Journal of Mechanical Science and Technology

, Volume 26, Issue 6, pp 1901–1909 | Cite as

A novel six-degrees-of-freedom series-parallel manipulator

  • J. Gallardo-Alvarado
  • R. Rodríguez-Castro
  • C. R. Aguilar-Nájera
  • L. Pérez-González
Article

Abstract

This paper addresses the description and kinematic analyses of a new non-redundant series-parallel manipulator. The primary feature of the robot is to have a decoupled topology consisting of a lower parallel manipulator, for controlling the orientation of the coupler platform, assembled in series connection with a upper parallel manipulator, for controlling the position of the output platform, capable to provide arbitrary poses to the output platform with respect to the fixed platform. The forward displacement analysis is carried-out in semi-closed form solutions by resorting to simple closure equations. On the other hand; the velocity, acceleration and singularity analyses of the manipulator are approached by means of the theory of screws. Simple and compact expressions are derived here for solving the infinitesimal kinematics by taking advantage of the concept of reciprocal screws. Furthermore, the analysis of the Jacobians of the robot shows that the lower parallel manipulator is practically free of singularities. In order to illustrate the performance of the manipulator, a numerical example which consists of solving the inverse/forward kinematics of the series-parallel manipulator as well as its singular configurations is provided.

Keywords

Parallel manipulator Compliant orientation Compliant translation Screw theory Kinematics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M. Zoppi, D. Zlatanov and R. Molfino, On the velocity analysis of interconnected chains mechanisms, Mech. Mach. Theory, 41 (2006) 1346–1358.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    V. E. Gough and S. G. Whitehall, Universal tire testing machine, Proc. of the FISITA Ninth International Technical Congress, IMechE 1 (1962) 117–137.Google Scholar
  3. [3]
    C. Innocenti, Forward kinematics in polynomial form of the general Stewart platform, ASME J. Mech. Des., 123 (2001) 254–260.CrossRefGoogle Scholar
  4. [4]
    L. Rolland, Certified solving of the forward kinematics problem with an exact algebraic method for the general parallel manipulator, Adv. Robotics, 19 (2005) 995–1025.CrossRefGoogle Scholar
  5. [5]
    J. Gallardo-Alvarado, C. R. Aguilar-Nájera, L. Casique-Rosas, J. M. Rico-Martínez and Md. Nazrul Islam, Kinematics and dynamics of 2(3-RPS) manipulators by means of screw theory and the principle of virtual work, Mech. Mach. Theory, 43 (2008) 1281–1294.MATHCrossRefGoogle Scholar
  6. [6]
    I. A. Bonev, Geometric analysis of parallel mechanisms, thèse de doctorat, Université Laval, Canada, November (2002).Google Scholar
  7. [7]
    I. A. Bonev, Direct kinematics of zero-torsion parallel mechanisms, Proc. IEEE International Conference on Robotics and Automation, Pasadena, California, USA, May 19–23, 2008.Google Scholar
  8. [8]
    J. S. Dai, Z. Huang and H. Lipkin, Mobility of overconstrained parallel mechanisms, ASME J. Mech. Des. 128 (2006) 220–229.CrossRefGoogle Scholar
  9. [9]
    K. H. Hunt, Structural kinematics of in-parallel actuated robot arms, ASME J. Mech. Transm. Automat. Des. 105 (1983) 705–712.CrossRefGoogle Scholar
  10. [10]
    K. J. Waldron, M. Raghavan and B. Roth, Kinematics of a hybrid series-parallel manipulation system, ASME J. Dyn. Syst. Meas. Control, 111 (1989) 211–221.CrossRefGoogle Scholar
  11. [11]
    K. M. Lee and S. A. Arjuman, 3-DOF micromotion inparallel actuated manipulator, IEEE Trans. Robotics Automat. 7 (1991) 634–640.CrossRefGoogle Scholar
  12. [12]
    G. H. Pfreundschuh, V. Kumar and T. H. Sugar, Design and control of a three-degree-of-freedom in-parallel actuated manipulator, Proc. of the IEEE International Conference on Robotics and Automation (1991) 1659–1664.Google Scholar
