Discrete & Computational Geometry

, Volume 30, Issue 2, pp 205–239

Blowing Up Polygonal Linkages

Article

DOI: 10.1007/s00454-003-0006-7

Cite this article as:
Connelly, R., Demaine, E. & Rote, G. Discrete Comput Geom (2003) 30: 205. doi:10.1007/s00454-003-0006-7

Abstract

{Consider a planar linkage, consisting of disjoint polygonal arcs and cycles of rigid bars joined at incident endpoints (polygonal chains), with the property that no cycle surrounds another arc or cycle. We prove that the linkage can be continuously moved so that the arcs become straight, the cycles become convex, and no bars cross while preserving the bar lengths. Furthermore, our motion is piecewise-differentiable, does not decrease the distance between any pair of vertices, and preserves any symmetry present in the initial configuration. In particular, this result settles the well-studied carpenter’s rule conjecture.

Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Department of Mathematics, Cornell University, Ithaca, NY 14853USA
  2. 2.Laboratory for Computer Science, Massachusetts Institute of Technology, 200 Technology Square, Cambridge, MA 02139USA
  3. 3.Institut für Informatik, Freie Universität Berlin, Takustraße 9, D-14195 Berlin Germany