Summary: Volume 5, Number 1, Pages 717
ON THE UNIVERSAL RIGIDITY OF GENERIC BAR
A. Y. ALFAKIH
Abstract. In this paper, we present a sufficient condition for the uni-
versal rigidity of a generic bar framework G(p) in terms of the Gale
matrix Z corresponding to G(p). We also establish a relationship be-
tween the stress matrix S and the Gale matrix Z for bar frameworks.
This allows us to translate back and forth between S and Z in recently
obtained results concerning universal rigidity, global rigidity and dimen-
sional rigidity of generic bar frameworks.
An r-configuration p is a finite set of points p1, . . . , pn in Rr whose affine
hull is Rr. A bar framework (or simply a framework), denoted by G(p), in
Rr is a simple graph G = (V, E) on the vertices 1, . . . , n together with an r-
configuration p, where each vertex i of G is located at point pi. With a slight
abuse of notation, sometimes we will refer to the vertices and edges of graph
G as the vertices and edges of the framework G(p). To avoid trivialities, we
assume that graph G is connected and not complete.