Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 249349, 12 pages
doi:10.1155/2009/249349
Research Article

Topological and Kinematic Singularities for a Class of Parallel Mechanisms

Nir Shvalb,1 Moshe Shoham,2 Hagay Bamberger,2 and David Blanc3

1Department of Mechanical Engineering, Ariel University Center, Ariel 47000, Israel
2Department of Mechanical Engineering, Technion, Haifa 32000, Israel
3Department of Mathematics, University of Haifa, Haifa 31905, Israel

Received 2 October 2008; Accepted 8 February 2009

Academic Editor: Giuseppe Rega

Copyright © 2009 Nir Shvalb et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study singularities for a parallel mechanism with a planar moving platform in ℝd  (d=2,3), with joints which are universal, spherical (spatial case), or rotational (planar case). For such mechanisms, we give a necessary condition for a topological singularity to occur, and describe the corresponding kinematic singularity. An example is provided.