are typically designed based on a specific geometrical configuration. Structures that are geometrically changeable are under constrained systems that do not possess a unique geometric configuration; they can move by finite displacements without generating deformations of the structural members. Such displacements reflect finite mechanisms. There are cases where kinematically indeterminate structures can admit certain degenerate configurations where their mobility can be constrained by pre-stress. In these cases, second-order and higherorder deformations are introduced in the structural elements when the mechanism is activated. Karnovsky and Lebed refer to such structures as instantaneously rigid structures [1]. Conversely, there are geometrically unchangeable structures that can admit degenerate configurations that eliminate first-order deformations in their structural members for a given set of infinitesimal displacements of their nodes. These structures are referred to as instantaneously changeable structures [1]. Investigations of the analytical statics and kinematics of systems with different forms of structural mobility started at the turn of the nineteenth century with the works of Maxwe
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