A NEW WORKSPACE ANALYSIS METHOD FOR 6-DOF 3-RRRS PARALLEL MANIPULATORS

R. Ramkumar, C. Karthikeyan, and Anjan K. Dash

References

  1. [1] C.M. Gosselin, Determination of the workspace of 6-DOFparallel manipulators, ASME Journal of Mechanical Design,112, 1990, 331–336.
  2. [2] E.F. Fichter, A Stewart platform-based manipulator: Generaltheory and practical construction, International Journal ofRobotics Research, 5(2), 1986, 157–182.
  3. [3] A.K. Dash, I.-M. Chen, S.H. Yeo, and G. Yang, Workspacegeneration and planning singularity-free path for parallelmanipulators, Mechanism and Machine Theory, 40, 2005,776–805.
  4. [4] T. Arai, T. Tanikawa, J.-P. Merlet, and T. Sendai, Developmentof a new parallel manipulator with fixed linear actuator,in ASME Japan/USA Symposium on Flexible Automation,Boston, 1996, vol. 1, pp. 145–149.
  5. [5] J.P. Conti, C.M. Clinton, G. Zhang, and A.J. Wavering,Technical Research Report 97-28, ISR, University of Maryland,MD, 1997.
  6. [6] O. Masory and J. Wang, Workspace evaluation of Stewartplatforms, ASME 22nd Biennial Mechanisms Conf., Scottsdale,1992, vol. 45, pp. 337–346.
  7. [7] G. Castelli, E. Ottaviano, and M. Ceccarelli, A fairly generalalgorithm to evaluate workspace characteristics of serial andparallel manipulators, Mechanics Based Design of Structuresand Machines, 36, 2008, 14–33.
  8. [8] E.J. Haug, C.M. Luh, F.A. Adkins, and J.Y. Wang, Numericalalgorithms for mapping boundaries of manipulator workspaces,ASME Journal of Mechanical Design, 118(1), 1996, 228–234.
  9. [9] Z. Wang, Z. Wang, W. Liu, Y. Lei, A study on workspace,boundary workspace analysis and workpiece positioning forparallel machine tools, Mechanism and Machine Theory; 36(3),2001, 605–622.
  10. [10] J. Zhao, Z. Feng, and K. Zhou, On the workspace of spatial parallel manipulator with multi-translational degrees of freedom,International Journal of Advanced Manufacturing Technology,27(1), 2005, 112–118.
  11. [11] J. Zhao, S. Zhang, J. Dong, Z. Feng, and K. Zhou, Optimizing the kinematic chains for a spatial parallel manipulatorvia searching the desired dexterous workspace, Robotics andComputer-integrated Manufacturing, 23, 2005, 38–46.
  12. [12] D. Chablat, P. Wenger, F. Majou, and J.P. Merlet, An intervalanalysis based study for the design and the comparison of three-degrees-of-freedom parallel kinematic machine, InternationalJournal of Robotics Research, 23(6), 2004, 615–624.
  13. [13] J.A. Snyman, L.J. du Plessis, and J. Duffy, An optimizationapproach to the determination of the boundaries of manipulatorworkspaces, ASME Journal of Mechanical Design, 122, 2000,447–456.
  14. [14] A.M. Hay and J.A. Snyman, The chord method for the determination of nonconvex workspaces of planar parallel manipulators, Computers & Mathematics with Applications, 43, 2002,1135–1151.
  15. [15] C.M. Gosselin, E. Lavoie, and P. Toutant, An efficientalgorithm for the graphical representation of the three dimensional workspace of parallel manipulators, ASME 22ndBiennial Mechanisms Conference, Scottsdale, 1992, vol. 45,pp. 323–328.
  16. [16] I.A. Bonev and J. Ryu, A new approach to orientationworkspace analysis of 6-dof parallel manipulators, Mechanismand Machine Theory, 36(1), 2001, 15–28.
  17. [17] I.A. Bonev and J. Ryu, A geometrical method for computing theconstant orientation workspace of 6-prrs parallel manipulators,Mechanism and Machine Theory, 36(1), 2001, 1–13.
  18. [18] O. Masory and J. Wang, Workspace evaluation of Stewartplatforms, Advanced Robotics, 9, 1994, 443–461.
  19. [19] H. Li, C.M. Gosselin, and M.J. Richard, Determination of themaximal singularity-free zones in the six-dimensional workspaceof the general Gough–Stewart platform, Mechanism and Ma-chine Theory, 42, 2007, 497–511.
  20. [20] K.Y. Tsai, I.-T. Lo, and P.J. Lin, Compatible reachableworkspaces of symmetrical Stewart–Gough parallel manipula-tors, Mechanism and Machine Theory, 77, 2014, 111–121.
