| On Reconfiguring Tree Linkages: Trees can Lock (1998) | |||||||||||||||
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| It is an open problem to determine whether a polygonal chain can be "straightened" in the plane if its links are not allowed to cross. This problem been raised independently by several researchers, including J. Mitchell, and W. Lenhart and S. Whitesides [LW95]. In this paper we propose a related question: whether a tree linkage can always be "straightened" in the plane, without allowing its links to cross. We prove that this is not always possible. 1 Introduction Consider a graph, each edge labelled with a positive number. Such a graph may be thought of as a collection of distance constraints between pairs of points in a Euclidean space. A realization of such a graph maps each vertex to a point, also called a joint, and maps each edge to the closed line segment, called a link, connecting its incident joints. The link length must equal the label of the underlying graph edge. If a graph has one or more such realizations, we call it a linkage. An embedding of a linkage in space is called... | |||||||||||||||
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