Infinitesimal Mechanism Modes of Tensegrity Modules

Tensegrity structures, invented by Snelson in 1948, are a class of truss structures consisting of a continuous set of tension members and a discrete set of compression members [1, 2]. Ingber [3] stated that the assembly pattern of organic structures such as cells, tissues, organs, and animals are described by a universal building rule of self-assembly at different scales based upon geodesic tensegrity. Furthermore, animal mechanisms, including that of humans, do not include any pins or gears that are representative components of machine. Therefore, in order to develop smart deployable structures as well as understand the role of cytoskeleton in cell mechanotransduction, it is necessary to understand infinitesimal mechanism modes of tensegrity modules [4, 5, 6]. The objectives of the paper are to analytically find initial configurations and pre-stress modes for regular truncated octahedral and cubic tensegrity modules and to classify a large number of infinitesimal mechanism modes by conducting modal analyses. In what follows, the static and dynamic characterization procedure proposed by the authors is employed using the same notation as that of [7, 8].