  21. [21] R.P. Podhorodeski and K.H. Pittens, A class of parallel manipulators based on kinematically simple branches, Journal ofMechanical Design, 116(3), 1994, 908–914.
  22. [22] L. Notash and R.P. Podhorodeski, Complete forward displacement solutions for a class of three branch-parallel manipulators,Journal of Robotics Systems, 11(6), 1994, 471–485.
  23. [23] J. Angeles, G. Yang, and I.-M. Chen, Singularity analysisof three-legged, six-DOF platform manipulators with RRRSlegs, IEEE/ASME International Conf. on Advanced IntelligentMechatronics, 2001, Italy, vol. 1, 32–36.
  24. [24] P. Ben-Horin and M. Shoham, Singularity analysis of a classof parallel robots based on Grassmann–Cayley algebra, Mechanism and Machine Theory, 41(8), 2006, 958–970.
  25. [25] Y. Qian, Q. Wang, G. Chen, J. Yu, and Y. Cao, Workspace andsingularity analysis of 3/3-rrrs parallel manipulator, Journal ofTheoretical and Applied Information Technology, 48(3), 2013,2005–2013.
  26. [26] A. Wolf and D. Glozman, Singularity analysis of large workspace3RRRS parallel mechanism using line geometry and linearcomplex approximation, Journal of Mechanisms and Robotics,3, 2011, 011004 1–9.
  27. [27] Z. Ji, Workspace analysis of Stewart platforms via vertex space,Journal of Robotic Systems, 11(7), 1994, 631–639.
  28. [28] B. Bihari, D. Kumar, C. Jha, V.S. Rathore, and A.K. Dash, Ageometric approach for the workspace analysis of two symmetricplanar parallel manipulators, Robotica, 34(4), 2016, 738–763.
  29. [29] Q. Jiang and C.M. Gosselin, Determination of the maximalsingularity-free orientation workspace for the Gough-Stewartplatform, Mechanism and Machine Theory, 44(6), 2009, 1281–1293.
  30. [30] H. Li, C.M. Gosselin, and M.J. Richard, Determination of themaximal singularity-free zones in the six-dimensional workspaceof the general Gough-Stewart platform, Mechanism and Ma-chine Theory, 42(4), 2007, 497–511.
  31. [31] L.S. Chkhartishvili, Volume of the intersection of three spheres,Mathematical Notes, 69(3), 2001, 421–428.
  32. [32] I.J. Nagrath and R.K. Mittal, Robotics and control, (TataMcGraw-Hill Education, 2003).
  33. [33] D. Chablat and P. Wenger, Working modes and aspects in fullyparallel manipulators, Proc. 1998 IEEE International Conf.on Robotics and Automation (Cat. No. 98CH36146), 1988,Belgium, vol. 3, 1964–1969.
  34. [34] Advances in robot kinematics: Analysis and control, J. Lenarcicand M.L. Husty (Eds.), (Kluwer Academic Publisher, 1998).
  35. [35] J.P. Merlet, Direct kinematics and assembly modes in parallelmanipulators, IJRR, 11(2), 1992, 150–162.
  36. [36] H. Yu, B. Li, X. Yang, and Y. Hu, Structural synthesisand variation analysis of a family of 6-DOF parallel mechanisms with three limbs, International Journal of Robotics andAutomation, 25(2), 2010, 121–131.
  37. [37] Y. Lu and B. Hu, Determining singularity of parallel manipulators with n linear active legs by CAD variation geometry, International Journal of Robotics and Automation, 23(3), 2008,160–167.
  38. [38] M. Zoppi, L.E. Bruzzone, and R.M. Molfino, Position analysisof a class of translational parallel mechanisms, InternationalJournal of Robotics and Automation, 19(3), 2004, 160–167.
  39. [39] A.K. Dash, Kinematics design of reconfigurable parallel manipulators, Ph.D. Thesis, Nanyang Technological University,Singapore, 2002.
  40. [40] A.K. Dash, I.-M. Chen, S.H. Yeo, and G. Yang, Instantaneouskinematics and singularity analysis of three legged parallelmanipulators, Robotica, 22(2), 2004, 189–203.
  41. [41] Y. Zhao, et al., Inverse kinematics and rigid-body dynamicsfor a three rotational degrees of freedom parallel manipulator,Robotics and Computer-integrated Manufacturing, 31, 2015,40–50.
  42. [42] Y. Zhao, Singularity, isotropy and velocity transmission evaluation of a three translational degrees of freedom parallel robot,Robotica, 31(2), 2013, 193–202.

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