Strongly rigid tensegrity graphs on the line

Rigid tensegrity labelings of graphs

Tensegrity frameworks are defined on a set of points in Rd and consist of bars, cables, and struts, which provide upper and/or lower bounds for the distance between their endpoints. The graph of the framework, in which edges are labeled as bars, cables, and struts, is called a tensegrity graph. It is said to be rigid inRd if it has an infinitesimally rigid realization inRd as a tensegrity frame...

Globally rigid frameworks and rigid tensegrity graphs in the plane

Robust Tensegrity Polygons

A tensegrity polygon is a planar cable-strut tensegrity framework in which the cables form a convex polygon containing all vertices. The underlying edgelabeled graph, in which the cable edges form a Hamilton cycle, is an abstract tensegrity polygon. It is said to be robust if every convex realization as a tensegrity polygon has an equilibrium stress which is positive on the cables and negative ...

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...

An Approach to Compliant Locomotion Systems Based on Tensegrity Structures

Tensegrity structures are prestressed compliant structures composed of a set of disconnected rigid compressed elements connected by continuous prestressed tensional elements. A spatially limited, local impact on tensegrity structures yields a global change of their shape. This essential property initiates the development of novel compliant locomotion systems with large shape variability and sim...