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Synthesis of branched chains with actuation redundancy for eliminating interior singularities of 3T1R parallel mechanisms

  • Mechanism and Robotics
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Abstract

Although it is common to eliminate the singularity of parallel mechanism by adding the branched chain with actuation redundancy, there is no theory and method for the configuration synthesis of the branched chain with actuation redundancy in parallel mechanism. Branched chains with actuation redundancy are synthesized for eliminating interior singularity of 3-translational and 1- rotational(3T1R) parallel mechanisms. Guided by the discriminance method of hybrid screw group according to Grassmann line geometry, all the possibilities are listed for the occurrence of interior singularities in 3T1R parallel mechanism. Based on the linear relevance of screw system and the principles of eliminating parallel mechanism singularity with actuation redundancy, different types of branched chains with actuation redundancy are synthesized systematically to indicate the layout and the number of the branched chainsinterior with actuation redundancy. A general method is proposed for the configuration synthesis of the branched chains with actuation redundancy of the redundant parallel mechanism, and it builds a solid foundation for the subsequent performance optimization of the redundant actuation parallel mechanism.

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References

  1. FANG Yuefa, TSAI L W. Structure synthesis of a class of 4-DOF and 5-DOF parallel manipulators with identical limb structures[J].The International Journal of Robotics Research, 2002, 21(9): 799–810.

    Google Scholar 

  2. LIU Yanbin, LI Zhisong, HAN Jianhai. Interior singularity elimination method for parallel mechanisms based on non-instantaneous branch link configuration design[J]. Journal of Mechanical Engineering, 2012, 48(11): 136–145.

    Article  Google Scholar 

  3. CHAKAROV D. Study of the Antagonistic stiffness of parallel manipulators with actuation redundancy[J]. Mechanism and Machine Theory, 2004, 39(6): 583–601.

    Article  MATH  Google Scholar 

  4. NOKLEBY S B, FISHERB R, PODHORODESKI R P, et al. Force capabilities of redundantly-actuated parallel manipulators[J]. Mechanism and Machine Theory, 2005, 40(5): 578–599.

    Article  MATH  Google Scholar 

  5. WU J, WANG J S, WANG L P, et al. Study on the stiffness of a 5-DOF hybrid machine tool with actuation redundancy[J]. Mechanism and Machine Theory, 2009, 44(2): 289–305.

    Article  MATH  Google Scholar 

  6. KOKKINIS T, MILLIES P. A parallel robot-arm regional structure with actuational redundancy[J]. Mechanism and Machine Theory, 1991, 26(6): 629–641

    Article  Google Scholar 

  7. NAHON M, ANGELES J. Optimization of dynamic force in mechanical hand[J]. ASME Journal Mechanical Design, 1991, 113(2): 167–173

    Article  Google Scholar 

  8. CAI Shengli, BAI Shixian. Characteristics of redundantly actuated paralle1 maniPulators[J]. Mechanical Science and Technology, 1996, 15(2): 235–238.

    Google Scholar 

  9. KIM S. Operational quality analysis of parallel manipulators with actuation redundancy[C]//Proceedings of IEEE International Conference on Robotics and Automation, Albuquerque, USA, 1997: 2651–2656.

    Google Scholar 

  10. HAN Xianguo, CHEN Wuyi, GUO Weidong. New approach to improve accuracy of PKMS by redundant control[J]. Acta Aeronautica Et Astronautica Sinica, 2002, 23(5): 487–490.

    Google Scholar 

  11. HAN Xianguo, CHEN Wuyi. Study on the kinematics of a new redundant actuated PKMs[C]//7th International Conference on Progress of Machining Technology, China, Beijing, 2004: 424–429.

    Google Scholar 

  12. HAN Xianguo, CHEN Wuyi. Solving deformation coordination equation of parallel mechanism based on kinematic constraint[J]. Mechanics and Practice, 2005, 27(3): 65–68.

    Google Scholar 

  13. TANG Haitao. Hybrid focre/position control and experimental investigation of 5-UPS/PRPU parallel machine tool with redundant actuation[D]. Qinhuangdao: Yanshan University, 2011.

    Google Scholar 

  14. KIM Hyung Wook, LEE Jae Hoon, SUH I Hong. Comparative study and experimental verification of singular-free algorithms for a 6 DOF parallel haptic device[J]. Mechatronics, 2005, 15(4): 403–422.

    Article  Google Scholar 

  15. SHIN H, KIM S, JEONG J,et al. Stiffness enhancement of a redundantly actuated parallel machine tool by dual support rims[J]. International Journal of Precision Engineering and Manufacturing, 2012, 13(9): 1539–1547.

    Article  Google Scholar 

  16. SHIN H, LEE S, JEONGJ I,et al. Antagonistic stiffness optimization of redundantly actuated parallel manipulators in a predefined workspace[J]. IEEE-ASME Transactions on Mechatronics, 2013, 18(3): 1161–1169.

    Article  Google Scholar 

  17. QU Haibo, LIANG Yihan, FANG Yuefa, et al. Statics and stiffness analysis of 4-RRS redundant spherical parallel mechanism[J]. Journal of Mechanical Engineering, 2015, 11: 8–15.

