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  JP Journal of Geometry and Topology  
 ISSN: 0972-415X
 
 
 

     JP Journal of Geometry and Topology
    Volume 9, Issue 2, Pages 137 - 167 (July 2009)


THE CONFIGURATION SPACE OF A PARALLEL POLYGONAL MECHANISM

Nir Shvalb (Israel), Moshe Shoham (Israel) and David Blanc (Israel)

Received December 18, 2007; Revised February 8, 2009

References:



[1] H. Bamberger, M. Shoham and A. Wolf, Kinematics of micro planar robot comprising large joint clearances, J. Lenarčič and B. Roth, eds., Advances in Robot Kinematics, Part 2: Mechanisms and Motion, Springer, Berlin, 2006.

[2] D. Blanc and N. Shvalb, Singularities and configuration spaces for graphs (in preparation).

[3] M. Farber, Invitation to topological robotics, European Mathematical Society (EMS), Zürich, 2008.

[4] M. Farber and D. Schütz, Homology of planar polygon spaces, Geom. Dedicata 125 (2007), 75-92.

[5] M. Farber, S. Tabachnikov and S. Yuzvinsky, Topological robotics: motion planning in projective spaces, Int. Math. Res. Not. 2003, no. 34, 1853-1870.

[6] D. H. Gottlieb, Robots and fibre bundles, Bull. Soc. Math. Belg. Sér. A 38 (1986), 219-223.

[7] A. S. Hall, Jr., Kinematics and Linkage Design, Prentice-Hall, Englewood Cliffs, NJ, 1961.

[8] J.-C. Hausmann, Sur la topologie des bras articulés, S. Jackowski, R. Oliver and K. Pawałowski, eds., Algebraic Topology, Poznán 1989, Springer Lecture Notes in Math. 1474, Berlin, New York, 1991, pp. 146-159.

[9] J.-C. Hausmann and A. Knutson, The cohomology ring of polygon spaces, Ann. Inst. Fourier (Grenoble) 48 (1998), 281-321.

[10] M. W. Hirsch, Differential Topology, Springer-Verlag, Berlin, New York, 1976.

[11] M. Holcomb, On the moduli spaces of multipolygonal linkages in the plane, Topology Appl. 154 (2007), 124-143.

[12] D. Jordan and M. Steiner, Compact surfaces as configuration spaces of mechanical linkages, Israel J. Math. 122 (2001), 175-187.

[13] Y. Kamiyama and M. Tezuka, Topology and geometry of equilateral polygon linkages in the Euclidean plane, Quart. J. Math. Oxford Ser. (2) 50 (1999), 463-470.

[14] Y. Kamiyama and S. Tsukuda, The configuration space of the n-arms machine in the Euclidean space, Topology Appl. 154 (2007), 1447-1464.

[15] M. Kapovich and J. Millson, On the moduli space of polygons in the Euclidean plane, J. Differential Geom. 42 (1995), 430-464.

[16] R. J. Milgram and J. C. Trinkle, The geometry of configuration spaces for closed chains in two and three dimensions, Homology Homotopy Appl. 6 (2004), 237-267.

[17] J. Milnor, Morse Theory, Princeton University Press, Princeton, NJ, 1963.

[18] J. O'Hara, The configuration space of planar spidery linkages, Topology Appl. 154 (2007), 502-526.

[19] N. Shvalb, M. Shoham and D. Blanc, The configuration space of arachnoid mechanisms, Forum Math. 17 (2005), 1033-1042.

Keywords and phrases: configuration space, work space, robotics, (planar) mechanism.

Communicated by Marcelo Alberto Aguilar

 


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