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Workspace Determination

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Singularities of Robot Mechanisms

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 41))

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Abstract

This chapter explains how the developments in Chaps. 2 and 3 can be extended to obtain the various workspaces of a mechanism. For a given workspace, we explain how its boundary can be found by computing a set of generalised singularities, and how the points of such set can be classified into traversable or barrier singularities. A detailed map of the workspace is obtained as a result, in which the interior and exterior regions, together with the motion impediments that separate them, become clearly identified.

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References

  1. B. Roth, Performance evaluation of manipulators from a kinematic viewpoint. Nat. Bur. Stand. Spec. Publ. 459, 39–62 (1976)

    Google Scholar 

  2. F. Freudenstein, E.J.F. Primrose, On the analysis and synthesis of the workspace of a three-link, turning-pair connected robot arm. ASME J. Mech. Des. 106(3), 365–370 (1984)

    Google Scholar 

  3. A.H. Soni, Y.C. Tsai, An algorithm for the workspace of a general \(n\)-R robot. ASME J. Mech. Des. 105, 52–57 (1983)

    Google Scholar 

  4. J.A. Hansen, K.C. Gupta, S.M.K. Kazerounian, Generation and evaluation of the workspace of a manipulator. Int. J. Robot. Res. 2(3), 22–31 (1983)

    Article  Google Scholar 

  5. J. Rastegar, B. Fardanesh, Manipulation workspace analysis using the Monte Carlo method. Mech. Mach. Theor. 25(2), 233–239 (1990)

    Article  Google Scholar 

  6. C.M. Gosselin, Determination of the workspace of 6-DOF parallel manipulators. ASME J. Mech. Des. 112, 331–336 (1990)

    Article  Google Scholar 

  7. J.-P. Merlet, Geometrical determination of the workspace of a constrained parallel manipulator, in Advances in Robot Kinematics (1992), pp. 326–329

    Google Scholar 

  8. J.-P. Merlet, C.M. Gosselin, N. Mouly, Workspaces of planar parallel manipulators. Mech. Mach. Theor. 33(1–2), 7–20 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  9. J.-P. Merlet, Determination of 6D workspaces of Gough-type parallel manipulator and comparison between different geometries. Int. J. Robot. Res. 18(9), 902–916 (1999)

    Article  Google Scholar 

  10. I.A. Bonev, J.-C. Ryu, A new approach to orientation workspace analysis of 6-DOF parallel manipulators. Mech. Mach. Theor. 36(1), 15–28 (2001)

    Article  MATH  Google Scholar 

  11. J.A. Snyman, L.J. du Plessis, J. Duffy, An optimization approach to the determination of the boundaries of manipulator workspaces. ASME J. Mech. Des. 122(4), 447–456 (2000)

    Article  Google Scholar 

  12. I.A. Bonev, C.M. Gosselin, Analytical determination of the workspace of symmetrical spherical parallel mechanisms. IEEE Trans. Robot. 22(5), 1011–1017 (2006)

    Article  Google Scholar 

  13. K. Abdel-Malek, H.J. Yeh, Analytical boundary of the workspace for general 3-DOF mechanisms. Int. J. Robot. Res. 16(2), 198–213 (1997)

    Article  Google Scholar 

  14. M. Ceccarelli, A formulation for the workspace boundary of general N-revolute manipulators. Mech. Mach. Theor. 31(5), 637–646 (1996)

    Article  Google Scholar 

  15. K. Abdel-Malek, H.J. Yeh, N. Khairallah, Workspace, void, and volume determination of the general 5-DOF manipulator. J. Struct. Mech. 27(1), 89–115 (1999)

    Google Scholar 

  16. M. Zein, P. Wenger, D. Chablat, An exhaustive study of the workspace topologies of all 3R orthogonal manipulators with geometric simplifications. Mech. Mach. Theor. 41(8), 971–986 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  17. E. Ottaviano, M. Husty, M. Ceccarelli, Identification of the workspace boundary of a general 3-R manipulator. ASME J. Mech. Des. 128(1), 236–242 (2006)

    Article  MATH  Google Scholar 

  18. D.-Y. Jo, Numerical Analysis of Workspaces of Multibody Mechanical Systems. Ph.D. Thesis (The University of Iowa, Iowa, 1988)

    Google Scholar 

  19. F. A. Adkins, Numerical Continuation and Bifurcation Methods for Mechanism Workspace and Controllability Issues. Ph.D. Thesis (The University of Iowa, Iowa, 1996)

    Google Scholar 

  20. K. Abdel-Malek, J. Yang, D. Blackmore, K. Joy, Swept volumes: fundation, perspectives, and applications. Int. J. Shape Model. 12(1), 87–127 (2006)

    Article  MATH  Google Scholar 

  21. Y. Lu, Y. Shi, B. Hu, Solving reachable workspace of some parallel manipulators by computer-aided design variation geometry. Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 222(9), 1773–1781 (2008)

    Article  Google Scholar 

  22. G. Castelli, E. Ottaviano, M. Ceccarelli, A fairly general algorithm to evaluate workspace characteristics of serial and parallel manipulators. Mech. Based Des. Struct. Mach. 36(1), 14–33 (2008)

    Article  Google Scholar 

  23. E.J. Haug, C.-M. Luh, F.A. Adkins, J.-Y. Wang, Numerical algorithms for mapping boundaries of manipulator workspaces. ASME J. Mech. Des. 118(2), 228–234 (1996)

    Article  Google Scholar 

  24. K. Abdel-Malek, F.A. Adkins, H.J. Yeh, E.J. Haug, On the determination of boundaries to manipulator workspaces. Robot. Comput. Integr. Manuf. 13(1), 63–72 (1997)

