DETERMINATION OF CLOSED-FORM MATHEMATICAL EXPRESSION OF VOLUME OF CONSTANT ORIENTATION WORKSPACE FOR GOUGH–STEWART PLATFORM

Raghav Rajaram P.,∗ Aravind G.,∗ Gokul Narasimhan S.,∗ and Anjan K. Dash∗

References

  1. [1] J.-P.Merlet, C. Gosselin, and T. Huang, Parallel mechanisms, in: Springer Handbook of Robotics (Springer, 2016), 443–462.
  2. [2] M. Furqan, et al., Studies on Stewart platform manipulator: A review, Journal of Mechanical Science and Technology, 31, 2017, 4459–4470.
  3. [3] Z. Tong, C. Gosselin, and H. Jiang, Dynamic decoupling analysis and experiment based on a class of modified Gough-Stewart parallel manipulators with line orthogonality, Mechanism and Machine Theory, 143, 2019, article 103636.
  4. [4] J.-P. Merlet, Geometrical determination of the workspace of a constrained parallel manipulator, in: ARK (1992), 326–329.
  5. [5] R. Clavel, Conception d’un robot parall’ele rapide ‘a 4 degr’es de libert’e, Ph.D. dissertation, EPFL, Lausanne, 1991, N. 925.
  6. [6] J. Borr`as and A.M. Dollar, Dimensional synthesis of threefingered robot hands for maximal precision manipulation workspace, The International Journal of Robotics Research, 34(14), 2015, 1731–1746.
  7. [7] L. Wang, et al., A geometric approach to solving the stable workspace of quadruped bionic robot with hand–foot-integrated function, Robotics and Computer-Integrated Manufacturing (Vol. 37, 2016), 68–78.
  8. [8] K.E.Ch. Vidyasagar et al., Laser based micro texturing of freeform surfaces of implants using a Stewart platform, Precision Engineering, 72, 2021, 294–303.
  9. [9] A. Berti, J.-P. Merlet, and M. Carricato, Solving the direct geometrico-static problem of underconstrained cable-driven parallel robots by interval analysis, The International Journal of Robotics Research, 35(6), 2015, 723–739.
  10. [10] A.N. Chaudhury and A. Ghosal, Optimum design of multidegree-of-freedom closed-loop mechanisms and parallel manipulators for a prescribed workspace using Monte Carlo method, Mechanism and Machine Theory, 118, December 2017, 115– 138.
  11. [11] J.-P. Merlet, Determination of 6D workspaces of Gough-type parallel manipulator and comparison between different geometries, International Journal of Robotics Research, 18(9), 1999, 902–916.
  12. [12] S. Nadar Nabavi, et al., Parametric design and multi-objective optimization of a general 6-PUS parallel manipulator, Mechanism and Machine Theory, 152, 2020, Article 103913.
  13. [13] S. Abdolshah, D. Zanotto, G. Rosati, and S.K. Agrawal, Optimizing stiffness and dexterity of planar adaptive cabledriven parallel robots, Journal of mechanism and Robotics, 9(3), 2017, 031004 (11 pages).
  14. [14] V. Kumar, Characterization of workspaces of parallel manipulators, ASME Journal of Mechanical Design, 114(3), September 1992, 368–375.
  15. [15] W. Li and J. Angeles, Full-mobility 3-CCC parallel-kinematics machines: Forward kinematics, singularity, workspace and dexterity analyses, Mechanism and Machine Theory, 126, 2018, 312–328.
  16. [16] Z. Ji, Workspace analysis of Stewart platforms via vertex space, Journal of Robotic Systems, 11(7), 1994, 631–639.
  17. [17] Z. Ji, Analysis of design parameters in platform manipulators, ASME Journal of Mechanical Design, 118(4), 1996, 526–531.
  18. [18] Z. Ji and M.C. Leu, Design reconfiguration and control of PKM, in: Parallel Kinematics Machines-Theoretical Aspects and Industrial Requirements, Italy (Springer, 1992), 111–129.
  19. [19] M. Wang, Q. Chen, H. Liu, T. Huang, H. Feng, and W. Tian, Evaluation of the kinematic performance of a 3-RRS parallel mechanism, Robotica, 39(4), 2021, 606–617.
  20. [20] H. Rastgar, H.R. Naeimi, and M. Agheli, Characterization, validation, and stability analysis of maximized reachable workspace of radially symmetric hexapod machines, Mechanism and Machine Theory, 137, August 2019, 315–335.
  21. [21] E. Rodriguez, C. Riaño, A. Alvares, and R. Bonnard, Design and dimensional synthesis of a linear Delta robot with single legs for additive manufacturing, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41, 2019, Article number: 536.
