Paper by Erik D. Demaine

Reference:

Erik D. Demaine, Stefan Langerman, and Joseph O'Rourke, “Short Interlocked Linkages”, in Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG 2001), Waterloo, Ontario, Canada, August 13–15, 2001, pages 69–72.

Abstract:

We study collections of O(1) linkages in 3-space, each with O(1) joints, that are interlocked in the sense that, without one link crossing through another, they cannot be separated from one another. Our main results are proofs that a triangle and an open 4-chain can interlock, as can a quadrilateral and an open 3-chain. For two 3-chains, we establish that an open 3-chain cannot interlock with a triangle but it can interlock with an open rigid 3-chain, and that two “revolute” 3-chains can interlock. Finally we make several conjectures on which pairs of short, open chains can interlock.

Comments:

This paper is also available from the electronic proceedings as http://compgeo.math.uwaterloo.ca/~cccg01/proceedings/short/eddemaine-27484.ps.gz.

Length:

The paper is 4 pages.

Availability:

The paper is available in PostScript (392k) and gzipped PostScript (120k).

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Related papers:

InterlockedLinkages_CGTA (Interlocked Open and Closed Linkages with Few Joints)

InterlockedLinkages_SoCG2002 (Interlocked Open Linkages with Few Joints)

Related webpages:

Carpenter's Rule Theorem