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Multibody System Dynamics

, 23:57 | Cite as

A new family of constrained redundant parallel manipulators

  • J. Gallardo-AlvaradoEmail author
  • G. Alici
  • L. Pérez-González
Article

Abstract

This paper addresses the description and kinematic analysis of a new family of redundant parallel manipulators. The primary feature of the new family is to have a compact topology consisting of multi-degree of freedom non-identical limbs. In order to simplify the forward position analysis, the motion of the end-effector (platform) is decoupled into translational and rotational components with respect to the base. This kind of topology is in agreement with the parallel manipulator definition of IFToMM—a parallel manipulator “…that controls the motion of its end-effector by means of at least two kinematic chains going from the end effector towards the frame…”. In fact, adding a kinematic pair to a limb of a non-redundant parallel manipulator creates asymmetrical parallel manipulator. Analytical expressions for the forward position, velocity, and acceleration of the parallel manipulators have been obtained and solved for an exemplary 7-DOF redundant parallel manipulator. The numerical results from the analytical expressions are verified by comparing them to the results from a mechanical system simulation software as if a real parallel manipulator is being run to collect the position, velocity, and acceleration data. Finally, based on the velocity formulation, the singularity analysis of the manipulator is also provided.

Keywords

Redundant parallel manipulator Decoupled motion Closed-form solution Klein form Screw theory Kinematics 

