Automatic construction of tensegrity structures with complex surfaces based on circle packing

Abstract

Tensegrities have attracted significant attention in many disciplines as a distinct type of truss network. However, with the increase in size and complexity, building complex tensegrities remains challenging. This study presents a systematic method to automatically construct large-scale tensegrity structures with complex surfaces by ingeniously combining circle packing. This method enables direct identification of the topology and configuration of tensegrities with specific shapes. First, circle packings on target surfaces are accomplished in a practical manner. On this basis, the triangulation connection is established as the basic assembly pattern, and its mobility is further analyzed using the screw theory to inspect the assembly rules. Then, the connection requirements of the elementary units are investigated, and a novel tensegrity torus is exemplarily utilized for assembly. To evaluate the tensegrity properties, the self-equilibrium and stability of the assembled structures are respectively examined. For illustration, four representative examples are produced to verify the effectiveness of the proposed method. In this study, an alternative method to automatically manufacture tensegrities satisfying the demands of both aesthetics and practicality is developed, which will significantly expand the application scenarios for tensegrity systems.