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Kinematics analysis and solution of the active/passive forces of a 4SPS+SPR parallel machine tool

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Abstract

A 5-dof 4SPS+SPR parallel machine tool with four SPS-type active legs and one SPR-type active leg is proposed. Its inverse kinematics is analysed by using an analytic approach and a CAD variation geometry approach. Some analytic formulae for solving the active/passive forces are derived by adopting a vector approach. First, a simulation mechanism of the 4SPS+SPR parallel machine tool is created and some kinematic characteristics are analysed. Second, the formulae for solving its inverse kinematics and the Jacobian matrix are derived and a reachable workspace is constructed. Third, the poses of the active/passive forces are analysed and an active/passive force transformation matrix and the analytic formulae for solving the active/passive forces of the 4SPS+SPR parallel machine tool are derived. The analytic results are verified by the simulation mechanism.

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References

  1. Zhang S, Heisel U (2003) Parallel machine tool. Machinery Industry Press, Beijing, China

    Google Scholar 

  2. Niku SB (2004) Introduction to robotics: analysis, systems, applications. Pearson Education, Inc. publishing as Prentice Hall, and the Publishing House of Electronics Industry, Beijing, China

    Google Scholar 

  3. Huang Z, Kong LF, Fang YF (1997) Theory on parallel robotics and control. Machinery Industry Press, Beijing, China

    Google Scholar 

  4. Zhang D, Wang L, Lang SYT (2005) Parallel kinematic machines: design, analysis and simulation in an integrated virtual environment. Trans ASME J Mech Des 127(4):580–588

    Article  Google Scholar 

  5. Lu Y (2006) Simulation of machining 3D free-form surface in normal direction using 6-SSP and 4SPS+UPU parallel machine tools. International Journal of Advanced Manufacturing Technology, ISSN: 0268–3768 (paper) 1433–3015 (Online)

  6. Lu Y (2005) Computer-aided geometric machining of a 3D free surface using a 3-UPU spatial parallel machine tool. Int J Adv Manuf Technol 26(9–10):1018–1025

    Google Scholar 

  7. Lu Y, Leinonen T (2002) A computer simulation approach to machining complicated shapes on an orthogonal 6-rod machine tool. Int J Mach Tools Manuf 42(3):441–447

    Google Scholar 

  8. Lu Y (2002) Computer simulation applied to an orthogonal three-rod machine tool for machining a complicated three-dimensional surface. Int J Mach Tools Manuf 42(11):1277–1284

    Article  Google Scholar 

  9. Dasgupta B, Mruthunjaya TS (1998) A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator. Mech Mach Theory 33(8):1135–1152

    MATH  MathSciNet  Google Scholar 

  10. Gallardo J, Rico JM, Frisoli A, Checcacci D, Bergamasco M (2003) Dynamics of parallel manipulators by means of screw theory. Mech Mach Theory 38(11):1113–1131

    Article  MATH  MathSciNet  Google Scholar 

  11. Russo A, Sinatra R, Xi F (2005) Static balancing of parallel robots. Mech Mach Theory 40(2):191–202

    Article  MATH  MathSciNet  Google Scholar 

  12. Ider SK (2005) Inverse dynamics of parallel manipulators in the presence of drive singularities. Mech Mach Theory 40(1):33–44

    Article  MATH  MathSciNet  Google Scholar 

  13. Li M, Huang T, Mei J, Zhao X, Chetwynd DG, Hu SJ (2005) Dynamic formulation and performance comparison of the 3-DOF modules of two reconfigurable PKM—the Tricept and the TriVariant. Trans ASME J Mech Des 127(5):1129–1136

    Article  Google Scholar 

  14. Dasgupta B, Mruthyunjaya TS (1998) Force redundancy in parallel manipulators: theoretical and practical issues. Mech Mach Theory 33(6):727–742

    Article  MATH  MathSciNet  Google Scholar 

  15. Nokleby SB, Fisher R, Podhorodeski RP, Firmani F (2005) Force capabilities of redundantly-actuated parallel manipulators. Mech Mach Theory 40(5):578–599

    Article  MATH  Google Scholar 

  16. Chakarov D (1999) Study of the passive compliance of parallel manipulators. Mech Mach Theory 34(3):373–389

    Article  MATH  Google Scholar 

  17. Wang S-C, Hikita H, Kubo H, Zhao Y-S, Huang Z, Ifukube T (2003) Kinematics and dynamics of a 6 degree-of-freedom fully parallel manipulator with elastic joints. Mech Mach Theory 38(5):439–461

    Article  MATH  Google Scholar 

  18. Lu Y (2006) Using virtual work theory and CAD functionalities for solving driving force and passive force of spatial parallel manipulators. Mech Mach Theory. DOI 10.1016/j.mechmachtheory.2006.06.011

  19. Lu Y (2004) Using CAD functionalities for the kinematics analysis of spatial parallel manipulators with 3-, 4-, 5-, 6-linearly driven limbs. Mach Mech Theory 39(1):41–60

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Robotics Research Centre, College of Mechanical Engineering, Yanshan University, Qinhuangdao, Hebei, 066004, People’s Republic of China

    Yi Lu, Bo Hu & Jia-Yin Xu

Authors
  1. Yi Lu
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  2. Bo Hu
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  3. Jia-Yin Xu
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Correspondence to Yi Lu.

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Lu, Y., Hu, B. & Xu, JY. Kinematics analysis and solution of the active/passive forces of a 4SPS+SPR parallel machine tool. Int J Adv Manuf Technol 36, 178–187 (2008). https://doi.org/10.1007/s00170-006-0833-7

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  • DOI: https://doi.org/10.1007/s00170-006-0833-7

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