Position Analysis of Planar Tensegrity Structures

摘要

Tensegrity is an abbreviation of tension and integrity. Tensegrity structures are spatial structures formed by a combination of rigid elements in compression (struts) and connecting elements that are in tension (ties). In three-dimensional tensegrity structures no pair of struts touches, and the end of each strut is connected to non-coplanar ties, which are in tension. In two- dimensional tensegrity structures, struts still do not touch. A tensegrity structure stands by itself in its equilibrium position and maintains its form solely because of the arrangement of its struts and ties. The potential energy of the system stored in the springs is at a minimum in the equilibrium position when no external force or torque is applied. A closed-form solution of a two- spring, three-spring, and fourspring planar tensegrity mechanism was developed to determine all possible equilibrium configurations when no external force or moment is applied. Here closed form means that all solution equilibrium poses will be determined, although for each case a high-degree polynomial will have to be solved numerically.