  22. [22] M.A. Hosseini and H.-R. Mohammadi Daniali, Dexterous workspace shape and size optimization of tricept parallel manipulator, International Journal of Robotics, 1, 2011, 18–25.
  23. [23] A. Nag and S. Bandyopadhyay, Singularity-free spheres in the position and orientation workspaces of Stewart platform manipulators, Mechanism and Machine Theory, 155, 2021, 104041, ISSN 0094-114X. doi: 10.1016/ j.mechmachtheory.2020.1040416. 8
  24. [24] I.A. Bonev and J. Ryu, A geometrical method for computing the constant-orientation workspace of 6-PRRS parallel manipulators, Mechanism and Machine Theory, 36, 2001, 1–13.
  25. [25] M. Arredondo-Soto, M.A. Garc´ıa-Murillo, J.J. CervantesSánchez, F.J. Torres, and H.A. Moreno-Avalos, Identification of geometric parameters of a parallel robot by using a camera calibration technique, Journal of Mechanical Science and Technology, 35, 2021, 729–737.
  26. [26] R. Kumar, C. Karthikeyan, and A.K. Dash, A new workspace analysis method for 6-DOF 3-RRRS parallel manipulators, International Journal of Robotics and Automation, 34(2), 2019.
  27. [27] M. Ganesh, B. Bihari, V.S. Rathore, C. Kumar, N. Sowmya, S. Ramya, and A.K. Dash, Determination of the closed-form workspace area expression and dimensional optimization of planar parallel manipulators, Robotica, 35(10), 2017, 2056– 2075.
  28. [28] L. Chkhartishvili and S.G. Narasimhan, Volume of intersection of six spheres: A special case of practical interest, Nano Studies, 11, 2015, 111–126.
  29. [29] A.N. Chaudhury and A. Ghosal, Determination of workspace volume of parallel manipulators using monte carlo method, in: S. Zeghloul, L. Romdhane, and M. Laribi (eds.), Computational Kinematics. Mechanisms and Machine Science, vol. 50 (Springer, Cham, 2018). https://doi.org/10.1007/978-3-31960867-9 37.
  30. [30] C. Gosselin, Determination of the workspace of 6-DOF parallel manipulators, IEEE Transactions on Robotics and Automation, 6(3), 1990, 281–290.
  31. [31] L. Kang, W. Kim, and B.-J. Yi, Modeling and analysis of parallel mechanisms with both kinematic and actuation redundancies via screw theory, Journal of Mechanisms and Robotics, 9(6), Dec 2017, 061007 (12 pages).
  32. [32] Z. Shao, H. Li, L. Wang, Z. Zhang, R. Yao, and J. Qie, Orientation optimization of cable-driven parallel manipulator for cleaning the deep sea fishing ground, International Journal of Robotics and Automation, 35, 2020, doi: 10.2316/J.2020.2060316.
  33. [33] Y. Cao, J. Gu, Y. Zang, X. Wu, S. Zhang, and M. Guo, Path planning-oriented obstacle avoiding workspace modelling for robot manipulator, International Journal of Robotics and Automation, 34(1), 2019, 4335, doi: 10.2316/J.2019.206-4335.
  34. [34] J. Bolboli, M.A. Khosravi, and F. Abdollahi, Stiffness feasible workspace of cable driven parallel robots with application to optimal design of a planar cable robot, Robotics and Autonomous Systems, 114, 2019, 19–28.
  35. [35] K.A. Arrouk, B.C. Bouzgarrou, and G. Gogu, Workspace characterization and kinematic analysis of general spherical parallel manipulators revisited via graphical based approaches, Mechanism and Machine Theory, 122, 2018, 404–431.
  36. [36] W. Li and J. Angeles, A novel three-loop parallel robot with full mobility: Kinematics, singularity, workspace, and dexterity analysis, Journal of Mechanisms and Robotics, 9(5), October 2017, 051003.
  37. [37] A. Khalifa, M. Fanni, and A.M. Mohamed, Geometrical/analytical approach for reciprocal screw-based singularity analysis of a novel dexterous minimally invasive manipulator, Robotics and Autonous Systems, 98, 2017, 56–66.
  38. [38] Z.D. Sheng, X. Yundou, Y. Jiantao, and Z. Yongsheng, Design of a novel 5-DOF hybrid serial-parallel manipulator and theoretical analysis of its parallel part, Robotics and Computer Integrated Manufacturing, 53, 2018, 228–239.

Important Links:

Go Back