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Abstract

This paper addresses an interval analysis based study that is applied to the design and the comparison of three-degrees-of-freedom (3-DoF) parallel kinematic machines. Two design criteria are used: (i) a regular workspace shape and (ii) a kinetostatic performance index that needs to be as homogeneous as possible throughout the workspace. The interval analysis based method takes these two criteria into account; on the basis of prescribed kinetostatic performances, the workspace is analyzed to find the largest regular dextrous workspace enclosed in the Cartesian workspace. An algorithm describing this method is introduced. Two 3-DoF translational parallel mechanisms designed for machining applications are compared using this method. The first machine features three fixed linear joints which are mounted orthogonally and the second features three linear joints which are mounted in parallel. In both cases, the mobile platform moves in the Cartesian x - y - z space with fixed orientation.

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References

Carricato, M., and Parenti-Castelli, V. 2002. Singularity-free fully-isotropic translational parallel mechanisms . International Journal of Robotics Research 21(2): 161-174 .

Chablat, D., and Wenger, Ph. 2003. Architecture optimization of a 3-DoF parallel mechanism for machining applications: the Orthoglide . IEEE Transactions on Robotics and Automation 19(3): 403-410 .

Chablat, D., Wenger, Ph., and Merlet, J.-P. June 2002. Workspace analysis of the Orthoglide using interval analysis . Proceedings of the 8th International Symposium on Advances in Robot Kinematics, Caldes de Malavella, Spain. Kluwer Academic, Dordrecht, pp. 397-406 .

Clavel, R. 1988. DELTA, a fast robot with parallel geometry . Proceedings of the 18th International Symposium of Industrial Robots, Lausanne, Switzerland, pp. 91-100 .

Company, O., and Pierrot, F. 2002. Modelling and design issues of a three-axis parallel machine tool . Mechanism and Machine Theory 37: 1325-1345 .

Gosselin, C., and Angeles, J. 1991. A global performance index for the kinematic optimization of robotic manipulators . Journal of Mechanical Design 113: 220-226 .

Gosselin, C., and Angeles, J. 1988. The optimum kinematic design of a planar three-degree-of-freedom parallel manipulator . ASME, Journal of Mechanisms, Transmissions, and Automation in Design 110(1): 35-41 .

Joshi, S., and Tsai, L. W. 2003. A Comparison study of two 3-DoF parallel manipulators: one with three and the other with four supporting legs . IEEE Transactions on Robotics and Automation 19(2): 200-209 .

Kim, J., Park, C., Kim, J., and Park, F. C. 1997. Performance analysis of parallel manipulator architectures for CNC machining applications . Proceedings of the IMECE Symposium on Machine Tools, Dallas, TX.

10.

Kong, X., and Gosselin, C. M. 2002. A class of 3-DoF translational parallel manipulators with linear I-O equations . Proceedings of Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, Québec, Canada (on CD-ROM).

11.

Luh, C.-M., Adkins, F. A., Haug, E. J., and Qui, C. C. 1996. Working capability analysis of Stewart platforms . Transactions of ASME, Journal of Mechanical Design 118(2): 221-227 .

12.

Merlet, J.-P. 1996. Workspace-oriented methodology for designing a parallel manipulator . Proceedings of the IEEE International Conference on Robotics and Automation, Minneapolis, MN, pp. 3726-3731 .

13.

Merlet, J.-P. 1999. Determination of 6D workspace of Goughtype parallel manipulator and comparison between different geometries . International Journal of Robotic Research 19(9): 902-916 .

14.

Merlet, J.-P. June 2000. ALIAS: an interval analysis based library for solving and analyzing system of equations. Séminaire Systèmes et équations algébriques, Toulouse, Automation pp. 1964-1969.

15.

Moore, R. E. 1979. Methods and Applications of Interval Analysis. SIAM Studies in Applied Mathematics, Philadelphia, PA .

16.

Neumaier, A. 1990. Interval Methods for Systems of Equations. Cambridge University Press, Cambridge .

17.

Ratscheck, H., and Rokne, J. 1995. Interval methods. Handbook of Global Optimization. R. Horst and P. M. Pardalos, editors. Kluwer, Dordrecht , pp. 751-819.

18.

Rehsteiner, F., Neugebauer, R., Spiewak, S., and Wieland, F. 1999. Putting parallel kinematics machines (PKM) to productive work . Annals of the CIRP 48(1): 345-350 .

19.

Stoughton, R. S., and Arai, T. 1993. A modified Stewart platform manipulator with improved dexterity . IEEE Transactions on Robotics and Automation 9(2): 166-173 .

20.

Tlusty, J., Ziegert, J., and Ridgeway, S. 1999. Fundamental comparison of the use of serial and parallel kinematics for machine tools . Annals of the CIRP 48(1): 351-356 .

21.

Treib, T., and Zirn, O. 1998. Similarity laws of serial and parallel manipulators for machine tools . Proceedings of the International Seminar on Improving Machine Tool Performance, San Sebastian, Spain, Vol. 1, pp. 125-131 .

22.

Wenger, Ph., and Chablat, D. 1997. Definition sets for the direct kinematics of parallel manipulators . Proceedings of the 8th International Conference on Advanced Robotics, Monterey, CA, pp. 859-864 .

23.

Wenger, P., Gosselin, C., and Chablat, D. 2001. A comparative study of parallel kinematic architectures for machining applications . Proceedings of the Workshop on Computational Kinematics 2001, Seoul, Korea, pp. 249-258 .

An Interval Analysis Based Study for the Design and the Comparison of Three-Degrees-of-Freedom Parallel Kinematic Machines

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