Truth and Myths about 2D Tensegrity Trusses

Abstract

The concept of tensegrity is understood in many ways. This term is often improperly used for structures that have some, but not necessarily the key, tensegrity properties. The concept of tensegrity systems is misused in reference to both mathematical models and completed engineering structures. The aim of the study is to indicate which of the plane (2D) trusses presented in the literature are erroneously classified as tensegrities. Singular value decomposition of the compatibility matrix and spectral analysis of the stiffness matrix with the effect of self-equilibrated forces is used for the analysis. A new precise definition of tensegrity trusses is proposed and implemented.

A simple layout optimization formulation for load-carrying tensegrity structures

“…Subsequent workers-after Fuller and Snelson-have sought to provide more precise definitions of what constitutes a viable tensegrity structure, bringing in additional considerations, such as the requirement that there exist a state of self-stress, or that there must exist infinitesimal mechanisms, resisted by self-stress forces. For example, on the basis of the latter, Obara et al (2019) have suggested that Snelson's well-known X-shaped module (comprising two diagonal struts compressed via a cable ring, Snelson (1965)) should not be considered as a true tensegrity. However, it should be borne in mind that when seeking to optimize a given problem, the more considerations (or 'constraints') that are included, the higher the objective function is likely to be.…”

Form-Finding Analysis of a Class 2 Tensegrity Robot

“…By solving the system of equations obtained by the equilibrium conditions embodied in Equations (22) and (23) for each of the n geometrical configurations, the magnitudes of the forces…”

“…This section presents the numerical examples used to corroborate and compare the results obtained from the static analysis using Equations (22) and (23) and static analysis using ANSYS c . Four different cases were reviewed, choosing values of the joint variables for positions within the workspace of the tensegrity robot.…”

“…The parameters remain the same from the previous section, and the selected values for the joint variables are shown in Table 3. The geometrical configurations adopted by the robot for these values of θ 1 and θ 2 were tested using Equations (22) and (23) and were found to be in static equilibrium satisfying Equation (27). Now, to corroborate these results, the software ANSYS c was used to perform a static analysis on a model of the moving platform oriented in the desired analysis position, adequately constrained, to check if this truly is a configuration capable of maintaining static equilibrium.…”

“…Similarly, Feng and Guo [21] presented a form-finding strategy that consists of a numerical algorithm designed to find the equilibrium position of class 1 and 2 tensegrity structures, without generating a hypothesis about the initial nodal coordinates, the lengths of the elements, the properties of the material, the symmetry of the structure or the condition of the force density matrix. Obara et al [22] used a qualitative analysis of truss matrices, which consist of the compatibility matrix and stiffness matrix with the effect of self-equilibrated forces, established using the finite element method, to search for a 2D tensegrity form. In addition to the methods already mentioned, Bayat and Crane [23,24] proposed a form-finding method based on the geometric relationships between its elements, for a tensegrity structure in two dimensions.…”