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Modelling of a special class of spherical parallel manipulators with Euler parameters

Published online by Cambridge University Press:  01 March 2009

Shaoping Bai ,
Michael R. Hansen  and
Torben O. Andersen
Shaoping Bai*
Affiliation:
Department of Mechanical Engineering, Aalborg University, Denmark
Michael R. Hansen
Affiliation:
Department of Mechanical Engineering, Aalborg University, Denmark
Torben O. Andersen
Affiliation:
Department of Energy Technology, Aalborg University, Denmark
*
*Corresponding author. E-mail: shb@ime.aau.dk
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Summary

A method of workspace modelling for spherical parallel manipulators (SPMs) of symmetrical architecture is developed by virtue of Euler parameters in the paper. The adoption of Euler parameters in the expression of spatial rotations of SPMs helps not only to eliminate the possible singularity in the rotation matrix, but also to formulate all equations in polynomials, which are more easily manipulated. Moreover, a homogeneous workspace can be obtained with Euler parameters for the SPMs, which facilitates the evaluation of dexterity. In this work, the problem of workspace modelling and analysis is formulated in terms of Euler parameters. An equation dealing with boundary surfaces is derived and branches of boundary surface are identified. Evaluation of dexterity is explored to quantitatively describe the capability of a manipulator to attain orientations. The singularity identification is also addressed. Examples are included to demonstrate the application of the proposed method.

Keywords

Spherical parallel manipulatorWorkspaceSingularityDexterity
Type
Article
Information
Robotica , Volume 27 , Issue 2 , March 2009 , pp. 161 - 170
Copyright
Copyright © Cambridge University Press 2008

