Platform Parallel Manipulators

  • Adam Morecki
  • Józef Knapczyk
Part of the International Centre for Mechanical Sciences book series (CISM, volume 402)


Parallel manipulators are closed chains with one or more loops where only some kinematic pairs are actively controlled. The most common arrangement comprises a base connected via serial, parallel, or hybrid (serial-parallel) chains to the output link (platform). Actuated pairs provide the platform with the desired degrees of freedom (DOF) relative to the base. Fully parallel manipulators are characterized by six binary legs, each attached to the base and the platform through spherical joints. There may be up to six legs of controllable, variable length, providing the platform with a corresponding number of dofs. Each leg can be regarded as a serial manipulator with six revolutes, or five revolutes and one prismatic pair. Usually, three of the revolutes with intersecting axes in one point constitute the spherical joint at the platform, while two more constitute a universal joint at the base, i.e. the concatenation of two revolutes with intersecting axes. Of these six joints, only one is actuated.


Parallel Manipulator Revolute Joint Spherical Joint Platform Manipulator Stewart Platform 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [7.1]
    Dasgupta B., Mruthyunjaya TS: A canonical formulation of the direct position kinematics problem for a general 6–6 Stewart Platform. Mech.Mach.Theory, Vol. 29, No 6, pp. 819–27, 1994.CrossRefGoogle Scholar
  2. [7.2]
    Gosselin C., Angeles J: The Optimum Kinematic Design of a Planar 3-DOF Parallel Manipulator. Trans. ASME, Jnl of Mech. Transm. Autom. Design, Vol. 110, pp. 35–41, March 1988.CrossRefGoogle Scholar
  3. [7.3]
    Gosselin C, Angeles J.: The Optimum Kinematic Design of a Spherical 3-DOF Parallel Manipulator. Trans. ASME, Jnl of Mech. Transm. Autom. Design, Vol.1 11, No 2, pp. 202207, 1989.Google Scholar
  4. [7.4]
    Gosselin C.M.: Parallel Computational Algorithms for the Kinematics and Dynamics of Spatial Parallel Manipulators. Trans.ASME, Jnl Dyn.Syst. Measur. Control, Vo1, 118, pp. 2228, March 1996.Google Scholar
  5. [7.5]
    Hunt K.H., Primrose E.I.: Assembly Configurations of Some In-Parallel-Actuated Manipulators. Mech. Mach. Theory, Vol.28, No 1, pp.31–42, 199 3.Google Scholar
  6. [7.6]
    Rusty M.L.: An Algorithm for solving the direct kinematics of general Stewart-Gough Platforms. Mech. Mach. Theory, Vol. 31, No 4, pp. 365–380, 1996CrossRefADSGoogle Scholar
  7. [7.7]
    Husain M, Waldron K.J.: Direct Position Kinematics of the 3–1–1–1 Stewart Platform. Trans.ASME, Jnl of Mech.Design, Vol.116, Dec.1994, pp. 1 102–7.Google Scholar
  8. [7.8]
    Innocenti C.: Algorithm for Kinematic Calibration of Fu Ily Parallel Manipulators. Computational Kinematics. Kluwer Acad.Publ. 1995, pp. 241–250.Google Scholar
  9. [7.9]
    Innocenti C’.: Direct Kinematics in Analytical Form of the 6–4 Fully-Prallel Mechanism. Trans.ASME, Jnl of Mech.Design, Vol.117, March 199. 5, pp. 89–95.Google Scholar
  10. [7.10]
    Innocenti C., Parenti-Castelli V.: Symbolic-Form Forward Kinematics of a 5–4 Fully-Parallel Manipulator. Advances in Robot Kinematics and Conip. Geometry, Kluwer Acad.Publ. 1994, pp. 429–438.Google Scholar
  11. [7.11]
    Innocenti C., Parenti-Castelli V.: Closed-Form Direct Positions Analysis of 5–5 Parallel Mechanism. Trans.ASME, Jnl of Mech.Design, Vol.115, Sept. 1993, pp. 515–521.Google Scholar
  12. [7.12]
    Innocenti C. Parenti-Castelli V.: Echelon Form Solution of Direct Kinematics for the General Fully-Parallel Spherical Wrist. Mech. Mach. Theory, Vol. 28, No 4, pp. 553–561, 1993.CrossRefGoogle Scholar
  13. [7.13]
