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Geometrical Interpretation of the CCT Stiffness Mapping for Serial Manipulators

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Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 6))

Abstract

Recent research results suggested a conservative transformation to correct the well-known congruence transformation between Cartesian and joint stiffness matrices of a serial manipulator. This paper utilizes screw geometry to interpret the conservative congruence transformation (CCT). The analysis using screw theory provides better geometric insights into the CCT. The effective geometrical stiffness matrix, due to the change of manipulator geometry under stiffness control in the presence of external force, is confirmed. This paper also points out several erroneous assumptions that may have led to the incorrect formulation of the conventional congruence transformation.

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References

  • Asada H, Slotine JE (1986) Robot analysis and control. John Wiley & Sons, New York.

    Google Scholar 

  • Ball RS (1986) A treatise on the theory of screws. Cambridge University Press, Cambridge.

    Google Scholar 

  • Chen SF, Kao I (1999) The conservative congruence transformation of stiffness control in robotic grasping and manipulation. In Proceedings of the 9th International Symposium of Robotics Research, pp 7–14, Snowbird.

    Google Scholar 

  • Chen SF, Kao I (2000) Conservative congruence transformation for joint and cartesian stiffness matrices of robotic hands and fingers. International Journal of Robotics Research, 19: 835–847.

    Article  Google Scholar 

  • Hunt KH (1978) Kinematic geometry of mechanisms. Clarendon Press, Oxford.

    MATH  Google Scholar 

  • Kao I, Ngo C (1999) Properties of grasp stiffness matrix and conservative control strategy. International Journal of Robotics Research, 18:159–167.

    Google Scholar 

  • Mckerrow PJ (1991) Introduction to robotics. Addison-Wesley, New York.

    Google Scholar 

  • Roth B (1984) Screws, motors, and wrenches that cannot be bought in a hardware store. In Proceedings of the 1st International Symposium of Robotics Research, pp 679–693.

    Google Scholar 

  • Salisbury JK (1980) Active stiffness control of a manipulator in cartesian coordinates. In Proceedings of the 19th IEEE Conference on Decision and Control, pp 87–97, Albuquerque.

    Google Scholar 

  • Salisbury JK (1982) Kinematic and force analysis of articulated hands. PhD thesis, Stanford University.

    Google Scholar 

  • Schilling RJ (1990) Fundamentals of robotics. Prentice-Hall, Upper Saddle River, New Jersey.

    Google Scholar 

  • Tsai LW (1999) Robot analysis: the mechanics of serial and parallel manipulators. John Wiley & Sons, New York.

    Google Scholar 

  • Waldron KJ, Wang SL, Bolin SJ (1985) A study of the jacobian matrix of serial manipulators. ASME Journal of Mechanisms, Transmissions, and Automation in Design, 107:230–238.

    Article  Google Scholar 

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© 2003 Springer-Verlag Berlin Heidelberg

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Huang, C., Kao, I. (2003). Geometrical Interpretation of the CCT Stiffness Mapping for Serial Manipulators. In: Jarvis, R.A., Zelinsky, A. (eds) Robotics Research. Springer Tracts in Advanced Robotics, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36460-9_28

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  • DOI: https://doi.org/10.1007/3-540-36460-9_28

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00550-6

  • Online ISBN: 978-3-540-36460-3

  • eBook Packages: Springer Book Archive

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