Mechanics of Tensegrity Prisms

Abstract

Tensegrity prisms are three-dimensional self-stressing cable systems with a relatively small number of disjoint compression members, invented by Buckminster Fuller. They form novel structural geometries and they constitute a class of mechanisms that have not been previously studied for possible application as variable geometry truss (VGT) manipulators. They have a number of seemingly advantageous properties -- they are self-erecting, in that tensioning the final cable transforms them from a compact group of members into a large three-dimensional volume, and they are predominately tension systems, in that they can function as a VGT manipulator while actuating members only In tension. These properties have not been explored but could be broadly useful, for applications ranging from temporary terrestrial construction to large on-orbit space structures. However, they have a number of properties that make them seemingly inappropriate for use -- they are not conventionally rigid, they exist only under specific conditions of geometry with a corresponding prestress state, and the governing equations that do exist include singular (non-invertible) matrices. In our opinion the advantages and application potential justify the study and discussion of tensegrity behavior. The mathematics of tensegrity geometry, statics, and kinematics have not been fully formulated, and such mathematical results must be developed and assembled before applications can be undertaken. This paper describes the physical behavior of a basic family of tensegrity prisms, presents the most useful available mathematical results, and outlines a preliminary simulation study of such a prism used as a VGT manipulator.