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.
The first author is supported by Grant-in-Aid for Scientific Research (B) and Grant-in-Aid for Scientific Research (C), JSPS. The second author is supported by Grant-in-Aid for JSPS Research Fellowships for Young Scientists.
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Katoh, N., Tanigawa, Si. (2009). On the Infinitesimal Rigidity of Bar-and-Slider Frameworks. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_54
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DOI: https://doi.org/10.1007/978-3-642-10631-6_54
Publisher Name: Springer, Berlin, Heidelberg
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