This project concerns the possible rigidity of structures which are composed of bars joined at their ends by universal joints and then reinforced by cables joining some of these joints to others. The rods are to be incompressible, and the cables are to be unstretchable. Simple and graphic as this model is, it embodies deep mathematical principles and calls for subtle analysis. Maria Terrell and Robert Connelly have been studying such cabled frameworks, asking questions including the following. Suppose a framework has its vertices and bars along the natural vertices and edges of a convex polyhedron in 3-dimensional space. How few cables need one add to render such a framework infinitesimally rigid? Can one calculate easily which cabled frameworks are globally rigid? To what extent can group representations be used to study the global rigidity of cabled frameworks exhibiting certain groups of symmetries? Answers to some specific questions of this sort may have value for the design of robot arms. Moreover, the mathematical tools which are called for in attacking questions about frameworks will be sharpened and thus improved for all possible uses.
