Article

# CLOSED-FORM EQUILIBRIUM ANALYSIS OF A PLANAR TENSEGRITY STRUCTURE

01/2004; DOI: 10.1115/DETC2007-34249

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**ABSTRACT:**This paper proposes and demonstrates a symbolic procedure to compute the stiffness of truss structures built up from simple basic units. Geometrical design parameters enter in this computation. A set of equations linear in the degrees-of-freedom, but nonlinear in the design parameters, is solved symbolically in its entirety. The resulting expres-sions reveal the values of the design parameters which yield desirable properties for the stiffness or stiffness-to-mass ratio. By enumerating a set of topologies, including the number of basic units, and a set of material distribution models, stiffness properties are optimized over these sets. This procedure is applied to a planar tensegrity truss. The results make it possible to optimize the structure with respect to stiffness properties, not only by appropriately selecting (continuous) design parameters like geometric dimensions, but also by selecting an appropriate topology for the structure, e.g., the number of basic units, and a material distribution model, all of which are discrete design decisions.International Journal of Solids and Structures - INT J SOLIDS STRUCT. 09/2005; 43(5). - [Show abstract] [Hide abstract]

**ABSTRACT:**Tensegrity mechanisms are new type of mechanisms whose analysis is different from that of the conventional ones. This article chooses a six degree of freedom tensegrity mechanism with active compliant limbs and presents kinematic and static analysis of it. In this regard, two types of kinematic problems, the inverse and forward problems, are considered and solved. Also, this article shows that by using compliant components of tensegrity mechanism as active components, static balancing of the mechanism is achieved. This point can be considered as a new optimum approach for static balancing of the mechanisms by using tensegrity system concepts.Journal of Intelligent and Robotic Systems 71(3-4). · 0.83 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**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.07/2006;

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