References

  1. 1.
    Ropponen, T., Nakamura, Y.: Singularity-free parameterization and performance analysis of actuation redundancy. In: IEEE International Conference on Robotics and Automation, Cincinnati, OH, pp. 806–811 (1990) Google Scholar
  2. 2.
    Zergeroglu, E., Dawson, D.D., Walker, I.W., Setlur, P.: Nonlinear tracking control of kinematically redundant robot manipulators. IEEE/ASME Trans. Mechatron. 9(1), 129–132 (2004) CrossRefGoogle Scholar
  3. 3.
    Kim, S.W., Park, K.B., Lee, J.J.: Redundancy resolution of robot manipulators using optimal kinematic control. In: IEEE International Conference on Robotics and Automation, pp. 683–688 (1994) Google Scholar
  4. 4.
    Hsia, T.C., Guo, Z.Y.: New inverse kinematic algorithms for redundant robots. J. Robot. Syst. 8(1), 117–132 (1991) zbMATHCrossRefGoogle Scholar
  5. 5.
    Suh, I.H., Shin, K.G.: Coordination of dual robot arms using kinematic redundancy. IEEE Trans. Robot. Autom. 5(2), 236–242 (1989) CrossRefGoogle Scholar
  6. 6.
    Nguyen, L.A., Walker, I.D., Defigueiredo, R.J.P.: Dynamic control of flexible kinematically redundant robot manipulators. IEEE Trans. Robot. Autom. 8(6), 759–767 (1992) CrossRefGoogle Scholar
  7. 7.
    Chen, T.H., Cheng, F.T., Sun, Y.Y., Hung, M.H.: Torque optimization schemes for kinematically redundant manipulators. J. Robot. Syst. 11(4), 257–269 (1994) zbMATHCrossRefGoogle Scholar
  8. 8.
    Dasgupta, B., Mruthyunjaya, T.S.: Force redundancy in parallel manipulators: theoretical and practical issues. Mech. Mach. Theory 33(6), 727–742 (1998) zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Mohamed, M.G., Gosselin, C.M.: Design and analysis of kinematically redundant parallel manipulators with configurable platforms. IEEE Trans. Robot. 21(3), 277–287 (2005) CrossRefGoogle Scholar
  10. 10.
    Wang, J., Gosselin, C.M.: Kinematic analysis and Design of kinematically redundant parallel manipulators. ASME J. Mech. Des. 126(1), 109–118 (2004) CrossRefGoogle Scholar
  11. 11.
    Nokleby, S.B., Fisher, R., Podhorodeski, R.P., Firmani, F.: Force capabilities of redundantly-actuated parallel manipulators. Mech. Mach. Theory 40(5), 578–599 (2005) zbMATHCrossRefGoogle Scholar
  12. 12.
    Merlet, J.-P.: Redundant parallel manipulators. Rep. Lab. Robot. Autom. 8(1), 17–24 (1996) CrossRefGoogle Scholar
  13. 13.
    O’Brien, J.F., Wen, J.T.: Redundant actuation for improving kinematic manipulability. In: IEEE International Conference on Robotics and Automation, Detroit, MI, USA, May 1999, pp. 1520–1525 (1999) Google Scholar
  14. 14.
    Cheng, H., Yiu, Y.K., Li, Z.: Dynamics and control of redundantly actuated parallel manipulators. IEEE/ASME Trans. Mechatron. 8(4), 483–491 (2003) CrossRefGoogle Scholar
  15. 15.
    Kim, S.: Operational quality analysis of parallel manipulators with actuation redundancy. In: IEEE International Conference on Robotics and Automation, Albuquerque, NM, USA, April 1997, pp. 2651–2656 (1997) Google Scholar
  16. 16.
    Kock, S., Schumacher, W.: A parallel x-y manipulator with actuation redundancy for high speed and active stiffness applications. In: IEEE International Conference on Robotics and Automation, Leuven, Belgium, May 1998, pp. 2295–2300 (1998) Google Scholar
  17. 17.
    Kurtz, R., Hayward, V.: Multiple-goal kinematic optimization of a parallel spherical mechanism and actuator redundancy. IEEE Trans. Robot. Autom. 8(5), 644–651 (1992) CrossRefGoogle Scholar
  18. 18.
    Müller, A.: Internal preload control of redundantly actuated parallel manipulators—its application to backlash avoiding control. IEEE Trans. Robot. 21(4), 668–677 (2005) CrossRefGoogle Scholar
  19. 19.
    Gallardo, J., Rico, J.M., Alici, G.: Kinematics and singularity analyses of a 4-DOF parallel manipulator using screw theory. Mech. Mach. Theory 41, 1048–1061 (2006) zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Rico, J.M., Aguilera, D., Gallardo, J., Orozco, H., Rodríguez, R.: A more general mobility criterion for parallel platforms. ASME J. Mech. Des. 128(1), 207–219 (2006) CrossRefGoogle Scholar
  21. 21.
    Sugimoto, K., Duffy, J.: Application of linear algebra to screw systems. Mech. Mach. Theory 17(1), 73–83 (1982) CrossRefGoogle Scholar
  22. 22.
    Rico, J.M., Duffy, J.: An application of screw algebra to the acceleration analysis of serial chains. Mech. Mach. Theory 31(4), 445–457 (1996) CrossRefMathSciNetGoogle Scholar
  23. 23.
    Rico, J.M., Gallardo, J., Duffy, J.: A determination of singular configurations of serial non-redundant manipulators, and their escapement from singularities using Lie products. In: Merlet, J.-P., Ravani, B. (eds.) Computational Kinematics ’95, pp. 143–152. Kluwer Academic, Dordrecht (1995) Google Scholar
  24. 24.
    Alici, G., Shirinzadeh, B.: Loci of singular configurations of a 3-DOF spherical parallel manipulator. J. Robot. Auton. Syst. 48, 77–91 (2004) CrossRefGoogle Scholar
  25. 25.
    Alici, G., Shirinzadeh, B.: Topology optimization and singularity analysis of a 3-SPS parallel manipulator with a passive constraining spherical joint. Mech. Mach. Theory 39(2), 215–235 (2004) zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • J. Gallardo-Alvarado
    • 1
    Email author
  • G. Alici
    • 2
  • L. Pérez-González
    • 1
  1. 1.Department of Mechanical EngineeringInstituto Tecnológico de CelayaCelaya, Gto.Mexico
  2. 2.School of Mechanical, Materials, and Mechatronic EngineeringUniversity of WollongongWollongongAustralia

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