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Comparison of 3-DOF Partially Decoupled Spherical Parallel Manipulators with Respect to Lateral Stabilities

  • Guanglei WuEmail author
  • Huiping Shen
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)

Abstract

This paper deals with the lateral dynamic stabilities for a family of 3-DOF partially decoupled spherical parallel manipulators featuring infinite end-effector rotation. Considering the influence of the rotating speed of the input shaft of the U-joint mechanism, the linearized equation of motion for the lateral vibrations of the manipulators is developed to analyze the stability problem, resorting to the Floquet theory. An approach based on the utilization of the monodromy matrix approach and Floquet theory is applied to the parallel mechanism with a U joint working as transmitting mechanism. Critical rotating speeds of the driving shaft are identified for the structural design and operational speeds of the manipulators.

Keywords

spherical parallel manipulator lateral stability monodromy matrix Floquet theory critical speed 

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Notes

Acknowledgement

The work is supported by the Natural Science Foundation of Liaoning Province (No. 20180520028), Doctoral Start-up Foundation of Liaoning Province (No. 20170520134) and Applied Basic Research Programs of Changzhou (No. CJ20180017).

References

  1. 1.
    Abramowitz, M., Stegun, I.A., Romain, J.E.: Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables, chap. 20. Dover Publications (1972)Google Scholar
  2. 2.
    Asada, H., Granito, J.: Kinematic and static characterization of wrist joints and their optimal design. In: IEEE Int. Conf. Robot. Autom., pp. 244–250 (1985)Google Scholar
  3. 3.
    Bulut, G., Parlar, Z.: Dynamic stability of a shaft system connected through a hooke’s joint. Mech. Mach. Theory 46(11), 1689–1695 (2011)CrossRefGoogle Scholar
  4. 4.
    Chicone, C.: Ordinary Differential Equations with Applications, chap. 2. Springer, New York, NY (2006)Google Scholar
  5. 5.
    Gosselin, C.: Stiffness mapping for parallel manipulators. IEEE Trans. Robot. Autom. 6(3), 377–382 (1990)CrossRefGoogle Scholar
  6. 6.
    Jalón, J.G.D., Bayo, E.: Kinematic and Dynamic Simulation of Multibody Systems: The Real-Time Challenge, chap. 4. Springer New York (1994)Google Scholar
  7. 7.
    Kang, Y., Shen, Y., Zhang,W., Yang, J.: Stability region of floating intermediate support in a shaft system with multiple universal joints. J. Mech. Sci. Technol. 28(7), 2733–2742 (2014)CrossRefGoogle Scholar
  8. 8.
    Kuchment, P.A.: Floquet Theory For Partial Differential Equations, chap. 4. Birkhauser Verlag (1993)Google Scholar
  9. 9.
    Mazzei Jr, A.J., Argento, A., Scott, R.A.: Dynamic stability of a rotating shaft driven through a universal joint. J. Sound Vib. 222(1), 19–47 (1999)Google Scholar
  10. 10.
    Nikravesh, P.: Computer-Aided Analysis of Mechanical Systems, chap. 11. Prentice Hall, Englewood Cliffs, New Jersey (1988)Google Scholar
  11. 11.
    Ota, H., Kato, M., Sugita, H.: Lateral vibrations of a rotating shaft driven by a universal joint–2nd report. Bulletin of the JSME 28, 1749–1755 (1985)Google Scholar
  12. 12.
    Porter, B., Gregory, R.W.: Non-linear torsional oscillation of a system incorporating a hooke’s joint. ARCHIVE J. Mech. Eng. Sci. 5(2), 191–209 (1963)CrossRefGoogle Scholar
  13. 13.
    Rosenberg, R.M.: On the dynamical behavior of rotating shafts driven by universal (hooke) couplings. ASME J. Appl. Mech. 25(1), 47–51 (1958)Google Scholar
  14. 14.
    Saigo, M., Okada, Y., Ono, K.: Self-excited vibration caused by internal friction in universal joints and its stabilizing method. J. Vib. Acoust. 119(2), 221–229 (1997)CrossRefGoogle Scholar
  15. 15.
    Szymkiewicz, R.: Numerical Solution of Ordinary Differential Equations, chap. 4. Academic Press (1971)Google Scholar
  16. 16.
    Teschl, G.: Ordinary Differential Equations and Dynamical Systems, chap. 3. Providence: American Mathematical Society (2012)Google Scholar
  17. 17.
    Wu, G.: Parameter-excited instabilities of a 2UPU-RUR-RPS spherical parallel manipulator with a driven universal joint. ASME J. Mech. Des. 140(9), 092,303 (2018)CrossRefGoogle Scholar
  18. 18.
    Wu, G., Caro, S., Wang, J.: Design and transmission analysis of an asymmetrical spherical parallel manipulator. Mech. Mach. Theory 94, 119–131 (2015)CrossRefGoogle Scholar
  19. 19.
    Wu, G., Zou, P.: Comparison of 3-dof asymmetrical spherical parallel manipulators with respect to motion/force transmission and stiffness. Mech. Mach. Theory 105, 369–387 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringDalian University of TechnologyDalianChina
  2. 2.School of Mechanical EngineeringChangzhou UniversityChangzhouChina

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