Kinematic Analysis of Tensegrity Structures

Tensegrity structures consist of isolated compression members (rigid bars) suspended by a continuous network of tension members (cables). Tensegrity structures can be used as variable geometry truss (VGT) mechanisms by actuating links to change their length. This paper will present a new method of position finding for tensegrity structures that can be used for actuation as VGT mechanisms. Tensegrity structures are difficult to understand and mathematically model. This difficulty is primarily because tensegrity structures only exist in specific stable tensegrity positions. Previous work has focused on analysis based on statics, dynamics, and virtual work approaches. This work considers tensegrity structures from a kinematic viewpoint. The kinematic approach leads to a better understanding of the conditions under which tensegrity structures exist in the stable positions. The primary understanding that comes from this kinematic analysis is that stable positions for tensegrity structures exist only on the boundaries of nonassembly of the structure. This understanding also allows the tensegrity positions to be easily found. This paper presents a method of position finding based on kinematic constraints and applies that method to several example tensegrity structures.