Skip to main content
Chinese Journal of Mechanical Engineering
Download PDF
  • Published:

Running accuracy analysis of a 3-RRR parallel kinematic machine considering the deformations of the links

Chinese Journal of Mechanical Engineering volume 27, pages 890–899 (2014)Cite this article

Abstract

Parallel kinematic machines have drawn considerable attention and have been widely used in some special fields. However, high precision is still one of the challenges when they are used for advanced machine tools. One of the main reasons is that the kinematic chains of parallel kinematic machines are composed of elongated links that can easily suffer deformations, especially at high speeds and under heavy loads. A 3-RRR parallel kinematic machine is taken as a study object for investigating its accuracy with the consideration of the deformations of its links during the motion process. Based on the dynamic model constructed by the Newton-Euler method, all the inertia loads and constraint forces of the links are computed and their deformations are derived. Then the kinematic errors of the machine are derived with the consideration of the deformations of the links. Through further derivation, the accuracy of the machine is given in a simple explicit expression, which will be helpful to increase the calculating speed. The accuracy of this machine when following a selected circle path is simulated. The influences of magnitude of the maximum acceleration and external loads on the running accuracy of the machine are investigated. The results show that the external loads will deteriorate the accuracy of the machine tremendously when their direction coincides with the direction of the worst stiffness of the machine. The proposed method provides a solution for predicting the running accuracy of the parallel kinematic machines and can also be used in their design optimization as well as selection of suitable running parameters.

References

  1. WECH M, STAIMER D. Parallel kinematic machine tools-current state and future[J]. CIRP Annals-Manufacturing Technology, 2012, 51(2): 671–683.

    Article  Google Scholar 

  2. LI Yangmin, XU Qingsong. Kinematic analysis of a 3-PRS parallel manipulator[J]. Robotics and Computer-Integrated Manufacturing, 2007, 23(4): 395–408.

    Article  Google Scholar 

  3. LEBRET G, LIU K, LEWIS F L. Dynamic analysis and control of a Stewart platform manipulator[J]. Journal of Robotic System, 1993, 10(5): 629–655.

    Article  MATH  Google Scholar 

  4. TANG Xiaoqiang, WANG Jinsong, GAO Men. Kinematic calibration of gantry hybrid machine tool based on estimation error and local measurement information[J]. International Journal of Advanced Manufacturing, 2005, 26(4): 382–390.

    Article  Google Scholar 

  5. YAO Rui, ZHU Wenbai, HUANG Peng. Accuracy analysis of stewart platform based on interval analysis method[J]. Chinese Journal of Mechanical Engineering, 2013, 26(1): 29–34.

    Article  Google Scholar 

  6. BIAN Bian, HUANG Hai. Integrated design for configuration/ vibration control of hexapod platform[J]. Chinese Journal of Mechanical Engineering, 2009, 45(11): 72–77. (in Chinese)

    Article  Google Scholar 

  7. SONG J, MOU J I, KING C. Error modeling and compensation for parallel kinematic machines[C]//The 1st European-American forum on Parallel Kinematic Machine, Milan, Italy, 1999: 171–187.

    Chapter  Google Scholar 

  8. BRIOT S, BONEV I A. Are parallel robots more accurate than serial robots[J]. Transactions of the Canadian Society for Mechanical Engineering, 2007, 31(4): 445–455.

    MATH  Google Scholar 

  9. BONEV I A, ZLATANOV D, GOSSELIN C M. Singularity analysis of a 3-DOF planar parallel mechanism via screw theory[J]. Journal of Mechanical Design, 2003, 125(3): 573–581.

    Article  Google Scholar 

  10. JOUBAIR A, SLAMANI M, BONEV I A. A novel XY-Theta precision table and a geometric procedure for its kinematic calibration[J]. Robotics and Computer-Integrated Manufacturing, 2012, 28(1): 57–65.

    Article  Google Scholar 

  11. JOUBAIR A, SLAMANI M, BONEV I A. Kinematic calibration of a five-bar planar parallel robot using all working modes[J]. Robotics and Computer-Integrated Manufacturing, 2013, 29(4): 15–25.

    Article  Google Scholar 

  12. CHANG Peng, LI Chengrong, LI Tiemin. Kinemaitc Calibration and forecast error compensation of a 2-DOF planar manipulator[J]. Chinese Journal of Mechanical Engineering, 2011, 24(6): 992–998.

    Article  Google Scholar 

  13. YU Yueqing, DU Zhaocai, YANG Jianxin, et al. An experimental study on the dynamics of a 3-RRR flexible parallel robot[J]. IEEE Transactions on Robotics, 2011, 27(5): 992–997.

    Article  Google Scholar 

  14. BRIOT S, BONEV I A. Accuracy analysis of 3-DOF planar parallel robots[J]. Mechanism and Machine Theory, 2008, 43(4): 445–458.