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References

1.Gosselin, C. M. and Hamel, J.-F., “The Agile Eye: A High-Performance Three-Degree-of-Freedom Camera-Orienting Device,” IEEE International Conference on Robotics and Automation, San Diego, CA, USA (1994) pp. 781–786.Google Scholar
2.Li, T. and Payandeh, S., “Design of spherical parallel mechanisms for application to laparoscopic surgery,” Robotica, 20 (2), 133–138 (2002).CrossRefGoogle Scholar
3.Cavallo, E. and Michelini, R.C., “A Robotic Equipment for the Guidance of a Vectored Thrustor,” Proceedings of 35th International Symposium on Robotics (ISR 2004), Paris (2004).Google Scholar
4.Craver, W. M. and Tesar, D., “Force and Deflection Determination for a Parallel Three Degree of Freedom Robotic Shoulder Module,” ASME 1990 Design Technical Conferences, Chicago, IL, USA (1990) pp. 473–479.Google Scholar
5.Gosselin, C. M. and Angeles, J., “The optimum kinematic design of a spherical three-degree-of-freedom parallel manipulator,” ASME J. Mech. Transm. Autom. Des. 111, 202–207 (1989).CrossRefGoogle Scholar
6.Bonev, I. A. and Gosselin, C. M., “Analytical determination of the workspace of symmetrical spherical parallel mechanisms,” IEEE Trans. Robot. 22 (5), 1011–1017 (2006).CrossRefGoogle Scholar
7.Yang, G.L. and Chen, I.-M., “Equivolumetric partition of solid spheres with applications to orientation workspace analysis of robot manipulators,” IEEE Trans. Robot. 22 (5), 869–879 (2006).CrossRefGoogle Scholar
8.Alizade, R. I., Tagiyiev, N. R. and Duffy, J., “A forward and reverse displacement analysis of an in-parallel spherical manipulator,” Mech. Mach. Theory, 29 (1), 125–137 (1994).CrossRefGoogle Scholar
9.Gosselin, C. M. and Lavoie, E., “On the kinematic design of spherical three-degree-of-freedom parallel manipulators,” Int. J. Robot. Res. 12 (4), 394–402 (1993).CrossRefGoogle Scholar
10.Gosselin, C. M., Sefrioui, J. and Richard, M. J., “On the direct kinematics of spherical three-degree-of-freedom parallel manipulators of general architecture,” ASME J. Mech. Des. 116 (2), 594–598 (1994).CrossRefGoogle Scholar
11.Gosselin, C. M. and Angeles, J., “A global performance index for the kinematic optimization of robotic manipulators,” ASME J. Mech. Des. 113 (3), 220–226 (1991).CrossRefGoogle Scholar
12.Leguay-Durand, S. and Reboulet, C., “Optimal design of a redundant spherical parallel manipulator,” Robotica 15 (4), 399–405 (1997).CrossRefGoogle Scholar
13.Asada, H. and Granito, J., “Kinematic and Static Characterization of Wrist Joints and Their Optimal Design,” IEEE International Conference on Robotics and Automation, St Louis, MO, USA (1985) pp. 244–250.Google Scholar
14.Trabia, M. and Davidson, J. K., “Design conditions for the orientation and attitude of a robot tool carried by a 3-R spherical wrist,” ASME J. Mech. Transm. Autom. Des. 111, 176–187 (1989).CrossRefGoogle Scholar
15.Larochelle, P. M., “Design of 3-dof Spherical Robotic Mechanisms,” Proceedings of the 9th IFToMM World Congress on the Theory of Machines and Mechanisms, Milan, Itali (1995) pp. 1826–1830.Google Scholar
16.Liu, X.-J., Jin, Z.-L. and Gao, F., “Optimum design of 3-dof spherical parallel manipulators with respect to the conditioning and stiffness indices,” Mech. Mach. Theory 35, 1257–1267 (2000).CrossRefGoogle Scholar
17.Gosselin, C. M. and Wang, J., “Singularity loci of a special class of spherical three-degree-of-freedom parallel mechanisms with revolute actuators,” Int. J. Robot. Res. 21 (7), 649–659 (2002).CrossRefGoogle Scholar
18.Bonev, I. A., Chablat, D. and Wenger, P., “Working and Assembly Modes of the Agile Eye,” IEEE International Conference on Robotics and Automation, Orlando, Florida, USA (2006) pp. 2317–2322.Google Scholar
19.Kurtz, R. and Hayward, V., “Multiple-goal kinematic optimization of a parallel spherical mechanism with actuator redundancy,” IEEE Trans. Robot. Autom. 8 (5), 644–651 (1992).CrossRefGoogle Scholar
20.Kong, X. and Gosselin, C. M., “Type synthesis of three-degree-of-freedom spherical parallel manipulators,” Int. J. Robot. Res. 23 (3), 237–245 (2004).CrossRefGoogle Scholar
21.Di Gregorio, R., “Kinematics of a new spherical parallel manipulator with three equal legs: The 3-URC wrist,” J. Robot. Syst. 18 (5), 213–219 (2001).CrossRefGoogle Scholar
22.Tandirci, M., Angeles, J. and Darcovich, J., “The Role of Rotation Representations in Computational Robot Kinematics,” IEEE International Conference on Robotics and Automation, Nice, France (1992) pp. 344–349.Google Scholar
23.Kuipers, J. B., Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality (Princeton University Press, NJ, 2002).Google Scholar
24.Bai, S. and Hansen, M. R., “Evaluation of Workspace of a Spherical Robotic Wrist,” Proceedings of 2007 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, ETH Zurich, Switzerland (Sep. 4–7, 2007).Google Scholar
25.Gosselin, C. M. and Angeles, J., “Singularity analysis of closed-loop kinematic chains,” IEEE Trans. Robot. Autom. 6 (3), 281–290 (1990).CrossRefGoogle Scholar
26.Davidson, J. K. and Hunt, K. H., “Rigid body location and robot workspace: Some alternative manipulator forms,” ASME J. Mech. Transm. Autom. Des. 109 (2), 224–232 (1987).CrossRefGoogle Scholar
27.Gupta, K. C. and Roth, B., “Design considerations for manipulator workspace,” ASME J. Mech. Des. 104 (4), 704–711 (1983).Google Scholar