On the infinitesimal rigidity of bar-and-slider frameworks

Abstract

A bar-slider framework is a bar-joint framework a part of whose joints are constrained by using line-sliders. Such joints are allowed to move only along the sliders. Streinu and Theran proposed a combinatorial characterization of the infinitesimal rigidity of generic bar-slider frameworks in two dimensional space. In this paper we propose a generalization of their result. In particular, we prove that, even though the directions of the sliders are predetermined and degenerate, i.e., some sliders have the same direction, it is combinatorially decidable whether the framework is infinitesimally rigid or not. Also, in order to prove that, we present a new forest-partition theorem. © 2009 Springer-Verlag Berlin Heidelberg.