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Geometric condition of 3UPS-S parallel mechanism in singular configuration

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Abstract

The existing researches on singularity of parallel mechanism are mostly limited to the property and regularity of singularity locus and there is no further research into the geometric relationship between uncontrolled kinematic screw and parallel mechanism in singularity. A 3UPS-S parallel mechanism is presented which fulfils 3-DOF in rotation. The regularity of nutation angle singularity is analyzed based on the Jacobian matrix, and the singularity surface of 3UPS-S parallel mechanisms is obtained. By applying the concept of reciprocal product in screw theory, the singular kinematic screw is derived when 3UPS-S parallel mechanism is in singularity. The geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism is investigated by using programs in MATLAB. It is revealed that there are two kinds of situation. Firstly, the three limbs of 3UPS-S parallel mechanism intersect the singular kinematic screw in space simultaneously; Secondly, two limbs cross the singular kinematic screw while the third limb parallels with that screw. It is concluded that the nutation angle singularity of 3UPS-S parallel mechanism belongs to the singular linear complexes. This paper sheds light into and clarifies the geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism.

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References

  1. PTAK A, FOUNDY K. Real-time spacecraft simulation and hardware-in-the-loop testing[C]//Proceedings of Real-time Technology and Applications Symposium, Fourth IEEE, USA: Colorado, 1998: 230–236.

    Google Scholar 

  2. STEWART D. A Platform with six degrees of freedom[J]. Proc. Instn. Mech. Engrs. (Part I), 1965, 180(15): 371–386.

    Article  Google Scholar 

  3. ZHANG Ying, LIAO Qizheng, SU Haijun, et al. A new closed-form solution to the forward displacement analysis of a 5-5 in parallel platform[J]. Mechanism and Machine Theory, 2012, 52: 47–58.

    Article  Google Scholar 

  4. LU Yi, HU Bo. Analyzing kinematics and solving active/constrained forces of a 3SPU+UPR parallel manipulator[J]. Mechanism and Machine Theory, 2007, 42(10): 1 298–1 313.

    Article  Google Scholar 

  5. FIRMANI Flavio, PODHORODESKI P Ron. Singularity analysis of planar parallel manipulators based on forward kinematic solution[J]. Mechanism and Machine Theory, 2009, 44(7): 1 386–1 399.

    Article  Google Scholar 

  6. CHOUDHURY Prasun, GHOSAL Ashitava. Singularity and controllability analysis of parallel manipulators and closed-loop mechanisms[J]. Mechanism and Machine Theory, 2000, 35(10):1 455–1 479.

    Article  MathSciNet  Google Scholar 

  7. HUANG Zhen, KONG Lingfu, FANG Yuefa. The mechanism theory and control of parallel robots[M]. Beijing: China Machine Press, 1997. (in Chinese)

    Google Scholar 

  8. ALICI Gursel, SHIRINZADEH Bijan. Loci of singular configurations of a 3-DOF spherical parallel manipulator[J]. Robotics and Autonomous Systems, 2004, 48(2): 77–91.

    MathSciNet  Google Scholar 

  9. CAO Yi, HUANG Zhen, DING Huafeng, et al. Property identification of singularity loci of Gough-Stewart manipulator[J]. Chinese Journal of Mechanical Engineering, 2006, 19(1): 41–44.

    Article  Google Scholar 

  10. LI Yanwen, HUANG Zhen. Method used in singularity research based on kinematics and its example in application[J]. Chinese Journal of Mechanical Engineering, 2004, 17(2): 161–165.

    Article  Google Scholar 

  11. CHEN Qiaohong, LI Qinchuan, WU Chuanyu, et al. Mobility constraint singularity and isotropy of the 3-P R R R R R translational parallel mechanism[J]. Chinese Journal of Mechanical Engineering, 2009, 22(6): 841–848.

    Article  Google Scholar 

  12. MA Jianming, HUANG Qitao, XIONG Haiguo, et al. Analysis and application of the singularity locus of the Stewart platform[J]. Chinese Journal of Mechanical Engineering, 2011, 24(1): 133–140.

    Article  Google Scholar 

  13. DONG Xin, YU Jingjun, CHEN Bin, et al. Geometric approach for kinematic analysis of a class of 2-DOF rotational parallel manipulators[J]. Chinese Journal of Mechanical Engineering, 2012, 25(2): 241–247.

    Article  Google Scholar 

  14. LI Baokun, CAO Yi, ZHANG Qiuju, et al. Orientation-singularity representation and orientation-capability computation of a special class of the Gough-Stewart parallel mechanisms using unit quaternion[J]. Chinese Journal of Mechanical Engineering, 2012, 25(6): 1 096–1 104.

    Article  Google Scholar 

  15. FANG Hairong, FANG Yuefa, ZHANG Ketao. Reciprocal screw theory based singularity analysis of a novel 3-DOF parallel manipulator[J]. Chinese Journal of Mechanical Engineering, 2012, 25(4): 647–653.

    Article  Google Scholar 

  16. LIU Xinjun, WU Chao, WANG Jinsong. A new approach for singularity analysis and closeness measurement to singularities of parallel manipulators[J]. Journal of Mechanism and Robotics, 2012, 4(4): 1–10.

    Google Scholar 

  17. LI Yanwen, HUANG Zhen. Study of regularity of general-linearcomplex singularity of 3/6-Stewart mechanism[J]. Chinese Journal of Mechanical Engineering, 2003, 16(3): 325–328.

    Article  Google Scholar 

  18. LI Haidong, GOSSELIN M Clement, RICHARD J Marc. Determination of the maximal singularity-free zones in the six-dimensional workspace of the general Gough-Stewart platform[J]. Mechanism and Machine Theory, 2007, 42(4): 497–511.

    Article  MATH  MathSciNet  Google Scholar 

  19. LI Haidong, GOSSELIN M Clement, RICHARD J Marc, et al. Analytic form of the six-dimensional singularity locus of the general Gough-Stewart platform[C]//Proceedings of the 2004 ASME International Design Engineering Technical Conference, September 28–October 2, Salt Lake City, USA 2004.

    Google Scholar 

  20. HAN Xianguo, CHEN Wuyi. Analysis on singularity distribution law of parallel mechanism using forward displacement solution[J]. Progress in Nature Science, 2005, 15(5): 631–635. (in Chinese)

    Google Scholar 

  21. MERLET J P. Singular configurations of parallel manipulators and Grassmann geometry[J]. The Int. J. of Rob. Res., 1989, 8(5): 45–56.

    Article  Google Scholar 

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Authors and Affiliations

  1. College of Mechanical Engineering and Automation, Beihang University, Beijing, 100191, China

    Xianguo Han & Yanlong Liu

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  1. Xianguo Han
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  2. Yanlong Liu
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Correspondence to Xianguo Han.

Additional information

This project is supported by Aeronautical Science Foundation of China (Grant No. 20081651025)

HAN Xianguo, born in 1970, is currently an associate professor at College of Mechanical Engineering and Automation, Beihang University, China. He obtained his PhD degree from Beihang University, China, in 2002 and his key areas of research are digital flexible assembly and parallel mechanism.

LIU Yanlong, born in 1988, is working for his master degree at College of Mechanical Engineering and Automation, Beihang University, China. He obtained his bachelor degree from Hu’nan University, China, in 2010. His research focuses on the design of parallel mechanism.

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Han, X., Liu, Y. Geometric condition of 3UPS-S parallel mechanism in singular configuration. Chin. J. Mech. Eng. 27, 130–137 (2014). https://doi.org/10.3901/CJME.2014.01.130

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  • DOI: https://doi.org/10.3901/CJME.2014.01.130

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