Characterizing the Workspace of the Spherical Image of Cooperating Robots
In this paper we consider the set of orientations available to the workpiece held by a pair of cooperating robot arms. The rotational terms in the kinematics equations of the system define constraints on the orientation of the workpiece that can be viewed as a spherical linkage, called the spherical image of the robot system. We determine the differential volume element for this orientation workspace and examine two cases, a near planar spherical 6R, and a 6R with orthogonal joint axes which is a model for the case of cooperating PUMA Robots.
KeywordsClifford Algebra Twist Angle Revolute Joint Wrist Joint Spherical Image
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- Bodduluri, R. M. C., Design and Planned Movement of Multi-degree of F3eedom Spatial Mechanisms. Dissertation, University of California, Irvine, 165pp., 1990. Google Scholar
- Do Carmo, M. P., Riemannian Geometry. Birkhauser, Boston, 300pp., 1992. Google Scholar
- Dooley, J. R., and McCarthy, J. M., On the Geometric Analysis of Optimum Trajectories for Cooperating Robots using Dual Quaternion Coordinates. Proc. IEEE Int. Conf. on Robotics and Automation. pp. 1031-1036., 1993.Google Scholar
- Duffy, J. Analysis of Mechanisms and Robot Manipulators. Edward Arnold, London, 419pp., 1980.Google Scholar
- Ge, Q. J., Kinematic Constraints as Algebraic Manifolds in the Clifford Algebra of Projective Three Space. Dissertation, University of California, Irvine, 160pp., 1990.Google Scholar
- Hsu, P., Adaptive Coordination of a Multiple Manipulator System. Proc. IEEE Int. Conf. on Robotics and Automation. pp. 259-264., 1993. Google Scholar
- Kerr, J., and Roth, B., Analysis of Multifingered Hands. Int. J. of Robotics Research. 4(4): 3-17, 1986. Google Scholar
- McCarthy, J. M., An Introduction to Theoretical Kinematics. MIT Press, Cambridge, MA, 1990.Google Scholar
- Paljug, E., and Yun, X., Experimental Results of Two Robot Arms Manipulating Large Objects. Proc. IEEE Int. Conf. on Robotics and Automation. pp. 517-522., 1993.Google Scholar
- Xi, N., Tarn, T. J., and Bejczy, A., Event-Based Planning and Control for Multiple Manipulator Systems. Proc. IEEE Int. Conf. on Robotics and Automation. pp. 251258,1993.Google Scholar