    Article  Google Scholar 

  18. CHOUDHURY P, GHOSAL A. Singularity and controllability analysis of parallel manipulators and closed-loop mechanisms[J]. Mechanism and Machine Theory, 2000, 35(10): 1455–1479.

    Article  MathSciNet  MATH  Google Scholar 

  19. CHANG Peng, LI Tiemin, LIU Xinjun. Step self calibration method for planar three degree of freedom redundant parallel machine tool[J]. Journal of Tsinghua University(Natural Science Edition), 2008, 48(5): 808–811.

    MathSciNet  Google Scholar 

  20. LIU Xin, QIU Yuanying, SHENG Ying, et al. Optimization design for the comprehensive performance of planar redundant parallel robot[J]. Journal of Southwest Jiaotong University, 2008, 43(5): 626–632.

    MATH  Google Scholar 

  21. WU Jun, WANG Jinsong, LI Tiemin, et al. Performance analysis and application of a redundantly actuated parallel manipulator for milling[J]. Journal of Intelligent & Robotic Systems, 2007, 50(2): 163–180.

    Article  Google Scholar 

  22. WU Jun, WANG Jinsong, WANG Liping, et al. Dynamics and control of a planar 3-DOF manipulator with actuation redundancy[J]. Mechanism and Machine Theory, 2009, 44(4): 835–849.

    Article  MATH  Google Scholar 

  23. NIU Xuemei, GAO Guoqin, LIU Xinjun, et al. Dynamic modeling and simplified analysis of a novel parallel mechanism with a redundant parallel mechanism[J]. Journal of Mechanical Engineering, 2014, 19: 41–49.

    Article  Google Scholar 

  24. KONG Deqing, WU Jun, LI Tiemin, et al. Control of a 4-DOF parallel kinematic machine with actuation redundancy[J]. Journal of Mechanical Engineering, 2009, 45(9): 152–157.

    Article  Google Scholar 

  25. LIU Dawei, WANG Liping, LI Tiemin, et al. Kinematic self calibration of a class of redundant branched parallel machines [J]. Journal of Mechanical Engineering, 2012, 1: 1–6.

    Google Scholar 

  26. YU J J, DONG X, PEI X, et al. Mobility and singularity analysis of a class of 2-DOF rotational parallel mechanisms using a visual graphic approach[J]. Journal of Mechanism and Robotics, Transaction of the ASME, 2012, 4(4): 1027–1036.

    Google Scholar 

  27. YU J J, LI S Z, PEI X, et al. A unified approach to type synthesis of both rigid and flexure parallel mechanisms[J]. Science China Technological Sciences, 2011, 54(5): 1206–1219.

    Article  MATH  Google Scholar 

  28. LI Shihua, DING Wenhua. Linear independency of hybrid screw group[J]. China Mechanical Engineering, 2009, 20(23): 2804–2807.

    Google Scholar 

  29. HUANG Zhen, ZHAO Yongsheng, ZHAO Tieshi. Advanced spatial mechanism[M]. Beijing: Higher Education Press 2006.

    Google Scholar 

  30. ZHANG Yanfei, GONG Jinliang, GAO Feng. Theory of singularity elimination by redundant actuation for parallel mechanism[J]. China Mechanical Engineering, 2006, 17(5): 445–448.

    Google Scholar 

  31. ZHAO Tieshi, CHEN Jiang, WANG Jiachun. 4-UPU parallel manipulator mechanism and kinematics[J]. China Mechanical Engineering, 2005, 16(22): 2034–2038.

    Google Scholar 

Download references

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Authors and Affiliations

Authors

Corresponding author

Correspondence to Shihua Li.

Additional information

Supported by Research Fund for the Doctoral Program of Higher Education, China(Grant No. 20131333110008)

Biographical notes

LI Shihua, male, born in 1966, is a professor and a doctoral tutor of mechanical engineering at Yanshan University, China. His main research direction is the theory and application of parallel robot mechanism.

LIU Yanmin, female, born in 1978, is a PhD of mechanical and electrical engineering, mechanical engineering at Yanshan University, China, and a lecture at College of Mechanical Engineering, Hebei Vocationa & Technical College of Building Materials. Her main research direction is the theory of parallel robotic mechanisms and application.

CUI Hongliu, female, born in 1988, is a master of mechanical and electrical engineering, mechanical engineering at Yanshan University, China. Her main research direction is the theory of parallel robotic mechanisms and application.

NIU Yunzhan, female, born in 1989, is a master of mechanical and electrical engineering, mechanical engineering, Yanshan University, China. Her main research direction is the theory of parallel robotic mechanisms and application.

ZHAO Yanzhi, male, born in 1981, is an associate professor of mechanical engineering at Yanshan University, China. His main research direction is the theory of parallel robotic mechanisms and application.

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Li, S., Liu, Y., Cui, H. et al. Synthesis of branched chains with actuation redundancy for eliminating interior singularities of 3T1R parallel mechanisms. Chin. J. Mech. Eng. 29, 250–259 (2016). https://doi.org/10.3901/CJME.2016.0104.001

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  • DOI: https://doi.org/10.3901/CJME.2016.0104.001

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