Flat-state connectivity of linkages under dihedral motions

Abstract

We explore which classes of linkages have the property that each pair of their flat states - that is, their embeddings in ℝ2 without self-intersection - can be connected by a continuous dihedral motion that avoids self-intersection throughout. Dihedral motions preserve all angles between pairs of incident edges, which is most natural for protein models. Our positive results include proofs that open chains with nonacute angles are flat-state connected, as are closed orthogonal unit-length chains. Among our negative results is an example of an orthogonal graph linkage that is flat-state disconnected. Several additional results are obtained for other restrictedclasses of linkages. Many open problems are posed. © Springer-Verlag Berlin Heidelberg 2002.