    Article  Google Scholar 

  25. D. Oblak, D. Kohli, Boundary surfaces, limit surfaces, crossable and noncrossable surfaces in workspace of mechanical manipulators. ASME J. Mech. Des. 110(4), 389–396 (1988)

    Google Scholar 

  26. S.G. Krantz, H.R. Parks, The Implicit Function Theorem: History (Theory and Applications, Birkhäuser, 2002)

    MATH  Google Scholar 

  27. E.L. Allgower, K. Georg, Numerical Continuation Methods (Springer, 1990)

    Google Scholar 

  28. R.E. Moore, R.B. Kearfott, M.J. Cloud, Introduction to Interval Analysis (Society for Industrial Mathematics, 2009)

    Google Scholar 

  29. J.M. Porta, L. Ros, F. Thomas, A linear relaxation technique for the position analysis of multi-loop linkages. IEEE Trans. Robot. 25(2), 225–239 (2009)

    Article  Google Scholar 

  30. The CUIK Project Home Page, http://www.iri.upc.edu/cuik. Accessed 16 Jun 2016

  31. C.W. Wampler, Solving the kinematics of planar mechanisms by Dixon’s determinant and a complex plane formulation. ASME J. Mech. Des. 123, 382–387 (2001). September

    Article  Google Scholar 

  32. J.M. Porta, L. Ros, T. Creemers, F. Thomas, Box approximations of planar linkage configuration spaces. ASME J. Mech. Des. 129(4), 397–405 (2007)

    Article  Google Scholar 

  33. E. Celaya, T. Creemers, L. Ros, Exact interval propagation for the efficient solution of position analysis problems on planar linkages. Mech. Mach. Theor. 54, 116–131 (2012)

    Article  Google Scholar 

  34. D.Y. Jo, E.J. Haug, Workspace analysis of closed-loop mechanisms with unilateral constraints. Adv. Des. Autom. 19(3), 53–60 (1989)

    Google Scholar 

  35. J.-P. Merlet, Determination of the orientation workspace of parallel manipulators. J. Intell. Robot. Syst. 13(2), 143–160 (1995)

    Article  Google Scholar 

  36. Q. Jiang, C.M. Gosselin, Determination of the maximal singularity-free orientation workspace for the Gough-Stewart platform. Mech. Mach. Theor. 44(6), 1281–1293 (2009)

    Article  MATH  Google Scholar 

  37. Y. Cao, Z. Huang, H. Zhou, W. Ji, Orientation workspace analysis of a special class of Stewart-Gough parallel manipulators. Robotica 28(7), 989–1000 (2010)

    Article  Google Scholar 

  38. C.-M. Luh, F.A. Adkins, E.J. Haug, C.C. Qiu, Working capability analysis of Stewart platforms. ASME J. Mech. Des. 118(2), 220–227 (1996)

    Article  Google Scholar 

  39. F. Pernkopf, M. Husty, Workspace analysis of Stewart-Gough-type parallel manipulators. Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 220(7), 1019–1032 (2006)

    Article  Google Scholar 

  40. J.-P. Merlet, C.M. Gosselin, Springer Handbook of Robotics, ch. Parallel Mechanisms and Robots (Springer, 2008), pp. 269–285

    Google Scholar 

  41. Companion web page of this book: http://www.iri.upc.edu/srm. Accessed 16 Jun 2016

  42. C.M. Gosselin, E. St.-Pierre, Development and experimentation of a fast three-degree-of-freedom camera-orienting device. International Journal of Robotics Research, vol. 16, no. 5 (1997), pp. 619–630

    Google Scholar 

  43. I.A. Bonev, D. Chablat, P. Wenger, Working and assembly modes of the Agile Eye, in Proceedings of the IEEE International Conference on Robotics and Automation, ICRA (Orlando, USA, 2006), pp. 2317–2322

    Google Scholar 

  44. B. Servatius, O. Shai, W. Whiteley, Combinatorial characterization of the Assur graphs from engineering. Eur. J. Comb. 31(4), 1091–1104 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  45. A. Sljoka, O. Shai, W. Whiteley, Checking mobility and decomposition of linkages via pebble game algorithms, in Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE (Washington, USA, 2011), pp. 493–502

    Google Scholar 

  46. O. Altuzarra, C. Pinto, R. Avilés, A. Hernández, A practical procedure to analyze singular configurations in closed kinematic chains. IEEE Trans. Robot. 20(6), 929–940 (2004)

    Article  Google Scholar 

  47. E. Macho, O. Altuzarra, E. Amezua, A. Hernández, Obtaining configuration space and singularity maps for parallel manipulators. Mech. Mach. Theor. 44(11), 2110–2125 (2009)

    Google Scholar 

  48. N. Rojas, F. Thomas, On closed-form solutions to the position analysis of Baranov trusses. Mech. Mach. Theor. 50, 179–196 (2011)

    Article  Google Scholar 

  49. N. Rojas, F. Thomas, Distance-based position analysis of the three seven-link Assur kinematic chains. Mech. Mach. Theor. 46(2), 112–126 (2010)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Institut de Robòtica i Informàtica Industrial (UPC-CSIC), Barcelona, Catalonia, Spain

    Oriol Bohigas, Montserrat Manubens & Lluís Ros

Authors
  1. Oriol Bohigas
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  2. Montserrat Manubens
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  3. Lluís Ros
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Correspondence to Oriol Bohigas .

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Bohigas, O., Manubens, M., Ros, L. (2017). Workspace Determination. In: Singularities of Robot Mechanisms. Mechanisms and Machine Science, vol 41. Springer, Cham. https://doi.org/10.1007/978-3-319-32922-2_4

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  • DOI: https://doi.org/10.1007/978-3-319-32922-2_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32920-8

  • Online ISBN: 978-3-319-32922-2

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