ROMANSY 11 pp 53-60 | Cite as

An Inverse Force Analysis of the Spherical 3-DOF Parallel Manipulator with Three Linear Actuators Considered as Spring System

  • J. Knapczyk
  • G. Tora
Part of the International Centre for Mechanical Sciences book series (CISM, volume 381)


The subject of our investigation is the spherical 3-DOF parallel manipulator with three linear actuators, any of them is attached to the base with a universal joint and to the platform with a spherical joint (see Fig.1). The fourth spherical joint between the platform and the base permits the spherical motion of the platform. Similar mechanical structures are widely used as mounting or supporting structures for solar panels, telescopes, radar and satellite antennas, mirrors for laser beams etc.


Parallel Manipulator Angular Displacement Spherical Joint Linear Actuator Compliance Matrix 
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  1. [1]
    Dietmaier P.: „An Inverse Force Analysis of a Tetrahedral Three-Spring System.“ Trans.ASME, Jnl of Mechanical Design, V.117, June 1995, pp.286–291.Google Scholar
  2. [2]
    Gosselin C.M., Sefriouri J., Richard M.J.: „On the Direct Kinematics of Spherical ThreeDegree-of-Freedom Parallel Manipulators of General Architecture.“ Trans.ASME, Jnl of Mechanical Design, V. 116, June 1994, pp. 594–598.CrossRefGoogle Scholar
  3. [3]
    Griffis M., Duffy J.: „Global Stiffness Modelling of a Class of Simple Compliant Couplings.“ Mech. Mach. Theory. V. 28, No. 2, pp. 207–224, 1993.CrossRefGoogle Scholar
  4. [4]
    Husain M., Waldron K.J.: „Kinematics of a Three-Limbed Mixed Mechanism.“ Trans.ASME, Jnl of Mechanical Design, Sept. 1994, pp. 924–929.Google Scholar
  5. [5]
    Innocenti C., Parenti-Castelli V.: „Echelon Form Solution of Direct Kinematics for the General Fully-Parellel Spherical Wrist.“ Mech.Mach.Theory, V. 28, No. 4, pp. 553–561, 1993.CrossRefMathSciNetGoogle Scholar
  6. [6]
    Knapczyk J., Dzierzek S.: „Displacement and Force Analysis of Five-Rod Suspension with Flexible Joints. Trans.ASME, Jnl of Mechanical Design, V. 117, Dec.1995, pp. 532–538.CrossRefGoogle Scholar
  7. [7]
    Wohlhart K.: „Displacement Analysis of the General Spherical Stewart Platform.“ Mech. Mach. Theory, V.29, No.4, pp.581–589, 1994.Google Scholar

Copyright information

© Springer-Verlag Wien 1997

Authors and Affiliations

  • J. Knapczyk
    • 1
  • G. Tora
    • 1
  1. 1.Cracow University of TechnologyCracowPoland

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