Superelastic tensegrities: Matrix formulation and antagonistic actuation

Superelastic tensegrity systems are prestressed structures composed by bars and cables in which some cables are realized with superelastic shape-memory alloys. These systems combine the peculiar features of tensegrity structures with those of shape-memory alloys and are particularly suitable for adaptive and variable-geometry systems. The main goal of this work is the design of systems with antagonistic actuation, that is to say, systems where two sets of superelastic cables can be actuated against each other in a reversible way. Superelasticity is here exploited to improve the stability of systems withstanding external loads. We show that the evolution of superelastic tensegrities, subjected to load and temperature changes, is described by a system of ordinary differential equations written in matrix form, a system that we solve by standard numerical routines. We then focus on a particular class of tensegrities and state a basic design criterion for an effective antagonistic actuation. Several case studies are presented. In particular, we applied our procedure to analyze different modules that can be assembled together in larger structures. Results show that the proposed procedure is able to replicate experimental data reasonably well and that it can be used to design complex systems in three-dimensions