Review of Form-Finding Methods for Tensegrity Structures

Abstract

Seven form-finding methods for tensegrity structures are reviewed and classified. The three kinematical methods include an analytical approach, a non-linear optimisation, and a pseudo-dynamic iteration. The four statical methods include an analytical method, the formulation of linear equations of equilibrium in terms of force densities, an energy minimisation, and a search for the equilibrium configurations of the struts of the structure connected by cables whose lengths are to be determined, using a reduced set of equilibrium equations. It is concluded that the kinematical methods are best suited to obtaining only configuration details of structures that are already essentially known. The force density method is best suited to searching for new configurations, but affords no control over the lengths of the elements of the structure. The reduced coordinates method offers a greater control on elements lengths, but requires more extensive symbolic manipulations.

Tensegrity frameworks: Static analysis review

“…Tibert and Pellegrino [76] presented a survey on form-finding methods for tensegrity structures in which they classify all the previous methods into two categories: kinematical methods and statical methods. The former methods are characterized by increasing (decreasing) the length of the struts (cables) and keeping the length of the cables (struts) constant until a maximum (minimum) is reached.…”

Influence of Spring Characteristics on the Behavior of Tensegrity Mechanisms

“…The output variable y is obtained for a given value of ρ by solving the direct static problem. An energy method, as described in [10], is here considered. The mechanism configuration is then obtained by determining the local minimum of the potential energy U stored in the mechanism springs.…”

“…The determination of a mechanism configuration requires for instance to take into account joint variables and external loads while respecting self-equilibrium state conditions. The corresponding static model is obtained using so-called form finding methods [10]. Up to now, related works have been focused on the analysis of tensegrity mechanisms, but not yet on their synthesis.…”

Accurate Numerical Methods for Studying the Nonlinear Wave-Dynamics of Tensegrity Metamaterials

“…Tensegrity lattices consists of networks of prestressable truss structures, obtained by connecting compressive members (bars or struts) through pre-stretched tensile elements (cables or strings). Special attention is receiving the formulation of analytical and numerical procedures for the optimal design of such structures, due to both their easy control (geometry, size, topology and prestress control) [5,6], and the fact that such structures provide minimum mass systems under different loading conditions [5,7,8,9,10,11,12].…”