Resolving Loads with Positive Interior Stresses ( Extended

If the load F produces a linear or angular momentum it cannot be resolved by any framework. Therefore we restrict ourselves to loads with ∑ pi fi = 0 and ∑ pi 〈pi , fi〉 = 0. (The vector pi denotes pi rotated by 90 degrees.) If a framework can resolve any load it is called statically rigid. Static rigidity is an equivalent condition for infinitesimal rigidity (see [3]). In general a statically rigid framework cannot avoid negative stresses on interior edges for some loads. We are interested in a framework that fullfils (1) with a stress that is positive on every interior edge. We look at special candidates for these frameworks, the so-called pointed pseudo-triangulations. A pseudo-triangulation of P is a partition of the convex hull of P into polygons with three corners such that every pi is part of some polygon. We call a pseudo-triangulation pointed if every point is incident to an angle greater 180 degrees. A pointed pseudo-triangulation is the embedding of a minimal rigid graph, and hence statically rigid. For a comprehensive discussion on pseudo-triangulations we direct the reader to the survey by Rote, Santos and Streinu [7].