Tensegrity frameworks: static analysis review

This paper hands in a review of the basic issues about the statics of tensegrity structures. Definitions and notation for the most important concepts, borrowed from the vast existing literature, are summarized. All of these concepts and definitions provide a complete mathematical framework to analyze the rigidity and stability properties of tensegrity structures from three different, but related, points of view: motions, forces and energy approaches. Several rigidity and stability definitions are presented in this paper and hierarchically ordered, from the strongest condition of infinitesimal rigidity to the more wide concept of simple rigidity, so extending some previous classifications already available. Important theorems regarding the relationship between these definitions are also put together to complete the static overview of tensegrity structures. Examples of different tensegrity structures belonging to each of the rigidity and stability ca\-tegories presented are described and analyzed. Concluding the static analysis of tensegrity structures, a review of existing form-finding methods is presented.This work was supported by projects: 'Estudio de estructuras tensegrity para el desarrollo de sensores manipuladores y robots móviles' (4798), 'Estudio y diseño de manipulador mecánico sobreactuado basado en estructuras tensigrity' (4801/Ref.CIT-020400-2007-78). This work has been partially supported by the projects CICyT DPI2006-14001 and PROFIT CIT-020400-2007-78 both financied by the Education and Science Ministry of the Spanish Government.Peer Reviewe