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On Reconfiguring Tree Linkages: Trees can Lock

Therese Biedl·Erik Demaine·Martin Demaine·Sylvain Lazard·Anna Lubiw·Joseph O'Rourke·Steve Robbins·Ileana Streinu·Godfried Toussaint·Sue Whitesides
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Abstract

It has recently been shown that any simple (i.e. nonintersecting) polygonal chain in the plane can be reconfigured to lie on a straight line, and any simple polygon can be reconfigured to be convex. This result cannot be extended to tree linkages: we show that there are trees with two simple configurations that are not connected by a motion that preserves simplicity throughout the motion. Indeed, we prove that an $N$-link tree can have $2^{Ω(N)}$ equivalence classes of configurations.

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Therese Biedl, Erik Demaine, Martin Demaine, Sylvain Lazard, Anna Lubiw, Joseph O'Rourke, Steve Robbins, Ileana Streinu, Godfried Toussaint, Sue Whitesides. 2000-09-29. On Reconfiguring Tree Linkages: Trees can Lock. https://arxiv.org/abs/cs/9910024

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