    Ji Z.: Analysis of Design Parameters in Platform Manipulators. Trans.ASME, Jill of Mech.Design, Vol. 1 18, Dec.1996, pp. 526–531.CrossRefGoogle Scholar
  14. [7.14]
    Knapczyk.1., Dzieriek S.: Displacement and Force Analysisi of Five-Rod Suspension with Flexible Joints. Trans.ASME, Jnl of Mech.Design, Vol. 117, Dec.1995, pp. 532–538.CrossRefGoogle Scholar
  15. [7.15]
    Knapczyk J., Dzieriek S.: Kinematic Analysis of 6S–5S Stewart Platform by Using Vector Method. Prc. of the 3rd Int. Workshop on Advances in Robot Kinematics, Ferrara 1992, pp. 123–128.Google Scholar
  16. [7.16]
    Knapczyk J., Tara G.: An Inverse Force Analysis of Spherical 3 DOF Parallel Manipulator with Three Linear Actuators Considered as Spring System. Proc. the 1 Ith CISM-IFToMM Symp. Romansy’ 11, Springer Wien New York 1997, pp. 53–62.Google Scholar
  17. [7.17]
    Lin W., Griffis M, Duffy J.: Forward Displacement Analysis of the 4–4 Stewart Platform. Trans.ASME, Jn1 of Mech.Design, Vol.114, Sept.1992, pp. 444–450.Google Scholar
  18. [7.18]
    Luh C.M. at all: Working Capability Analysis of Stewart Platforms. Trans.ASME, Jill of Mech.Design, Vol.118, June. 1996, pp. 220–227.Google Scholar
  19. [7.19]
    Merlet J.P.: Les robots paralles. Hermes, Paris 1990.Google Scholar
  20. [7.20]
    Murthy V., Waldron K.J.: Position Kinematics of the Generalized Lobster Arm and Its Series-Parallel Dual. Trans.ASME, Jn1 of Mech.Design, Vol. 114, Sept.1992, pp. 406–413.CrossRefGoogle Scholar
  21. [7.21]
    Nielsen J., Roth B.: The direct kinematics of the general 6–5 Stewart-Gough mechanism. Recent Advances in Robot Kinematics. Kluwer Acad.Publ. 1996, pp. 7–16.Google Scholar
  22. [7.22]
    Parenti-Castelli V.: Recent techniques for direct position analysis of the generalized Stewart platform mechanism. Proc. of the 3rd Int. Workshop on Advances in Robot Kinematics, Ferrara 1992, pp. 129–135.Google Scholar
  23. [7.23]
    Raghavan M: The Stewart Platform of General Geometry Has 40 Configurations. Trans.ASME, Jnl of Mech.Design, Vol.115, June 1993, pp. 277–282.Google Scholar
  24. [7.24]
    Pennock G.R., Kassner D.J.: Kinematic Analysis of a Planar Eight-Bar Linakage: Application to Platform Type Robot. Trans.ASME, Jnl of Mech.Design, Vol. 114, March 1992, pp. 87–95.CrossRefGoogle Scholar
  25. [7.25]
    Shi X, Fenton R.G.: Solution to the Forward Instantaneous Kinematics for a General 6-DOF Stewart Platform. Mech. Mach. Theory, Vol. 27, No 3, pp. 251–259, 1992.CrossRefGoogle Scholar
  26. [7.26]
    Sternheim F.: Computation of the direct and inverse geometric models of the Delta 4 parallel robot. Robotersysteme 3, pp. 199–203, 1987.Google Scholar
  27. [7.27]
    Waldron K.J., Raghavan M, Roth B.: Kinematics of a Hybrid Series-Parallel Manipulation System. Trans.ASME, Jnl of Dyn. Syst. Meas. Control, Vol. 3, pp. 211–221, 1980.Google Scholar
  28. [7.28]
    Wohlhart K.: Direct Kinematic Solution of the General Planar Stewart Platform. Proc. Of Int. Conf. on Computer Integrated Manufacturing, pp.401–411, Zakopane 1992.Google Scholar
  29. [7.29]
    Wohlhart K: A Parallel Redundant Manipulator Based on the Assur Group (3,4). Proc. Of Int. Conf. on Computer Integrated Manufacturing, pp.371–8, Zakopane 1994.Google Scholar
  30. [7.30]
    Wohlhart K: Position Analysis of the Rhombic Assur Group. Proc. of the 10th CISMIFToMM Symp. Romansy’ 10, Gdansk 1994.Google Scholar
  31. [7.31]
    Yang P.H., Waldron K.J.: Kinematics of a 3-DOF Motion Platform for a Low-Cost Driving Simulator. Recent Advances in Robot Kinematics, pp. 89–98, Kluwer Acad. Publ. 1996.Google Scholar

Copyright information

© Springer-Verlag Wien 1999

Authors and Affiliations

  • Adam Morecki
    • 1
  • Józef Knapczyk
    • 2
  1. 1.Warsaw University of TechnologyPoland
  2. 2.Cracow University of TechnologyPoland

Personalised recommendations