Frontiers of Mechanical Engineering

, Volume 8, Issue 3, pp 252–260 | Cite as

Kinematic calibration of precise 6-DOF Stewart platform-type positioning systems for radio telescope applications

  • Juan Carlos JáureguiEmail author
  • Eusebio E. Hernández
  • Marco Ceccarelli
  • Carlos López-Cajún
  • Alejandro García
Research Article


The pose accuracy of a parallel robot is a function of the mobile platform posture. Thus, there is no a single value of the robot’s accuracy. In this paper, two novel methods for estimating the accuracy of parallel robots are presented. In the first method, the pose accuracy estimation is calculated by considering the propagation of each error, i.e., error variations are considered as a function of the actuator’s stroke. In the second method, it is considered that each actuator has a constant error at any stroke. Both methods can predict pose accuracy of precise robots at design stages, and/or can reduce calibration time of existing robots. An example of a six degree-of-freedom parallel manipulator is included to show the application of the proposed methods.


pose errors error estimation parallel robot radio telescopes 


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  1. 1.
    Merlet J P. Parallel Robots. Springer, 2006zbMATHGoogle Scholar
  2. 2.
    Masory O, Wang J. On the accuracy of a stewart platform-part I: The effect of manufacturing tolerances. In: IEEE Int. Conf. on Robotics and Automation, Atlanta, 1993, 725–731Google Scholar
  3. 3.
    Merlet J P. Parallel Robots: Open Problems. In: ASME Conference DECT, 2002Google Scholar
  4. 4.
    Castillo E, Takeda Y. Improving path accuracy of a crank-type 6-DOF parallel mechanism by stiction compensation. Mechanism and Machine Theory, 2008, 43(1): 104–114zbMATHCrossRefGoogle Scholar
  5. 5.
    Zhuang H, Roth Z. Method for kinematic calibration of stewart platforms. Journal of Robotic Systems, 1993, 10(3): 391–405zbMATHCrossRefGoogle Scholar
  6. 6.
    Ziegert J C. Volumetric performance of hexapod machine tools, Hexapod Machine Tool Users Group. Internal report 13, 1996Google Scholar
  7. 7.
    Soons J A. Error Analysis of a hexapod machine tool. In: 3rd International Conference and Exhibition on Laser Metrology and Machine Performance, Lamdamap, 1997, 347–358Google Scholar
  8. 8.
    Rudder F F. Thermal expansion of long slender rods with forced convection cooling along the rod length. Report NISTIR, 1997, 5975: 46Google Scholar
  9. 9.
    Gupta K. Measure of positional error for a rigid body. Journal of Mechanical Design, ASME, 1997, 119(3): 346–348CrossRefGoogle Scholar
  10. 10.
    Parenti-Castelli V, Di Gregorio R, Lenarcic J. Sensitivity to geometric parameter variation of a 3 DOF fully-parallel manipulator. In: 3rd International Conference on Advanced Mechatronics JSME, 1998, 364–369Google Scholar
  11. 11.
    Oiwa T, Tamaki M. Study on abbe’s principle in parallel kinematics. In: 2nd Chemnitz Parallel Kinematics Seminar, Chemnitz, 354–352, 2000.Google Scholar
  12. 12.
    Cui H, Zhu Z, Gan Z, Brogangrdh T. Kinematic analysis and error modeling of TAU parallel robot. Robotics and Integrated Manufacturing, 2005, 21(6): 497–505CrossRefGoogle Scholar
  13. 13.
    Brogangrdh T. Device for relative movement of two elements. United States Patent 6425303, 2002.Google Scholar
  14. 14.
    Oiwa T. Error compensation system for joints, links and machine frame of parallel kinematics machines. International Journal of Robotics Research, 2005, 24(12): 1087–1102CrossRefGoogle Scholar
  15. 15.
    Yu A, Bonev I, Zsombor P. Geometric approach to the accuracy of a class of 3-DOF planar parallel robots. Mechanism and Machine Theory, 2008, 43(3): 364–375zbMATHCrossRefGoogle Scholar
  16. 16.
    Briota S, Bonev I. Accuracy analysis of 3-DOF planar parallel robots. Mechanism and Machine Theory, 2008, 43(4): 445–458CrossRefGoogle Scholar
  17. 17.
    Chebbia A, Affia Z, Romdhaneb L. Prediction of the pose errors produced by joints clearance for a 3-UPU parallel robot. Mechanism and Machine Theory, 2009, 44(9): 1768–1783CrossRefGoogle Scholar
  18. 18.
    Pashkevich A, Chablat D, Wenger P. Kinematic Calibration of orthoglide-type mechanism from observation of parallel leg motions. Mechatronics, 2009, 19(4): 478–488CrossRefGoogle Scholar
  19. 19.
    Ren X, Feng Z, Su C A. New calibration method for parallel kinematic machine tools using orientation constraint. International Journal of Machine Tools & Manufacture, 2009, 49(9): 708–721CrossRefGoogle Scholar
  20. 20.
    Hernandez-Martinez E, Ceccarelli M, Carbone G, Lopez-Cajun C, Jauregui-Correa J C. Characterization of a cable-based parallel mechanism for measurement purposes. Mechanism Based Design of Structures and Machines an International Journal, 2010, 38(1): 25–49CrossRefGoogle Scholar
  21. 21.
    Angeles J. On the Nature of the Cartesian Stiffness Matrix. Ingenieria Mecanica Tecnologia Y Desarrollo, 2010, 3(5): 163–170Google Scholar
  22. 22.
    Bohm J, Hefele J, Fritsch D. Towards on-line pose measurement for robots. In: Pattern Recognition, 23rd DAGM Symposium, LCNS-2191, 2003, 298–303Google Scholar
  23. 23.
    Minor M, Merrel R. Instrumentation and algorithms for posture estimation in compliant framed modular mobile robots. International Journal of Robotics Research, 2007, 26(5): 491–512CrossRefGoogle Scholar
  24. 24.
    Gosselin C, Angeles J. Singularity analysis of closed-loop kinematic chains. IEEE Transactions on Robotics and Automation, 1990, 6(3): 281–290CrossRefGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Juan Carlos Jáuregui
    • 1
    Email author
  • Eusebio E. Hernández
    • 2
  • Marco Ceccarelli
    • 3
  • Carlos López-Cajún
    • 4
  • Alejandro García
    • 5
  1. 1.División de Estudios de Posgrado, Facultad de IngenieríaUniversidad Autónoma de Quéretaro QuéretaroQro.Mexico
  2. 2.National Polytechnic Institute, IPN, Section of Graduate Studies and ResearchESIME-UPTMéxico D.F.Mexico
  3. 3.Laboratory of Robotics and Mechatronics University of CassinoCassinoItaly
  4. 4.Universidad Autónoma de Quéretaro QuerétaroQro.México
  5. 5.CIATEQA.C. AguascalientesAgs.México

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