  13. [13]
    Y. G. Li, H. T. Liu, X. M. Zhao, T. Huang and D. Chetwynd, Design of a 3-DOF PKM module for large structural component machining, Mech. Mach. Theory, 45 (2010) 941–954.MATHCrossRefGoogle Scholar
  14. [14]
    J. Gallardo-Alvarado, H. Orozco-Mendoza and J. M. Rico-Martínez, A novel five-degrees-of-freedom decoupled robot, Robotica, 28 (2010) 909–917.CrossRefGoogle Scholar
  15. [15]
    J. Gallardo-Alvarado, DeLiA: a new redundant partially decoupled robot, Adv. Robotics, 25 (2011) 1295–1310.CrossRefGoogle Scholar
  16. [16]
    Y. Lu and T. Leinonen, Solution and simulation of position-orientation for multi-spatial 3-RPS parallel mechanisms in series connection, Multibody Syst. Dyn. 14 (2005) 47–60.MATHCrossRefGoogle Scholar
  17. [17]
    J. Gallardo-Alvarado, C. R. Aguilar-Nájera, L. Casique-Rosas, L. Pérez-González and J. M. Rico-Martínez, Solving the kinematics and dynamics of a modular spatial hyperredundant manipulator by means of screw theory, Multibody Syst. Dyn. 20 (2008) 307–325.MathSciNetMATHCrossRefGoogle Scholar
  18. [18]
    Y. Lu, B. Hu and T. Sun, Analyses of velocity, acceleration, statics, and workspace of a 2(3-SPR) serial-parallel manipulator, Robotica, 27 (2009) 529–538.CrossRefGoogle Scholar
  19. [19]
    G. Gogu, Mobility of mechanisms: a critical review, Mech. Mach. Theory, 40 (2005) 1068–1097.MathSciNetMATHCrossRefGoogle Scholar
  20. [20]
    R. I. Alizade, N. R. Tagiyev and J. Duffy, A forward and reverse displacement analysis of a 6-DOF in-parallel manipulator, Mech. Mach. Theory, 29 (1994) 115–124.CrossRefGoogle Scholar
  21. [21]
    C. Innocenti and V. Parenti-Castelli, Direct position analysis of the Stewart platform mechanism, Mech. Mach. Theory, 35 (1990) 611–621.CrossRefGoogle Scholar
  22. [22]
    S. K. Agrawal, Study of an in-parallel mechanism using reciprocal screws, Proc. of the 8-th World Congress on TMM (1991) 405–408.Google Scholar
  23. [23]
    Z. Huang and Y. F. Fang, Kinematic characteristics analysis of 3 DOF in-parallel actuated pyramid mechanism, Mech. Mach. Theory, 31 (1996) 1009–1018.CrossRefGoogle Scholar
  24. [24]
    Z. Huang and J. Wang, Identification of principal screws of 3-DOF parallel manipulators by quadric degeneration, Mech. Mach. Theory, 16 (2001) 893–911.CrossRefGoogle Scholar
  25. [25]
    Z. Huang, J. Wang and Y. F. Fang, Analysis of instantaneous motions of deficient-rank 3-RPS parallel manipulators, Mech. Mach. Theory, 37 (2002) 229–240.MATHCrossRefGoogle Scholar
  26. [26]
    J. Gallardo, H. Orozco and J. M. Rico, Kinematics of 3-RPS parallel manipulators by means of screw theory, Int. J. Adv. Manufact. Tech. 36 (2008) 598–605.CrossRefGoogle Scholar
  27. [27]
    J. M. Rico-Martínez and J. Duffy, Forward and inverse acceleration analyses of in-parallel manipulators, ASME J. Mech. Des. 122 (2000) 299–303.CrossRefGoogle Scholar
  28. [28]
    H. Lipkin and J. Duffy, The elliptic polarity of screws, ASME J. Mech. Transm. Automat. Des. 107 (1985) 377–388.CrossRefGoogle Scholar
  29. [29]
    J. M. Rico and J. Duffy, An application of screw algebra to the acceleration analysis of serial chains, Mech. Mach. Theory, 31 (1996) 445–457.CrossRefGoogle Scholar
  30. [30]
    J. Gallardo-Alvarado, H. Orozco-Mendoza and R. Rodríguez-Castro, Finding the jerk properties of multibody systems using helicoidal vector fields, Inst. Mech. Engrs. Part C: J. Mech. Eng. Sci., 222 (2008) 2217–2229.CrossRefGoogle Scholar
  31. [31]
    C. Gosselin and J. Angeles, Singularity analysis of closedloop kinematic chains, IEEE Trans. Robotics & Autom., 6 (1990) 261–290.Google Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • J. Gallardo-Alvarado
    • 1
  • R. Rodríguez-Castro
    • 1
  • C. R. Aguilar-Nájera
    • 1
  • L. Pérez-González
    • 1
  1. 1.Department of Mechanical EngineeringInstituto Tecnológico de CelayaCelaya, GTOMéxico

Personalised recommendations