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Kinematics of A Three-Dof Platform with Three Extensible Limbs

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Recent Advances in Robot Kinematics

Abstract

A three degree-of-freedom manipulator that has a fairly large translational workspace is presented. The mechanism consists of a fixed base, a moving platform, and three extensible limbs. Each limb consists of a prismatic joint and two universal joints connecting the moving platform to the fixed base. Both the direct and inverse kinematics are investigated. The inverse kinematics problem yields two equal and opposite limb lengths for each limb while the direct kinematics problem is reduced to a second-degree polynomial in one unknown. Further, the workspace and singular conditions of the manipulator are discussed.

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References

  1. Arai, T., Cleary, K., Homma, K., Adachi, H. and Nakamura, T., 1991, “Development of Parallel Link Manipulator for Underground Excavation Task,” 1991 Int’l Symposium on Advanced Robot Technology, pp. 541–548.

    Google Scholar 

  2. Clavel, R., 1988, “A Fast Robot With Parallel Geometry,” 18th Int’l Symposium on Industrial Robots, Sydney, Australia, pp. 91–100.

    Google Scholar 

  3. Fichter, E.F., 1986, “A Stewart Platform Based Manipulator: General Theory and Practical Construction,” Int’l Journal of Robotics Research, Vol. 5, pp. 157–182.

    Article  Google Scholar 

  4. Giddings and Lewis, 1995, Giddings and Lewis Automation Technology, P.O. Box 590, Fond Dulac, WI.

    Google Scholar 

  5. Gosselin, C. and Angeles, J., 1989, “The Optimum Kinematic Design of a Spherical Three-Degree-of-Freedom Parallel Manipulator,” ASME Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 111, pp. 202–207.

    Article  Google Scholar 

  6. Gosselin, C. and Hamel, J., 1994, “The Agile Eye: A High-Performance Three-Degree-of-Freedom Camera-Orienting Device,” IEEE Intl. Conference on Robotics and Automation, pp. 781–786.

    Google Scholar 

  7. Gough V.E. and Whitehall, S.G., 1962, “Universal Tyre Test Machine,” Proc. 9th Int’l Tech. Congress, F.I.S.I.T.A., 177 (Institution of Mechanical Engineers).

    Google Scholar 

  8. Grffis, M. and Duffy, J., 1989, “Forward Displacement Analysis of a Class of Stewart Platforms,” Journal of Robotic Systems, Vol. 6, pp. 703–720.

    Article  Google Scholar 

  9. Hudgens, J.C. and Tesar, D., 1988, “A Fully-Parallel Six Degree-of-Freedom Micromanipulator: Kinematic Analysis and Dynamic Model,” Trends and Developments in Mechanisms, Machines, and Robotics, Proc. of the 20th ASME Biennial Mechanisms Conf., DE-Vol. 15.3, pp. 29–37.

    Google Scholar 

  10. Hunt, K.H., 1983, “Structural Kinematics of In-Parallel-Actuated Robot-Arms,” ASME Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 105, pp. 705–712.

    Article  Google Scholar 

  11. Innocenti, C. and Parenti-Castelli, V., 1990, “Direct Position Analysis of the Stewart Platform Mechanism,” Mechanism and Machine Theory, Vol. 25, pp. 611–612.

    Article  Google Scholar 

  12. Innocenti, C. and Parenti-Castelli, V., 1993, “Forward Kinematics of the General 6–6 Fully Parallel Mechanism: An Exhaustive Numerical Approach Via a Mono-Dimensional Search Algorithm,” ASME Journal of Mechanical Design, Vol. 115, pp. 932–937.

    Article  Google Scholar 

  13. Kohli, D., Lee, S.H., Tsai, K.Y. and Sandor, G.N., 1988, “Manipulator Configurations Based on Rotary-Linear (R-L) Actuators and Their Direct and Inverse Kinematics,” ASME Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 110, pp. 397–404.

    Article  Google Scholar 

  14. Lee, K. and Shah, D.K., 1987, “Kinematic Analysis of a Three Degrees of Freedom In-Parallel Actuated Manipulator,” Proc. IEEE Int’l Conf. on Robotics and Automation, Vol. 1, pp. 345–350.

    Google Scholar 

  15. Lin, W., Crane, CD. and Duffy, J., 1994, “Closed Form Forward Displacement Analysis of the 4–5 In Parallel Platforms,” ASME Journal of Mechanical Design, Vol. 116, pp. 47–53.

    Article  Google Scholar 

  16. Mohamed, M.G. and Duffy, J., 1985, “A Direct Determination of the Instantaneous Kinematics of Fully Parallel Robotic Manipulators,” ASME Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 107, pp.226–229

    Article  Google Scholar 

  17. Nanua, P., Waldron, K.J. and Murthy, V., 1990, “Direct Kinematic Solution of a Stewart Platform,” IEEE Trans, on Robotics and Automation, Vol. 6, pp. 438–444.

    Article  Google Scholar 

  18. Pierrot, F., Fournier, A. and Dauchez, P., 1991, “Toward a Fully Parallel 6 DOF Robot for High-Speed Applications,” Proc. of the 1991 IEEE Int’l Conf. on Robotics and Automation, pp. 1288–1293.

    Google Scholar 

  19. Raghavan, M., 1993, “The Stewart Platform of General Geometry Has 40 Configurations,” ASME Journal of Mechanical Design, Vol. 115, pp. 277–282.

    Article  Google Scholar 

  20. Reinholz, C. and Gokhale, D., 1987, “Design and Analysis of Variable Geometry Truss Robot,” Proc. 9th Applied Mechanisms Conference, Oklahoma State University.

    Google Scholar 

  21. Sternheim, F., 1987, “Computation of the Direct and Inverse Kinematic Model of the Delta 4 Parallel Robot,” Robotersysteme 3, pp. 199–203.

    Google Scholar 

  22. Stewart, D., 1965, “A Platform with Six Degrees of Freedom,” Proc. Institute of Mechanical Engr., London, England, Vol. 180, pp. 371–386.

    Google Scholar 

  23. Tsai, L.W., Walsh, G.C. and Stamper, R., 1996, “Kinematics of a Novel Three DOF Translational Platform,” accepted for presentation at the IEEE 1996 Int’l Conf. on Robotics and Automation, Minneapolis, MN.

    Google Scholar 

  24. Tsai, L.W. and Tahmasebi, F., 1993, “Synthesis and Analysis of a New Class of Six-DOF Parallel Mini-manipulators,” Journal of Robotic Systems, Vol. 10, No. 5, pp. 561–580.

    Article  MATH  Google Scholar 

  25. Zhang, C. and Song, S.M., 1994, “Forward Position Analysis of Nearly General Stewart Platforms,” ASME Journal of Mechanical Design, Vol. 116, pp. 54–60.

    Article  Google Scholar 

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© 1996 Kluwer Academic Publishers

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Tsai, LW. (1996). Kinematics of A Three-Dof Platform with Three Extensible Limbs. In: Lenarčič, J., Parenti-Castelli, V. (eds) Recent Advances in Robot Kinematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1718-7_40

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  • DOI: https://doi.org/10.1007/978-94-009-1718-7_40

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7269-4

  • Online ISBN: 978-94-009-1718-7

  • eBook Packages: Springer Book Archive

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