**Linkage and Rigidity Bibliography **(11/18/02)

Prepared by:

Joseph Malkevitch

Department of Mathematics and Computer Science

York College (CUNY)

Jamaica, New York 11451

Email: malkevitch@york.cuny.edu (for additions, suggestions, and corrections)

Biedl, T. and E. Demaine, M. Demaine, S. Lazard. A. Lubiw, J. O'Rourke, M Overmars, S. Robbins, I. Streinu, G. Toussaint, S. Whitesides, Locked and unlocked polygonal chains in 3d. Proc. 10th. ACM-SIAM Symposium on Discrete Algorithms, 1999, p. 866-867.

Bolker, E. and H. Crapo, How to brace a one-story building, Environ. Plan. B. 4 (1977) 125-152.

Borcea, C. and I. Streinu, On the number of embeddings of minimally rigid graphs, preprint.

Connelly, R., A flexible sphere, Math. Intelligencer, 1 (1978) 130-131.

Connelly, R. and E. Demaine, G. Rote, Straightening polygonal arcs and convexifying polygonal cycles, Discrete and Computational Geometry, to appear. (See Erik Demaine's web page: http://theory.lcs.mit.edu/~edemaine/)

Connelly, R. and E. Demaine, G. Rote, Infinitesimally locked self-touching linkages with applications to locked trees, preprint.

Graver, J., and B. Servatius, H. Servatius, Combinatorial Rigidity, American Mathematical Society, Providence, 1993.

Graver, J., Counting on Frameworks, American Mathematical Association, Washington, 2001.

Hopcroft, J. and D. Joseph, S. Whitesides, Movement problems for 2-dimensional linkages, SIAM J. Computing 13 (1984) 610-629.

Hopcroft, J. and D. Joseph, S. Whitesides, On the movement of robot arms in 2-dimensional bounded region, SIAM J. Computing 14 (1985) 315-333.

Jordan, D. and M. Steiner, Configuration spaces of mechanical linkages, Disc. and Comp. Geometry 22 (1999) 297-315.

Laman, G., On graphs and rigid plane skeletal structures, J. Engrg. Math. 4 (1970) 331-330.

Lenhart, W. and S. Whitesides, Reconfiguring closed polygonal chains in Euclidean d-space, Disc. Comput. Geo. 13 (1995) 123-140.

Lovasz, L. and Y. Yemini, On generic rigidity in the plane, SIAM J. Alg. Disc. Methods 3 (1982) 91-98.

Recski, A., Matroid Theory and its Applications in Electrical Theory and in Statics, Springer-Verlag, Berlin, 1989.

Sharir, M., Algorithmic motion planning, in Handbook of Discrete and Computational Geometry, Chapter 40, J. Goodman and J. O'Rourke, (eds.), CRC Press, Boca Raton, 1997, p. 733-754.

Streinu, I., A combinatorial approach to planar non-colliding robot arm motion planning, Proceedings 41st Annual Symp. Foundations of Computer Science, IEEE Press, Washington, p. 353-370.

Toussaint, G., Simple proofs of a geometric property of four-bar linkages, preprint. (Available on Gotfried Toussaint's web page.)

Whiteley, W., Matroids and rigid structures, in Matroid Applications, N. White, (ed.), Encyclopedia of Mathematics and Its Applications, Cambridge U. Press, New York, 1992, p. 1-53.

Whiteley, W., Rigidity and Scene Analysis, in Handbook of Discrete and Computational Geometry, Chapter 40, J. Goodman and J. O'Rourke, (eds.), CRC Press, Boca Raton, 1997, 893-916.

Whitesides, S., Algorithmic issues in the geometry of planar linkage movement, The Australian Computer J., Special Issue on Algorithms, May, 1992, p. 42-50.

Whitesides, S. Chain reconfiguration: the ins and outs, ups and downs of moving polygons and polygonal linkages, (to appear in Lecture Notes in Computer Science, Springer-Verlag).

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