Initial shape-finding and modal analyses of cyclic frustum tensegrity modules

Initial equilibrium and modal analyses of Kenneth Snelson's cyclic frustum tensegrity modules with an arbitrary number of stages are presented. There are m (⩾3) bars at each stage. The Maxwell number of the modules is 6−2 m and is independent of the number of stages in the axial direction. Calladine's relations reveals that there are 2−5 m infinitesimal mechanism modes. For multi-stage modules the necessary conditions for axial assembly of one-stage modules with the same internal element-forces are investigated. One-stage modules with geometrically similar frustum modules satisfy the necessary conditions. For pre-stressed configurations, modal analyses were conducted to investigate the mode shapes of infinitesimal mechanism modes.