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Linear motion analysis for a novel 4-DOF parallel kinematic machine

  • Sina Akhbari
  • Mehran MahboubkhahEmail author
  • Ali Gadimzadeh
Technical Paper
  • 31 Downloads

Abstract

Motion accuracy is significantly influenced by nonlinear behavior of parallel mechanisms. In this paper, an interpolation algorithm suitable for linear motions of a novel 4-DOF parallel kinematic machine is developed. In this interpolation scheme, velocity and orientation deviations are realized along with path nonlinearity of mechanism. Simulations showed that this algorithm has the capability of sustaining the kinematical constraints and maintaining the nonlinear error below the specified tolerances. Furthermore, to evaluate the linear motion capability of presented 4-DOF parallel mechanism, two digital data loggers recorded the nonlinear error during motion of end effector with pre-defined paths having various lengths and locations in workspace. Results indicated that the developed algorithm based on reducing the kinematic nonlinearity produces more accurate motions.

Keywords

Parallel kinematic machines Nonlinearity Motion error Linear interpolation 

Notes

Acknowledgements

This research received no specific grant from any funding agency in the public, commercial or nonprofit organizations, and there are no conflicts of interest to the authors’ recollection. Moreover, authors assure that there were no human participants involved in this research and the whole research was the result of the research and work done by the authors listed in the title page. In addition, no animals were used or involved while conducting the experiments for this research.

