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Dimensional synthesis of a 3-DOF parallel manipulator based on dimensionally homogeneous Jacobian matrix

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Abstract

A study of dimensional synthesis of a 3-DOF parallel manipulator with coupling of translation and rotation is carried out. The architecture of the manipulator is composed of a moving platform attached to a fixed base through three identical PRS (prismatic-revolute-spherical) serial limbs, whose unique topology leads to the physical unit inconsistency of the conventional Jacobian matrix and the emergence of the parasitic motion. Then this paper introduces a kinetostatic performance index of the manipulator based on the condition of a dimensionally homogeneous Jacobian matrix, later, the workspace of the aforementioned manipulator is searched and the influence of the crucial design variables on the workspace is analyzed. Finally, a dimensional synthesis method of the manipulator is proposed, which may be regarded as a nonlinear programming problem with subject to the parasitic motion and other several engineering constraints.

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References

  1. The DS Technologie Company. http://www.ds-technologie.de, 2008

  2. Hennes N. Ecospeed: an innovative machining concept for high performance 5-axis-machining of large structural component in aircraft engineering. In: Proceedings of the 3rd Chemnitz Parallel Kinematic Seminar, Chemnitz, Germany, 2002. 763–774

  3. Carretero J A, Nahon M, Gosselin C M, et al. Kinematic analysis of a three-DOF parallel mechanism for telescope application. In: Proceedings of the 2007 ASME Design Automation Conference, Sacramento, California, 1997

  4. Tsai M S, Shiau T N, Tsai Y J, et al. Direct kinematic analysis of a 3-PRS parallel mechanism. Mech Mach Theory, 2003, 38(1): 71–83

    Article  MATH  Google Scholar 

  5. Li Y G, Song Y M, Feng Z Y, et al. Inverse dynamics of 3-PRS parallel mechanism by Newton-Euler formulation (in Chinese). Acta Aeron Astron Sin, 2007, 28: 1210–1215

    Google Scholar 

  6. Zhang F, Yang J G, Li B Z. Kinematic characteristic analysis of 3-PRS parallel manipulator. J Donghua U, 2008, 25: 78–81

    MathSciNet  Google Scholar 

  7. Carretero J A, Nahon M A, Pondhorodeski R P. Workspace analysis and optimization of a novel 3-DOF parallel manipulator. Int J Robotics Autom, 2000, 15: 178–188

    Google Scholar 

  8. Cheng X, Huang Y, Gao F, et al. Research on gesture distribution in the reachable workspace of 3-DOF parallel robot (in Chinese). Mach Des Res, 2005, 21: 22–25

    Google Scholar 

  9. Kumar V. Characterization of workspace of parallel manipulators. J Mech Des, 1992, 114: 368–375

    Article  Google Scholar 

  10. Carretero J A, Podhorodeski R P, Nahon K A, et al. Kinematic analysis and optimization of a new three degree-of-freedom (DOF) spatial manipulator. J Mech Des, 2000, 122: 17–24

    Article  Google Scholar 

  11. Geoffrey P, Carretero G A. Formulating Jacobian matrices for dexterity analysis of parallel mechanism. Mech Mach Theory, 2006, 41: 1505–1519

    Article  MATH  MathSciNet  Google Scholar 

  12. Kim S K, Ryu J. New dimensionally homogeneous Jacobian matrix formulation by Three End-Effector Points for optimal design of parallel manipulators. IEEE Trans Robotics Automat, 2003, 19: 731–737

    Article  Google Scholar 

  13. Gosselin C M. The optimum design of robotic manipulators using dexterity indices. Robot Auton Syst, 1992, 9: 213–226

    Article  Google Scholar 

  14. Ottaviano E, Ceccarelli M. Optimal design of CaPaMan (cassino parallel manipulator) with a specified orientation workspace. Robotica, 2002, 20: 159–166.

    Article  Google Scholar 

  15. Gosselin C, Angeles J. The optimum kinematic design of a spherical three-degree-of-freedom parallel manipulator. ASME J Mech Transm Autom Des, 1989, 111: 202–207

    Google Scholar 

  16. Chablat D, Wenger P. Architecture optimization of a 3-DOF parallel mechanism for machining applications: the orthoglide. IEEE Trans Rob Autom, 2003, 19: 403–410

    Article  Google Scholar 

  17. Liu X J, Wang J S. A new methodology for optimal kinematic design of parallel mechanisms, Mech Mach Theory, 2007,42: 1210–1224

    Article  MATH  Google Scholar 

  18. Liu X J, Bonev I A. Orientation capability, error analysis, and dimensional optimization of two articulated tool heads with parallel kinematics, ASME J Manuf Sci Eng, 2008, 130, 011015: 1–9

    Google Scholar 

  19. Huang T, Whitehouse D J, Wang J. Local dexterity, optimum architecture and design criteria of parallel machine tools. CIRP Ann, 1998, 47: 347–351

    Article  Google Scholar 

  20. Huang T, Gosselin C M, Whitehouse D J. Analytic approach for optimal design of a type of spherical parallel manipulators. Part C: J Mech Eng Sci, 2003, 217: 447–455

    Article  Google Scholar 

  21. Gosselin C M, Angeles J. Global performance index for the kinematics optimization of robotic manipulators. ASME J Mech Des Trans, 1991, 113: 220–226

    Article  Google Scholar 

  22. Huang T, Li M, Zhao X M, et al. Conceptual design and dimensional synthesis for a 3-DOF module of the TriVariant-A novel 5-DOF reconfigurable hybrid robot. IEEE Trans Robotics, 2005, 21: 449–456

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Mechanical Engineering, Tianjin University, Tianjin, 300072, China

    Tao Sun, YiMin Song & LinShan Liu

  2. School of Mechanical Engineering, Tianjin University of Technology and Education, Tianjin, 300222, China

    YongGang Li

Authors
  1. Tao Sun
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  2. YiMin Song
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  3. YongGang Li
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  4. LinShan Liu
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Corresponding author

Correspondence to YiMin Song.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 50535010, 50675151), National High-Tech Research and Development Program of China (Grant No. 2007AA042001), and Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20060056018).

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Sun, T., Song, Y., Li, Y. et al. Dimensional synthesis of a 3-DOF parallel manipulator based on dimensionally homogeneous Jacobian matrix. Sci. China Ser. E-Technol. Sci. 53, 168–174 (2010). https://doi.org/10.1007/s11431-009-0375-y

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  • DOI: https://doi.org/10.1007/s11431-009-0375-y

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