    Article  MATH  Google Scholar 

  15. DWIVEDY S K, EBERHARD P. Dynamic analysis of flexible manipulators, a literature review[J]. Mechanical and Machine Theory, 2006, 41(7): 749–777.

    Article  MathSciNet  MATH  Google Scholar 

  16. PIRAS G, CLEGHORN W L, MILLS J K. Dynamic finite-element analysis of a planar high-speed, high-precision parallel manipulator with flexible links[J]. Mechanism and Machine Theory, 2005, 40(7): 849–862.

    Article  MATH  Google Scholar 

  17. ZHANG Xuping, MILLS J K, CLEGHORN W L. Dynamic modeling and experimental validation of a 3-PRR parallel manipulator with flexible intermediate links[J]. Journal of Intelligent and Robotic Systems, 2007, 50(4): 323–340.

    Article  MATH  Google Scholar 

  18. WANG Xiaoyun, MILLS J K. FEM dynamic model for active vibration control of flexible linkages and its application to a planar parallel manipulator[J]. Applied Acoustics, 2005, 66(10): 1151–1161.

    Article  Google Scholar 

  19. ZHOU Z, XI J, MECHEFSKE C K. Modeling of a fully flexible 3PRS manipulator for vibration analysis[J]. Journal of Mechanical Design, 2006, 128(2): 403–412.

    Article  Google Scholar 

  20. GOSSELIN C M. The optimum design of robotic manipulators using dexterity indices[J]. Robotics and Autonomous Systems, 1992, 9(4): 213–226.

    Article  Google Scholar 

  21. GOSSELIN C M, ANGELES J. A global performance index for the kinematic optimization of robotic manipulators[J]. Journal of Mechanical Design, 1991, 113(3): 220–226.

    Article  Google Scholar 

  22. YU A, BONEV I A, ZSOMBOR-MURRAY P. Geometric approach to the accuracy analysis of a class of 3-DOF planar parallel robots[J]. Mechanism and Machine Theory, 2008, 43(3): 364–375.

    Article  MATH  Google Scholar 

  23. MERLET J P. Computing the worst case accuracy of a PKM over a workspace or a trajectory[C]//The 5th Chemnitz Parallel Kinematics Seminar, Chemnitz, Germany, 2006: 83–96.

    Google Scholar 

  24. BRIOT S, BONEV I A. A pair of measures of rotational error for axisymmetric robot end-effectors[C]//Advances in Robot Kinematics, 11th International Symposium, France, 2008: 345–352.

    Google Scholar 

  25. MERLET J P. Jacobian, manipulability, condition number, and accuracy of parallel robots[J]. Journal of Mechanical Design, 2006, 128(1): 199–206.

    Article  Google Scholar 

  26. ARSENAULT M, BOUDREAU R. Synthesis of planar parallel mechanisms while considering workspace, dexterity, stiffness and singularity avoidance[J]. Journal of Mechanical Design, 2006, 128(1): 69–78.

    Article  Google Scholar 

  27. ARAKELIAN V H, SMITH M R. Design of planar 3-DOF 3-RRR reactionless parallel manipulators[J]. Mechantronics, 2008, 18(10): 601–606.

    Article  Google Scholar 

  28. SHAO Zhufeng, TANG Xiaoqiang, CHEN Xu, et al. Inertia match of a 3-RRR reconfigurable planar parallel manipulator[J]. Chinese Journal of Mechanical Engineering, 2009, 22(6): 791–799.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, China

    Liping Wang, Yao Jiang & Tiemin Li

Authors
  1. Liping Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yao Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tiemin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yao Jiang.

Additional information

Supported by National Natural Science Foundation of China(Grant No. 51272560), National Basic Research Program of China(973 Program, Grant No. 2011CB302404), and National Science Foundation for Distinguished Young Scholars of China(Grant No. 51225503)

WANG Liping, born in 1967, is currently a professor and a PhD candidate supervisor at Manufacturing Engineering Institute, Department of Mechanical Engineering, Tsinghua University, China. He received his PhD degree from Jilin University of Technology, China, in 1997. His research interests include advanced equipment and parallel kinematic machines.

JIANG Yao, born in 1989, is currently a PhD candidate at Manufacturing Engineering Institute, Department of Mechanical Engineering, Tsinghua University, China. He received his bachelor degree from Nanjing University of Technology, China, in 2011. His research interests include dynamics and control of redundant kinematic parallel machines.

LI Tiemin, born in 1971, is currently an associate research fellow at Manufacturing Engineering Institute, Department of Mechanical Engineering, Tsinghua University, China. He received his PhD degree from Tsinghua University, China, in 2000. His interests include robotics and parallel kinematic machines.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, L., Jiang, Y. & Li, T. Running accuracy analysis of a 3-RRR parallel kinematic machine considering the deformations of the links. Chin. J. Mech. Eng. 27, 890–899 (2014). https://doi.org/10.3901/CJME.2014.0618.113

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3901/CJME.2014.0618.113

Keywords