Planar Tensegrity Structure Research Articles

A metaheuristic‐based method for analysis of tensegrity structures

SummaryTensegrity systems are construction system that offers solutions for lighter designs compared with a standard truss system consisting of tension and compression elements. Due to their structure, they are recommended in the design of space structures due to the use of lighter and easy‐to‐assemble structural elements such as cables, ropes, and similar to provide the desired durability. In this study, energy minimization was carried out to solve the structural element displacements. It is expected to reduce the total potential energy of the system with minimization. By minimizing the total potential energy of the tensegrity system models, the displacement of each building element is found for the equilibrium condition. Tensegrity models were analyzed by minimizing energy via the adaptive harmony search (AHS) algorithm. In this research, two distinct tensegrity structure specimens were employed. One comprised a cantilever beam, while the other adopted a cyclic model, forming eight equal octagons from eight nodes at both the base and the top. Additionally, an examination was conducted on a two‐layer iteration of the cyclic model. The method is robust for both space and planar tensegrity structures, allowing the determination of deformed shapes under various loads without design assumptions. The TPO/MA method demonstrates superiority in handling nonlinear and barely stable systems, as evidenced by examples illustrating its efficacy in maintaining structural form under increasing loads and challenging conditions.

Optimal self-stress determination of tensegrity structures

In traditional methods for self-stress determination of a tensegrity structure, member grouping, which highly relies on geometric simplicity of the structure, is a key component. For this reason, these methods are not efficient to handle complex or irregular tensegrity structures. In addition, most of optimization algorithms used in traditional methods are based on gradients. Therefore, exponential increase of computational effort is inevitable for self-stress determination of large-scale tensegrity structures. To resolve those issues, a new method called the stochastic fixed nodal position method is developed for self-stress determination of tensegrity structures. This method utilizes a derivative-free stochastic algorithm in numerical optimization with the starting point being obtained by solving a linear system of equations, so that the computation cost is reduced, and member grouping is no longer required. The proposed method is suitable for large-scale, complex, and irregular tensegrity structures. The proposed method is applied to self-stress determination of a planar tensegrity structure, a spatial four-way tensegrity grid, and an irregular tensegrity structure in the simulation. Results show that the proposed method can handle both regular and irregular tensegrity structures, and has a low computational cost, a super linear rate of convergence, and high accuracy.

Closed-Form Solutions for the Form-Finding of Regular Tensegrity Structures by Group Elements

An analytical form-finding method for regular tensegrity structures based on the concept of force density is presented. The self-equilibrated state can be deduced linearly in terms of force densities, and then we apply eigenvalue decomposition to the force density matrix to calculate its eigenvalues. The eigenvalues are enforced to satisfy the non-degeneracy condition to fulfill the self-equilibrium condition. So the relationship between force densities can also be obtained, which is followed by the super-stability examination. The method has been developed to deal with planar tensegrity structure, prismatic tensegrity structure (triangular prism, quadrangular prism, and pentagonal prism) and star-shaped tensegrity structure by group elements to get closed-form solutions in terms of force densities, which satisfies the super stable conditions.

Generation of planar tensegrity structures through cellular multiplication

Tensegrity structures are frameworks in a stable self-equilibrated prestress state that have been applied in various fields in science and engineering. Research into tensegrity structures has resulted in reliable techniques for their form finding and analysis. However, most techniques address topology and form separately. This paper presents a bio-inspired approach for the combined topology identification and form finding of planar tensegrity structures. Tensegrity structures are generated using tensegrity cells (elementary stable self-stressed units that have been proven to compose any tensegrity structure) according to two multiplication mechanisms: cellular adhesion and fusion. Changes in the dimension of the self-stress space of the structure are found to depend on the number of adhesion and fusion steps conducted as well as on the interaction among the cells composing the system. A methodology for defining a basis of the self-stress space is also provided. Through the definition of the equilibrium shape, the number of nodes and members as well as the number of self-stress states, the cellular multiplication method can integrate design considerations, providing great flexibility and control over the tensegrity structure designed and opening the door to the development of a whole new realm of planar tensegrity systems with controllable characteristics.

