Topology identification for super-stable tensegrity structure from a given number of nodes in two dimensional space

Abstract

Finding a super stable tensegrity structure is very significant as far as the applications of tensegrity structures are concerned. One of the biggest advantages of super-stable tensegrity structure is that it does not fail if the level of pre-stresses of its members increases. However, the available literatures do not suggest any systematic method for predicting a topology from a given number of nodes that will guarantee to underlie a super-stable tensegrity structure. This paper addresses this fundamental question and proposes a systematic method for identifying a topology that certainly underlie a super-stable tensegrity structure. This not only identifies a single topology but also multiple topologies from the same set of given nodes where all of them are capable to underlie super-stable tensegrity structures. The procedure for finding such super-stable tensegrity structures starts by identifying the topology of fundamental super-stable tensegrities from their abstract graphs and then combined to arrive at larger tensegrity structures which are again super-stable in nature. The principle of getting larger super-stable tensegrity by combining the fundamental tensegrity structures has been established by two examples. In the first example the nodes are placed symmetrically whereas in the second example the nodes are placed asymmetrically. H owever, the primary application of this procedure is expected to produce multiple number of large super-stable tensegrity structures from a set of nodes placed unevenly in space. A more complex super-stable tensegrity structure in two dimension has also been provided.