Form-Finding Of Spherical Tensegrity Structures

The concept of tensegrity systems, which came from the natural principle of continuous tension and isolated compression, was originally proposed in 1950"s. Nowadays, tensegrity systems have drawn extensive attention from researchers all over the world.Firstly, the author reviews the history and presents the state-of-the-art of the tensegrity systems. Their structural characteristics are also summarized. Based on the geometry of polyhedron, the relationship between the polyhedron and elementary tesegrityies are discussed. Then, the main research interest is focused on the morphology configurations and the form finding of spherical tensegrities.Based on the geometric characteristics of spherical tensegrities, it is discovered that polyhedra with "valence 3"1 or "valence 4" vertices can be exploited to generate various kinds of spherical tensegrity, but the only obstacle is the very limited amount of regular polyhedra. To break this limitation, the geodesic polyhedra are introduced by geodesic subdivisions, which solve the transformation from Platonic polyhedra to geodesic polyhedra. One important feature of these geodesic polyhedra is that most of their vertices belong to "valence 6" type, which is then transformend to the "valence 3" or "valence 4" type by deleting certain edges of its subtriangles. After that, the wanted spherical tensegrities could be generated. The whole process can be summarized as Platonic polyhedron→Geodesic polyhedron→Spherical tensegrity.Further research reveals that the above method can solve the form-finding of one type of tensegrities, but not sufficient to sovle the form-finding of the other two types, due to the slight drift of their vertices. Thus, a unified mathematical model is established on the principle of tendon system minima, which transforms the form-finding problem into a mathematical problem of seeking minimum subject to constraints. The author also makes realistic models to verify the feasibility of the above method and how to make these models are summarized.Lastly, based on the summary of this paper, the future research work is proposed.