References

  1. 1.
    Youssef HA, El-Hofy H (2008) Machining technology: machine tools and operations. CRC Press, Boca RatonCrossRefGoogle Scholar
  2. 2.
    Zhang D (2009) Parallel robotic machine tools. Springer, BerlinGoogle Scholar
  3. 3.
    Boër CR, Tosatti LM, Smith KS (2012) Parallel kinematic machines: theoretical aspects and industrial requirements. Springer, BerlinGoogle Scholar
  4. 4.
    Jean-Pierre M (2012) Parallel robots, vol 74. Springer, BerlinzbMATHGoogle Scholar
  5. 5.
    Wang J, Wang Z, Huang T, Whitehouse DJ (2002) Nonlinearity for a parallel kinematic machine tool and its application to interpolation accuracy analysis. Sci China Ser E Technol Sci 45(1):97–105.  https://doi.org/10.1360/02ye9012 CrossRefzbMATHGoogle Scholar
  6. 6.
    Wang Y, Huang T, Gosselin CM (2004) Interpolation error prediction of a three-degree parallel kinematic machine. J Mech Des 126(5):932–937CrossRefGoogle Scholar
  7. 7.
    Kui-Jing Z, Jian-she G, Yong-Sheng Z (2005) Path control algorithms of a novel 5-DOF parallel machine tool. IEEE Int Conf Mechatron Autom 1383:1381–1385.  https://doi.org/10.1109/icma.2005.1626755 CrossRefGoogle Scholar
  8. 8.
    Karimi D, Nategh MJ (2014) Development of a novel adaptive nonuniform rational basis spline interpolator with limited kinematic error for hexapod machine tools. Proc Inst Mech Eng Part B J Eng Manuf 228(3):319–327CrossRefGoogle Scholar
  9. 9.
    Dasgupta B, Mruthyunjaya TS (1998) Singularity-free path planning for the Stewart platform manipulator. Mech Mach Theory 33(6):711–725.  https://doi.org/10.1016/S0094-114X(97)00095-5 MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Shaw D, Chen Y-S (2001) Cutting path generation of the Stewart-platform-based milling machine using an end-mill. Int J Prod Res 39(7):1367–1383.  https://doi.org/10.1080/00207540010023529 CrossRefGoogle Scholar
  11. 11.
    Dash AK, Chen IM, Yeo SH, Yang G (2005) Workspace generation and planning singularity-free path for parallel manipulators. Mech Mach Theory 40(7):776–805.  https://doi.org/10.1016/j.mechmachtheory.2005.01.001 MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Oen K-T, Wang L-CT (2007) Optimal dynamic trajectory planning for linearly actuated platform type parallel manipulators having task space redundant degree of freedom. Mech Mach Theory 42(6):727–750.  https://doi.org/10.1016/j.mechmachtheory.2006.05.006 MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Chen C-T, Pham H-V (2012) Trajectory planning in parallel kinematic manipulators using a constrained multi-objective evolutionary algorithm. Nonlinear Dyn 67(2):1669–1681.  https://doi.org/10.1007/s11071-011-0095-2 MathSciNetCrossRefGoogle Scholar
  14. 14.
    Li Z (2000) Reconfiguration and tool path planning of hexapod machine tools. PhD thesis, New Jersey Institute of Technology, New JerseyGoogle Scholar
  15. 15.
    Bates DM, Watts DG (1988) Nonlinear regression analysis and its applications, vol 2. Wiley, New YorkCrossRefGoogle Scholar
  16. 16.
    Li C, Yunfeng Z, Yongsheng Z (2007) Motion control algorithm of a 5-DOF parallel machine tool. IEEE Int Conf Robot Biomim.  https://doi.org/10.1109/robio.2007.4522510 CrossRefGoogle Scholar
  17. 17.
    Chalak Qazani M, Pedrammehr S, Nategh M (2014) A study on motion of machine tools’ hexapod table on freeform surfaces with circular interpolation. Int J Adv Manuf Technol 1:1–9.  https://doi.org/10.1007/s00170-014-6264-y CrossRefGoogle Scholar
  18. 18.
    Chalak Qazani M, Pedrammehr S, Rahmani A, Shahryari M, Khani Sheykh Rajab A, Ettefagh M (2014) An experimental study on motion error of hexarot parallel manipulator. Int J Adv Manuf Technol 72(9–12):1361–1376.  https://doi.org/10.1007/s00170-014-5685-y CrossRefGoogle Scholar
  19. 19.
    Pedrammehr S, Chalak Qazani MR, Abdi H, Nahavandi S (2016) Mathematical modelling of linear motion error for Hexarot parallel manipulators. Appl Math Model 40(2):942–954.  https://doi.org/10.1016/j.apm.2015.07.004 MathSciNetCrossRefGoogle Scholar
  20. 20.
    Liu X-J, Wang J (2003) Some new parallel mechanisms containing the planar four-bar parallelogram. Int J Robot Res 22(9):717–732CrossRefGoogle Scholar
  21. 21.
    Craig JJ (2005) Introduction to robotics: mechanics and control, vol 3. Pearson Prentice Hall, Upper Saddle RiverGoogle Scholar
  22. 22.
    Hee-Byoung C, Konno A, Uchiyama M (2003) Closed-form solutions for the forward kinematics of a 4-DOFs parallel robot H4. In: Proceedings of 2003 IEEE/RSJ International conference on intelligent robots and systems, (IROS 2003), vol 3313, pp 3312–3317.  https://doi.org/10.1109/iros.2003.1249667
  23. 23.
    Huang X, Liao Q, Wei S (2010) Closed-form forward kinematics for a symmetrical 6-6 Stewart platform using algebraic elimination. Mech Mach Theory 45(2):327–334.  https://doi.org/10.1016/j.mechmachtheory.2009.09.008 CrossRefzbMATHGoogle Scholar
  24. 24.
    Edwards CH (1990) Calculus and analytic geometry. Prentice Hall PTR, Englewood CliffsGoogle Scholar
  25. 25.
    Karimi D, Nategh MJ (2015) Contour maps for developing optimal toolpath and workpiece setup in hexapod machine tools by considering the kinematics nonlinearity. In: Proceedings of the institution of mechanical engineers, part b: journal of engineering manufacture, pp 0954405415592123Google Scholar
  26. 26.
    Karimi D, Nategh MJ (2014) Kinematic nonlinearity analysis in hexapod machine tools: Symmetry and regional accuracy of workspace. Mech Mach Theory 71:115–125.  https://doi.org/10.1016/j.mechmachtheory.2013.09.007 CrossRefGoogle Scholar
  27. 27.
    Karimi A, Masouleh MT, Cardou P (2014) Singularity-free workspace analysis of general 6-UPS parallel mechanisms via convex optimization. Mech Mach Theory 80:17–34.  https://doi.org/10.1016/j.mechmachtheory.2014.04.005 CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of TabrizTabrizIran

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