Soft Tensegrity Systems for Planetary Landing and Exploration

The self-equilibrium problem of the Class-Theta tetrahedral tensegrity module

A reduced-order model for the dynamic and post-buckling behavior of tensegrity structures

Rather than the traditional vector differential equation, this paper introduces rigid body dynamics in a new form, as a matrix differential equation. We focus on axisymmetric rigid bodies which are adequate to describe a large class of problems, including tensegrity systems. For a system of beta rigid bodies, the forces are characterized in terms of network theory, and the kinematics are characterized in terms of the bar vectors (directed connections between two nodes attached to a rigid body). The dynamics are characterized by a second order differential equation in a 3 times 2beta configuration matrix. The first contribution of the paper is the dynamic model of a broad class of systems of rigid bodies, characterized in a compact form, requiring no inversion of a variable mass matrix. The second contribution is the derivation of all equilibria as a linear algebra problem in the control variables. The third contribution is the derivation of a linear model of the system of rigid bodies. One significance of these equations is the exact characterization of the statics and dynamics of all class 1 tensegrity structures, where rigid bar lengths are constant and the string force densities are control variables, which appear linearly. This will offer a significant advantage in control design tasks

This paper presents an overview of the previous research on the form finding structures which include tensegrity and biotensegrity structure. Tensegrity systems have been widely used for many applications due to the stability and flexibility of the structures. On technologies era nowadays, a stable structure is needed to implement for new developments especially robotics and machineries. Therefore, the importance of finding the shape or design configuration is to ensure it is in self-equilibrium which able to support itself. In order to build new structures which lies on general requirement, previous researchers have proposed several form-finding methods for instance by using force density method, advance force density method, finite element method, dynamic relaxation method, genetic algorithm, novel linear approach and Monte Carlo method. What kind of stable structures can be produced and how efficient the structures by using those methods? In this paper, understanding on the form-finding methods and various numerical examples of form-finding conducted in previous studies are presented to enhance researchers’ knowledge on the form-finding of tensegrity structures. Â

Since tensegrity systems are often topologically and geometrically complex it is important to have a simple and effective method to describe and classify them in an orderly manner. This paper sets forth a system of relating any convex polyhedron to a tensegrity by defining a one-to-one correspondence between the elements of the polyhedron and the elements of the tensegrity. This system, which was first introduced by the author in a 1978 booklet while working in Buckminster Fuller's Philadelphia office, is now extended to include agglomerations of convex polyhedra — both regular and irregular space-filling arrays. In both the original system and its extension, the principle of geometric duality is clearly demonstrated. More importantly for engineers, the method will allow those familiar with space structures an easy and convenient way to relate any space frame or truss to a corresponding tensegrity structure.

Background/Objectives: Sustainability in the use of material and economy are the watchwords of the modern engineering fraternity. Many structural systems have been evolved for this purpose. At present, the qualities of the tensegrity structures, which make the technology attractive for human use, are their resilience and ability to use the material in a very economical way. Thus, the construction of the structures using tensegrity principle will make them highly resilient and reasonably economical at the same time. Methods: Though a lot of research has been carried out on the behaviour of tensegrity systems, the area requires further research for a complete understanding. Hence, this project is aimed at analysis of a tensegrity based roof structure. The prototype module used is half-cuboctahedron. Findings: First, a single module measuring 1 m x 1 m in size, is modelled and analysed using an FEM based software. The investigations are then extended to a 2 x 2 grid, measuring 2 m x 2 m in size. The behavior of the grid is studied under the application of external loads varying the prestressing forces on the members. Later, a 4 x 4 grid, measuring 4 m x 4 m in size and an 8 x 8 grid, measuring 8 m x 8 m in size are modelled and analysed based on the 2 x 2 grid system. From the analysis, it is found that the displacements of the system satisfy the permissible limits as per previous research values. The member forces have also been analysed. Applications/Improvements: The performance of the half-cuboctahedron tensegrity grid structure proves to be more suitable for larger span structures.

This work establishes a tensegrity model of spider dragline silk. Tensegrity systems are ubiquitous in nature, being able to capture the mechanics of biological shapes through simple and effective modes of deformation via extension and contraction. Guided by quantitative microstructural characterization via air plasma etching and low voltage scanning electron microscopy, we report that this model is able to capture experimentally observed phenomena such as the Poisson effect, tensile stress-strain response, and fibre toughness. This is achieved by accounting for spider silks’ hierarchical organization into microfibrils with radially variable properties. Each fibril is described as a chain of polypeptide tensegrity units formed by crystalline granules operating under compression, which are connected to each other by amorphous links acting under tension. Our results demonstrate, for the first time, that a radial variability in the ductility of tensegrity chains is responsible for high fibre toughness, a defining and desirable feature of spider silk. Based on this model, a discussion about the use of graded tensegrity structures for the optimal design of next-generation biomimetic fibres is presented.

