A new approach to the analytical and numerical form-finding of tensegrity structures

•A new formulation for the form-finding of tensegrity structures is developed.•The new formulation is the natural counterpart of the force density formulation.•Both an analytical and a numerical implementation of the formulation are described.•The numerical method needs a random set of force densities, and converges quickly.•A symmetric geometry for a symmetric tensegrity can be obtained directly.

We develop a new formulation for the form-finding of tensegrity structures in which the primary variables are the Cartesian components of element lengths. Both an analytical and a numerical implementation of the formulation are described; each require a description of the connectivity of the tensegrity, with the iterative numerical method also requiring a random starting vector of member force densities. The analytical and numerical form-finding of tensegrity structures is demonstrated through six examples, and the results obtained are compared and contrasted with those available in the literature to verify the accuracy and viability of the suggested methods.