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Error modeling and sensitivity analysis of a parallel robot with SCARA(selective compliance assembly robot arm) motions

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Abstract

Parallel robots with SCARA(selective compliance assembly robot arm) motions are utilized widely in the field of high speed pick-and-place manipulation. Error modeling for these robots generally simplifies the parallelogram structures included by the robots as a link. As the established error model fails to reflect the error feature of the parallelogram structures, the effect of accuracy design and kinematic calibration based on the error model come to be undermined. An error modeling methodology is proposed to establish an error model of parallel robots with parallelogram structures. The error model can embody the geometric errors of all joints, including the joints of parallelogram structures. Thus it can contain more exhaustively the factors that reduce the accuracy of the robot. Based on the error model and some sensitivity indices defined in the sense of statistics, sensitivity analysis is carried out. Accordingly, some atlases are depicted to express each geometric error’s influence on the moving platform’s pose errors. From these atlases, the geometric errors that have greater impact on the accuracy of the moving platform are identified, and some sensitive areas where the pose errors of the moving platform are extremely sensitive to the geometric errors are also figured out. By taking into account the error factors which are generally neglected in all existing modeling methods, the proposed modeling method can thoroughly disclose the process of error transmission and enhance the efficacy of accuracy design and calibration.

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References

  1. FICHTER E F. A Stewart platform-based manipulator: general theory and practical construction[J]. The International Journal of Robotics Research, 1986, 5(2): 157–182.

    Article  Google Scholar 

  2. CLAVEL R. Device for the movement and positioning of Delta parallel robot: US, 4976582[P/OL]. 1990-12-11[2013-11-07]. http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fsearch-bool.html&r=1&f=G&l=50&co1=AND&d=PTXT&s1=4976582.PN.&OS=PN/4976582&RS=PN/4976582.

  3. PIERROT F, REYNAUD C, FOURNIER A. DELTA: a simple and efficient parallel robot[J]. Robotica, 1990, 8(1): 105–109.

    Article  Google Scholar 

  4. COMPANY O, MARQUET F, PIERROT F. A new high-speed 4-DOF parallel robot synthesis and modeling issues[J]. IEEE Transactions on Robotics and Automation, 2003, 19(3): 411–420.

    Article  Google Scholar 

  5. PIERROT F. High-speed parallel robot with four degrees of freedom: US, 36916163[P/OL]. 2010-06-15[2013-11-07]. http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fsearch-bool.html&r=1&f=G&l=50&co1=AND&d=PTXT&s1=%22High-speed+parallel+robot+four+degrees+freedom%22.TI.&OS=TTL/.

  6. XIE Fugui, LIU Xinjun, ZHOU Yanhua. A parallel robot with SCARA motions and its kinematic issues[C]//Proceedings of the 3th IFToMM International Symposium on Robotics and Mechatronics, Singapore, October 2–4, 2013: 53–62.

  7. XIE Fugui, Li Tiemin, LIU Xinjun. Type synthesis of 4-DOF parallel kinematic mechanisms based on Grassmann line geometry and atlas method[J]. Chinese Journal of Mechanical Engineering, 2013, 26(6): 1073–1081.

    Article  Google Scholar 

  8. WECK M, STAIMER D. Accuracy issues of parallel kinematic machine tools[J]. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 2002, 216(1): 51–57.

    Google Scholar 

  9. WECK M, STAIMER D. Parallel kinematic machine tools-current state and future potentials[J]. CIRP Annals-Manufacturing Technology, 2002, 51(2): 671–683.

    Article  Google Scholar 

  10. RAMESH R, MANNAN M A, POO A N. Error compensation in machine tools-a review: part I: geometric, cutting-force induced and fixture-dependent errors[J]. International Journal of Machine Tools and Manufacture, 2000, 40(9): 1235–1256.

    Article  Google Scholar 

  11. Gao WEI, XU BIN, TAKEISHI T, et al. Self-calibration and compensation of setting errors for surface profile measurement of a microstructured roll workpiece[J]. Chinese Journal of Mechanical Engineering, 2014, 27(1): 14–22.

    Article  Google Scholar 

  12. SCHELLEKENS P, ROSIELLE N, VERMEULEN H, et al. Design for precision: current status and trends[J]. CIRP Annals-Manufacturing Technology, 1998, 47(2): 557–586.

    Article  Google Scholar 

  13. TSAI L W. Robot analysis: The mechanics of serial and parallel manipulators[M]. New York: Wiley press, 1999.

    Google Scholar 

  14. ROTH Z, MOORING B, RAVANI B. An overview of robot calibration[J]. IEEE Journal of Robotics and Automation, 1987, 3(5): 377–385.

    Article  Google Scholar 

  15. KARAN B, VUKOBRATOVIĆ M. Calibration and accuracy of manipulation robot models-An overview[J]. Mechanism and Machine Theory, 1994, 29(3): 479–500.

    Article  Google Scholar 

  16. WEN Xiulan, ZHAO Yibing, WANG Dongxia, et al. Accurate evaluation of free-form surface profile error based on quasi particle swarm optimization algorithm and surface subdivision[J]. Chinese Journal of Mechanical Engineering, 2013, 26(2): 406–413.

    Article  Google Scholar 

  17. EVERETT L, DRIELS M, MOORING B. Kinematic modelling for robot calibration[C]//Proceedings of the IEEE International Conference on Robotics and Automation, Nagoya, Japan, May 21–27, 1987, 4: 183–189.

