Minimal mass optimization of tensegrity torsional structures

The advantage of high strength-to-mass ratio renders tensegrity structures suitable for application as lightweight structures. Therefore, the minimal mass optimization problem is one of the focal points in the research of tensegrity structures. Various minimal mass optimization configurations have been proposed for different types of loads. In this paper, we will continue this topic to deal with the minimal mass optimization problem of the tensegrity structure under torsional loads. The inspiration for this study stems from the constant radial angle feature of Michell structures, which is also present in the logarithmic spiral. By employing inverse stereographic projection with conformality, the logarithmic spiral can be mapped onto the sphere, the angle between the curve and the lines of latitude remains constant. On this basis, a type of tensegrity sphere structure combining the spherical logarithmic spiral and DHT (Double Helix Tensegrity) topology is proposed. Compared to the other two spheres with identical topology, the proposed tensegrity sphere structure significantly reduces the minimal mass under torsional loads. Furthermore, we have observed that when logarithmic spiral curves with opposite chirality are orthogonal, the optimal solution with minimal mass occurs. These findings demonstrate the potential of the combination of logarithmic spirals and conformal transformations, and positive effect of the orthogonal arrangement of members for mass optimization of tensegrity structures.