Enumeration-screening method for the design of simple polygonal tensegrities

Tensegrities, consisting of axially pre-compressed bars and pre-stretched strings, hold broad applications in the design of, for instance, architectures, soft robotics and metamaterials. In this paper, we propose an enumeration-screening method to design planar tensegrities of simple polygonal shapes. In such a polygonal tensegrity, the strings are joined pair-wise to form a simple polygon (a planar shape consisting of straight, non-intersecting line segments) and only one bar is added at each node. The total number of simple polygonal tensegrities designed by this scheme increases exponentially with the number of bars. Moreover, we demonstrate that each of these designed topologies can produce a self-equilibrated and stable tensegrity configuration. This work helps understand the topological features of simple polygonal tensegrities, which can be used as elementary cells to design some novel two- and three-dimensional tensegrity structures.