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Physical Sciences and Mathematics Commons™
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Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Interlocked Open And Closed Linkages With Few Joints, Erik D. Demaine, Stefan Langerman, Joseph O'Rourke, Jack Snoeyink
Interlocked Open And Closed Linkages With Few Joints, Erik D. Demaine, Stefan Langerman, Joseph O'Rourke, Jack Snoeyink
Computer Science: Faculty Publications
We study collections of linkages in 3-space that are interlocked in the sense that the linkages cannot be separated without one bar crossing through another. We explore pairs of linkages, one open chain and one closed chain, each with a small number of joints, and determine which can be interlocked. In particular, we show that a triangle and an open 4-chain can interlock, a quadrilateral and an open 3-chain can interlock, but a triangle and an open 3-chain cannot interlock.
Interlocked Open Linkages With Few Joints, Erik D. Demaine, Stefan Langerman, Joseph O'Rourke, Jack Snoeyink
Interlocked Open Linkages With Few Joints, Erik D. Demaine, Stefan Langerman, Joseph O'Rourke, Jack Snoeyink
Computer Science: Faculty Publications
We advance the study of collections of open linkages in 3-space that may be interlocked in the sense that the linkages cannot be separated without one bar crossing through another. We consider chains of bars connected with rigid joints, revolute joints, or universal joints and explore the smallest number of chains and bars needed to achieve interlock. Whereas previous work used topological invariants that applied to single or to closed chains, this work relies on geometric invariants and concentrates on open chains.
Polygonal Chains Cannot Lock In 4d, Roxana Cocan, Joseph O'Rourke
Polygonal Chains Cannot Lock In 4d, Roxana Cocan, Joseph O'Rourke
Computer Science: Faculty Publications
We prove that, in all dimensions d ≥ 4, every simple open polygonal chain and every tree may be straightened, and every simple closed polygonal chain may be convexified. These reconfigurations can be achieved by algorithms that use polynomial time in the number of vertices, and result in a polynomial number of “moves.” These results contrast to those known for d = 2, where trees can “lock,” and for d = 3, where open and closed chains can lock.