Finding member connectivities and nodal positions of tensegrity structures based on force density method and mixed integer nonlinear programming

This chapter presents a simplified procedure for the assessment of buckling of ship strength members. The main strength members of longitudinally and transversely stiffened bottom and deck structures sustaining compressive forces are identified. The compressive loadings are the compound in-plane stresses induced by the hull girder, secondary, and tertiary stresses. The assessment of buckling of strength members of bottom structure is carried out when the ship is in hogging condition and for strength members of deck structure when the ship is in sagging condition. For both cases, the compounding of stresses is carried out when the secondary and tertiary loadings are inducing compressive stresses. The assessment of buckling of web plates and face plates of deck and bottom girders is presented. The assessment of buckling of side shell plating for the various induced in-plane loading conditions is introduced. Assessment of buckling strength of plating for different end support conditions and for a variety of loading patterns is given. The importance of providing ship strength members sustaining compressive forces with adequate strength against buckling failure is stressed.

Tensegrity structure is constructed from small number of compression members like a rigid rod, and a lot of tension materials like a wire. Compared with other kinds of structures, such as truss structure the tensegrity structure is more lightweight, resists mechanical shock and has large internal space. Therefore, this structure is suitable for temporary housing or basic module of large space structure. However, the construction and the dismantling of the tensegrity structure requires a lot of people and special knowledge. In case of space structure, it is required that it is a compact and lightweight structure for efficient transportation. Therefore, it is necessary to develop the lightweight deployable structure with a simple assembly system. However, for the development of this structure, we should analyze the deployment process of tensegrity structure. In this study, simulation for design of effective automatic deployment tensegrity structure and the trial production of light deployment mechanism are discussed.

The use of mechanically compliant tensegrity structures in mobile robots is an attractive research topic. This paper describes a new concept for rolling locomotion of mobile robots based on tensegrity structures. In particular, an untethered locomotion system based on a simple tensegrity structure, consisting of two rigid disconnected compressed curved members connected to a continuous net of twelve prestressed tensioned members with pronounced elasticity, is considered. The locomotion is induced by the movement of two internal masses. The working principle of the system is discussed with the help of kinematic considerations and verified with experimental tests.

Traditional tensegrity structures comprise isolated compression members lying inside a continuous network of tension members. In this contribution, a simple numerical layout optimization formulation is presented and used to identify the topologies of minimum volume tensegrity structures designed to carry external applied loads. Binary variables and associated constraints are used to limit (usually to one) the number of compressive elements connecting a node. A computationally efficient two-stage procedure employing mixed integer linear programming (MILP) is used to identify structures capable of carrying both externally applied loads and the self-stresses present when these loads are removed. Although tensegrity structures are often regarded as inherently ‘optimal’, the presence of additional constraints in the optimization formulation means that they can never be more optimal than traditional, non-tensegrity, structures. The proposed procedure is programmed in a MATLAB script (available for download) and a range of examples are used to demonstrate the efficacy of the approach presented.

Tensegrity structures are pre-stressed pin-joint structures inclusive tensile members and compressive members. Form-finding is very important for Tensegrity structures need to determine shape and pre-stress value for self-equilibrium. In the form-finding of tensegrity structures, Infomation are usually introduced for initial geometry and pre-determined member types. In this study, Form-finding of tensegrity structures by using genetic easy and versatile form-finding processing requires only a minimal information 'topology'. Genetic Algorithms was determined the type of members. The form-finding of tensegrity structures are found by a full iteration pocedure until a state of self-stress is obtained.

This paper presents a new approach to simultaneously obtain the optimal design parameters of tensegrity structures, including pre-stress force and sectional area of elements. The proposed method is based on minimizing the static compliance in terms of some linear and nonlinear constraints using a genetic algorithm tool. This work is devoted to optimize the concurrent cross sectional area of element and pre-stress of a tensegrity system which works under the applied external loading along with a fixed topology and shape. An increase in the rigidity of systems is one of the outcomes of modifying of tensegrity structures according to optimal design parameters. The validation, efficiency and characteristics of proposed algorithm to find the optimum values for design variables of tensegrity structures is tested through three known tensegrity structures.

Tensegrity structures become important components of various engineering structures due to their high stiffness, light weight, and deployable capability. Existing studies on their dynamic analyses mainly focus on responses of their nodal points while overlook deformations of their cable and strut members. This study proposes a non-contact approach for the experimental modal analysis of a tensegrity structure to identify its three-dimensional (3D) natural frequencies and full-field mode shapes, which include modes with deformations of its cable and strut members. A 3D scanning laser Doppler vibrometer is used with a mirror for extending its field of view to measure full-field vibration of a novel three-strut metal tensegrity column with free boundaries. Tensions and axial stiffnesses of its cable members are determined using natural frequencies of their transverse and longitudinal modes, respectively, to build its theoretical model for dynamic analysis and model validation purposes. Modal assurance criterion (MAC) values between experimental and theoretical mode shapes are used to identify their paired modes. Modal parameters of the first 15 elastic modes of the tensegrity column identified from the experiment, including those of the overall structure and its cable members, can be classified into five mode groups depending on their types. Modes paired between experimental and theoretical results have MAC values larger than 78%. Differences between natural frequencies of paired modes of the tensegrity column are less than 15%. The proposed non-contact 3D vibration measurement approach allows accurate estimation of 3D full-field modal parameters of the tensegrity column.