The Inverse Kinematics of Manipulators

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


The objective of inverse kinematics task is to find all the possible sets of angular or linear displacements (configuration coordinates) in the joints that allow of the end-effector (gripper or tool) of the manipulator to assume a certain position and/or orientation. This is a fundamental problem in the programming and control of manipulator motion, when it is necessary to determine how particular configuration coordinates change in time, in order to have the end-effector perform a desired motion of [4.2, 4.6–4.17]. For instance, in the simplest positioning task, “take and place”, the initial and final position of the end-effector are given as the time it takes to cover the distance between those two positions. The inverse kinematics solution entails determining the values of the configuration coordinates corresponding to these positions.


Unit Vector Position Vector Robot Manipulator Inverse Kinematic Kinematic Chain 
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.


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  1. [4.1]
    Angeles J: Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms. New York, Springer Verlag. 1997.CrossRefMATHGoogle Scholar
  2. [4.2]
    Craig JJ: Introduction to Robotics. Addison-Wesley 1989Google Scholar
  3. [4.3]
    Duffj J: Analysis of Mechanisms and Robot Manipulators. London, E. Arnold, 1980.Google Scholar
  4. [4.4]
    Frolov K. V, Vorobiev E. J.: Mechanics of Industrial Robots. Vyssaja Skola, Moscow 1988.Google Scholar
  5. [4.5]
    Fu K. S, Gonzales R. C., Lee C. S. G.: Robotics: Control, Sensing, Vision, and Inteligence. McGraw-Hill 1987.Google Scholar
  6. [4.6a]
    Hunt K. H.: Robot Kinematics. A Compact Analytic Inverse Solution for Velocities. Trans. ASME, Mech., Transm. and Autom. in Design, vol. 109, s. 42–49, 1987.Google Scholar
  7. [4.6b]
    Hunt K. H.: The particular or the general? (some examples from robot kinematics). Mech. and Mach. Theory, vol. 21, no 6, s. 481–487, 1989.Google Scholar
  8. [4.7]
    Knapczyk J, Lebiediew P. A.: Theory of Spatial Mechanisms and Manipulators. Warszawa, WNT, 1990 (in Polish).Google Scholar
  9. [4.8]
    Lee H. Y., Woernle C., Hiller M.: A Complete Solution for the Inverse Kinematic Problem of the General 6R Robot Manipulator. Trans. ASME, Mech., Transm. and Autom. in Design, vol. 113, s. 481–486, 1991.Google Scholar
  10. [4.9]
    Lipkin H., Duffy J.: A Vector Analysis of Robot Manipulators. Recent Advances in Robotics. New York, Wiley, 1985.Google Scholar
  11. [4.10]
    Litvin F. L., Parenti Castelli V, Phillips R. H.: Manipulators: Execution of Prescribed Trajectories. Special Link Positions and Versions of Assembly. Mech. and Mach. Theory, vol. 21, no 2, s. 173–185, 1986.Google Scholar
  12. [4.11]
    Lloyd J., Hayward V.: Kinematics of Common Industrial Robots. Robotics 4 (1988), s. 169–191.Google Scholar
  13. [4.12]
    Manseur R., Doty K. L.: A Fast Algorithm for Inverse Kinematic Analysis of Robot Manipulators. Int. Robotics Research, vol. 7, no 3, s. 52–63, 1988.Google Scholar
  14. [4.13]
    Paul R. P.: Robot Manipulators: Mathematics, Programming and Control. Cambridge, MIT Press, 1981.Google Scholar
  15. [4.14]
    Pennock G. R., Yang A. T: Application of Dual-Number Matrices to the Inverse Kinematics Problem of Robot Manipulators. Trans. ASME, Mech. Transm. and Autom. in Design, vol. 107, no 2, s. 201–208, 1985.Google Scholar
  16. [4.15]
    Pieper D.L.: The Kinematics of Manipulators under Computer Control. Ph. D.Thesis, Stanford Univ. 1968.Google Scholar
  17. [4.16]
    Raghavan M, Roth B.: A General Solution for the Inverse Kinematics of all Series Chains. Proc. of the 8th CISM-IFToMM Symp. RoManSy’90 Cracow 1990, s.21–28.Google Scholar
  18. [4.17]
    Ranky P. G., Ho C. Y.: Robot Modelling Control and Applications with Software. Kempston, JFS 1985.Google Scholar
  19. [4.18]
    Tsai L. W., Morgan A.: Solving the Kinematics of the Most General Six-and Five-Degreeof-Freedom Mnipulators by Continuation Methods. Trans. ASME, Mech., Transm. and Autom. in Design, vol. 107, s. 189–200, 1985.Google Scholar
  20. [4.19]
    Angeles J, Zanganeh K E.: The semigraphical Determination of All Real Solutions of General Six-Revolute Manipulators. Proc. of the 9th CISM-IFToMM Symp. RoManSy’92, Udine. Springer Verlag 1993, s. 23–32.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

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