Article

# On Advances in Robot Kinematics

01/2004; DOI: 10.1115/DETC2007-34249

ABSTRACT

This paper presents a closed-form analysis of a two-spring planar tensegrity mechanism to determine all possible equilibrium configurations for the device when no external forces or moments are applied. The equilibrium position is determined by identifying the configurations at which the potential energy stored in the two springs is a minimum. A 28th degree polynomial expressed in terms of the length of one of the springs is developed where this polynomial identifies the cases where the change in potential energy with respect to a change in the spring length is zero. A numerical example is presented.

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• "They can be found in various applications including tensegrity systems [4] [5] [6], remote center compliance devices [7] for industrial robots, statically balanced devices [8] and so on. Numerous pieces of work have been done on the kinematics of traditional or rigid body Stewart-Gough platforms. "
##### Article: Classification and complete solution of the kinetostatics of a compliant Stewart–Gough platform
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ABSTRACT: This paper studies a compliant Stewart–Gough platform whose six flexible links balance external loads, including force and moment, applied to a general point at the platform. Soma coordinates are used to express the location of the moving plate with respect to the base plate. The mathematical modeling involves both the kinematics and the statics. Seven kinematic and six static constraints are obtained. Vector dot- and cross-products are also cast in quaternion form which reduces the degree of the resulting constraints. By classifying the parameters to the knowns and the unknowns, five major problem types are recognized. Four of them are mathematically decoupled and the remaining one is coupled for which the obtained 13 polynomials are of the total degree of 5,971,968 which to the authors' best of knowledge is the largest kinematic problem ever investigated. After solving the equations with the numerical polynomial solver Bertini, we conclude that the upper bound to the number of nonsingular solutions is 29,272. In addition, for practical problems a parameter continuation is devised to recompute for only 29,272 generically nonsingular solutions. At last a numerical example is provided to demonstrate the solution process.
Mechanism and Machine Theory 01/2011; 49. DOI:10.1016/j.mechmachtheory.2011.10.011 · 1.66 Impact Factor
• ##### Article: Kinematic and Static Analyses of Statically Balanced Spatial Tensegrity Mechanism with Active Compliant Components
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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 09/2012; 71(3-4). DOI:10.1007/s10846-012-9784-4 · 1.18 Impact Factor
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##### Article: Stiffness of planar tensegrity truss topologies
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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 09/2005; 43(5). DOI:10.1016/j.ijsolstr.2005.06.049 · 2.21 Impact Factor
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