Compliant multistable tensegrity structures

In this paper, a method to identify compliant tensegrity structures with multiple states of self-equilibrium is described. The considered algorithm is based on the repeated use of a form-finding procedure, using the static Finite-Element-Method. The algorithm can be used in the development process of compliant multistable tensegrity structures with simple topologies, consisting of only few members. As examples four planar tensegrity structures with two or three stable equilibrium configurations are considered and verified experimentally. Furthermore, a specific kind of multistable tensegrity structures, which have identical convex hulls, but differing prestressed states in their equilibrium configurations, is investigated. The potential technical use of the considered structures is discussed in the context of shape-changing locomotion systems using transitions between their equilibrium configurations.

An approach to the dynamics and control of a planar tensegrity structure with application in locomotion systems

The use of mechanically compliant tensegrity structures in vibration-driven mobile robots is an attractive research topic, due to the principal possibility to adjust their dynamic properties reversibly during locomotion. In this paper vibration driven planar locomotion of mobile robots, based on a simple tensegrity structure, consisting of two rigid disconnected compressed members connected to a continuous net of four prestressed tensional members with pronounced elasticity, is discussed. The dynamic behaviour of the considered system is nonlinear, due to large vibration amplitudes and friction between robot and environment, and is mainly influenced by the magnitude of prestress. Therefore, the movement performance of the robot can be essentially influenced by the actuation parameters, e.g. by modifying the frequency or the magnitude of actuation the locomotion direction of the system varies. To study the system behaviour, the nonlinear equations of motion are derived and transient dynamic analyses are performed, including the consideration of chaotic system behaviour near to the primary and secondary eigenfrequencies. The dependency of the movement behaviour on the actuation parameters and on the prestress are discussed focused on single-actuated systems with minimal control effort.

A Form-finding of Planar Tensegrity Structures

A form-finding procedure is presented for planar tensegrity structures. Notably, a simple decision criteria is proposed to select the desirable candidate position vector from the unitary matrix produced by the eigenvalue decomposition of force density matrix. The soundness of the candidate position vector guarantees faster convergence and produces a desirable form of tensegrity without any member having zero-length. Several numerical examples are provided to demonstrate the capability of the proposed form-finding process.

Input-output selection for planar tensegrity models

The input-output selection approach followed in this brief uses a rigorous and systematic procedure, efficiently selecting actuators and/or sensors that guarantee a desired level of performance, embedded in a heuristic. The procedure generates all so-called minimal dependent sets and uses a closed-loop criterion. The heuristic is a divide-and-conquer one. This approach is applied to controlled tensegrity structures, using as criterion efficiently computable conditions for the existence of a stabilizing H/sub /spl infin// controller achieving a desired level of performance. Structural systems, like controlled tensegrities, are a prime example for application of techniques that address system design issues, because they present opportunities in choosing actuators/sensors and in choosing their mechanical structure. Results for a three-unit planar tensegrity structure, where all 26 tendons can be used as actuator or sensor devices, making up 52 devices from which to choose, demonstrate the approach. Two design specifications were explored, one is related to the dynamical stiffness of the structure, the other to vibration isolation. The feasible sets of actuators and sensors depend on the specifications and really differ for both, but are mostly composed of much less than 52 devices.

Symbolic Stiffness Optimization of Planar Tensegrity Structures

During the design of mechanical systems one normally exploits numerical analysis and optimization tools. We make a plea for symbolic computation and give an example where structural displacements under load are computed symbolically. Geometrical design parameters enter in this computation. The set of equilibrium conditions, linear in the displacements, but nonlinear in the design parameters, is solved symbolically. The resulting expressions reveal the geometry which yield optimal properties for stiffness or stiffnessto-mass. This technique is applied to a class of repetitive mechanical systems, namely tensegrity structures. A large scale example with 1533 degrees-of-freedom is computed successfully. The results make it possible to optimize the structure with respect to stiffness properties, not only by appropriately selecting (continuous) design parameters, influencing geometry, but also by selecting the number of stages used to build up the structure (a discrete design parameter), influencing topology.