Main Theorem. We consider a simple polygon in the plane as a system of rigid bars with movable joints at the vertices (a linkage or framework). We show that such a polygon can always be continuously reconfigured into convex position while avoiding self-intersection. Similarly, an open polygonal path (chain) can always be straightened. During this motion, whereas the lengths of the bars remain fixed, all other pairwise distances increase. 1.1. History and Applications; Related Work. This type of problem has been considered in discrete and computational geometry since an early work of Erd&quot;&quot;os , in knot theory, and in molecular biology and polymer physics. Its applications include wire bending, hydraulic tube folding, and the study of macromolecule folding
To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.