Tensegrity Frameworks

Tensegrity Frameworks in the One-Dimensional Space

The edge set of a graphG is partitioned into two subsets EC∪ES. A tensegrity framework with underlying graph G and with cables for EC and struts for ES is proved to be rigidly embeddable into a 1-dimensional line if and only if G is 2-edge-connected and every 2-vertex-connected component of G intersects both EC and ES. Polynomial algorithms are given to nd an embedding of such graphs and to che...

One-Dimensional Synthesis of Graphs as Tensegrity Frameworks

The edge set of a graph G is partitioned into two subsets EC∪ES. A tensegrity framework with underlying graph G and with cables for EC and struts for ES is proved to be rigidly embedable into a 1-dimensional line if and only if G is 2-edge-connected and every 2-vertex-connected component of G intersects both EC and ES. Polynomial algorithms are given to find an embedding of such graphs and to c...

Globally rigid frameworks and rigid tensegrity graphs in the plane

Tensegrity frameworks: Dynamic analysis review and open problems

The main objective of this paper is twofold. First, to conclude the overview about tensegrity frameworks, started by the same authors in a previous work, covering the most important dynamic aspects of such structures. Here, the most common approaches to tensegrity dynamic modeling used so far are presented, giving the most important results about their dynamic behavior under external action. Al...

Second-Order Rigidity and Prestress Stability for Tensegrity Frameworks

This paper defines two concepts of rigidity for tensegrity frameworks (frameworks with cables, bars, and struts): prestress stability and second-order rigidity. We demonstrate a hierarchy of rigidity--first-order rigidity implies prestress stability implies second-order rigidity implies rigiditymfor any framework. Examples show that none of these implications are reversible, even for bar framew...