  18. TAHMASEBI F. Kinematic synthesis and analysis of a novel class of six-DOF parallel mini manipulators[D]. University of Maryland, 1992.

    Google Scholar 

  19. WANG J, GOSSELIN C M. Static balancing of spatial three-degree-of-freedom parallel mechanisms[J]. Mechanism and Machine Theory, 1999, 34(3): 437–452.

    Article  MathSciNet  MATH  Google Scholar 

  20. CHUNG Y H, LEE J W. Design of a new 2 DOF parallel mechanism[C]//Proceedings of IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Como, Italy, July 08–12, 2001, 1: 129–134.

  21. LIU Xinjun, WANG Jingsong. Parallel kinematics: Type, kinematics and optimal design[M]. Berlin: Springer Press, 2014.

    Book  Google Scholar 

  22. FAN K C, WANG H, ZHAO J W, et al. Sensitivity analysis of the 3-PRS parallel kinematic spindle platform of a serial-parallel machine tool[J]. International Journal of Machine Tools and Manufacture, 2003, 43(15): 1561–1569.

    Article  Google Scholar 

  23. HUANG Peng, WANG Jingsong, WANG Liping, et al. Identification of structure errors of 3-PRS-XY mechanism with Regularization method[J]. Mechanism and Machine Theory, 2011, 46(7): 927–944.

    Article  MATH  Google Scholar 

  24. HUANG TIAN, WHITEHOUSE D J, CHETWYND D G. A unified error model for tolerance design, assembly and error compensation of 3-DOF parallel kinematic machines with parallelogram struts[J]. CIRP Annals-Manufacturing Technology, 2002, 51(1): 297–301.

    Article  Google Scholar 

  25. O’BRIEN S M, CARRETERO J A, LAST P. Self calibration of 3-PRS manipulator without redundant sensors[J]. Transactions of the Canadian Society for Mechanical Engineering, 2007, 31(4): 483–494.

    Google Scholar 

  26. LEE S J, GILMORE B J. The determination of the probabilistic properties of velocities and accelerations in kinematic chains with uncertainty[J]. Journal of Mechanical Design, 1991, 113: 84–90.

    Article  Google Scholar 

  27. WANG S M, EHMANN K F. Error model and accuracy analysis of a six-DOF Stewart platform[J]. Transactions-American Society of Mechanical Engineering Journal of Manufacturing Science and Engineering, 2002, 124(2): 286–295.

    Article  Google Scholar 

  28. HUANG Tian, CHETWYND D G, MEI J P, et al. Tolerance design of a 2-DOF overconstrained translational parallel robot[J]. IEEE Transactions on Robotics, 2006, 22(1): 167–172.

    Article  Google Scholar 

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Author information

Authors and Affiliations

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

    Yuzhen Chen, Fugui Xie, Xinjun Liu & Yanhua Zhou

  2. Beijing Key Lab of Precision/Ultra-precision Manufacturing Equipments and Control, Tsinghua University, Beijing, 100084, China

    Xinjun Liu

  3. Institute of Aircraft Engineering, Naval Aeronautical and Astronautical University, Yantai, 264000, China

    Yanhua Zhou

Authors
  1. Yuzhen Chen
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  2. Fugui Xie
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  3. Xinjun Liu
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  4. Yanhua Zhou
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Corresponding author

Correspondence to Fugui Xie.

Additional information

Supported by National Natural Science Foundation of China(Grant No. 51305222), and National Key Scientific and Technological Program of China(Grant No. 2013ZX04001-021)

CHEN Yuzhen, born in 1990, is currently a master candidate at State Key Laboratory of Tribology & Institute of Manufacturing Engineering, Department of Mechanical Engineering, Tsinghua University, China. He received his bachelor degree from Dalian University of Technology, China, in 2012. His research interests include parallel manipulator kinematics and calibration.

XIE Fugui, born in 1982, is currently a postdoctoral fellow at State Key Laboratory of Tribology & Institute of Manufacturing Engineering, Department of Mechanical Engineering, Tsinghua University, China. He received his PhD degree from Tsinghua University, China, in 2012, and received his bachelor degree from Tongji University, China, in 2005. His research interests include parallel mechanisms and hybrid machine tools.

LIU Xinjun, born in 1971, is currently a professor at State Key Laboratory of Tribology & Institute of Manufacturing Engineering, Department of Mechanical Engineering, Tsinghua University, China. He received his PhD degree from Yanshan University, Qinhuangdao China, in 1999. His research interests include parallel mechanisms, parallel kinematic machines and advanced manufacturing equipments. He patented more than 40 inventions and published around 110 papers.

ZHOU Yanhua, born in 1973, is currently a PhD candidate at State Key Laboratory of Tribology & Institute of Manufacturing Engineering, Department of Mechanical Engineering, Tsinghua University, China. She received her bachelor degree from Shandong University of Technology, China, in 1995. Her research interests include parallel mechanism and advanced manufacturing equipments.

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Chen, Y., Xie, F., Liu, X. et al. Error modeling and sensitivity analysis of a parallel robot with SCARA(selective compliance assembly robot arm) motions. Chin. J. Mech. Eng. 27, 693–702 (2014). https://doi.org/10.3901/CJME.2014.0423.082

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  • DOI: https://doi.org/10.3901/CJME.2014.0423.082

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