Abstract
This book has presented new methods for singularity set computation and singularity-free path planning. Unlike in previous works, the two problems have been addressed assuming a general kinematic architecture and geometry of the robotic systems under consideration. By design, the methods are applicable to any nonredundant mechanism with lower-pair joints, the only limitation coming from the computational power available. Special emphasis has been put on illustrating the methods in mechanisms with complex architectures because they are those typically arising in today’s robotics, where the development of new machines with increasingly complex motions is a growing trend. To conclude the book, we summarise the presented results and highlight points for future attention.
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D. Zlatanov, Generalized singularity analysis of mechanisms. PhD thesis, University of Toronto, 1998
O. Bohigas, M.E. Henderson, L. Ros, J.M. Porta, A singularity-free path planner for closed-chain manipulators, in Proceedings of the IEEE International Conference on Robotics and Automation, ICRA (St. Paul, USA) (2012), pp. 2128–2134
B. Schulze, Symmetry as a sufficient condition for a finite flex. SIAM J. Discrete Math. 24(4), 1291–1312 (2010)
B. Schulze, W. Whiteley, The orbit rigidity matrix of a symmetric framework. Discrete Comput. Geom. 46(3), 561–598 (2011)
A. Sljoka, Algorithms in rigidity theory with applications to protein flexibility and mechanical linkages. PhD Thesis, York University, 2012
B. Schulze, A. Sljoka, W. Whiteley, How does symmetry impact the rigidity of proteins? Philos. Trans. Ser. A, Math. Phys. Eng. Sci. 372(2008), 20120041 (2014)
J.M. Porta, L. Ros, B. Schulze, A. Sljoka, W. Whiteley, On the symmetric molecular conjectures, in Computational Kinematics, ed. by F. Thomas, A. Pérez Gracia (Springer 2014), pp. 175–184
O. Bohigas, D. Zlatanov, M. Manubens, L. Ros, On the numerical classification of the singularities of robot manipulators, in Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE (Chicago, USA) (2012), pp. 1287–1296
E.J. Haug, J.-Y. Wang, J.K. Wu, Dextrous workspaces of manipulators, part I: Analytical criteria. J. Struct. Mech. 20(3), 321–361 (1992)
J.-Y. Wang, J.K. Wu, Dextrous workspaces of manipulators, part II: Computational methods. J. Struct. Mech. 21(4), 471–506 (1993)
C.C. Qiu, C.-M. Luh, E.J. Haug, Dextrous workspaces of manipulators, part III: Calculation of continuation curves at bifurcation points. J. Struct. Mech. 23(1), 115–130 (1995)
L.J. Du Plessis, J.A. Snyman, A numerical method for the determination of dextrous workspaces of Gough-Stewart platforms. I. J. Numer. Methods Eng. 52(4), 345–369 (2001)
A.M. Hay, J.A. Snyman, A multi-level optimization methodology for determining the dextrous workspaces of planar parallel manipulators. Struct. Multi. Optim. 30(6), 422–427 (2005)
F.-C. Yang, E.J. Haug, Numerical analysis of the kinematic dexterity of mechanisms. ASME J. Mech. Des. 116(1), 119–126 (1994)
L. Jaillet, J.M. Porta, Path planning under kinematic constraints by rapidly exploring manifolds. IEEE Trans. Robot. 29(1), 105–117 (2013)
L. Jaillet, J.M. Porta, Asymptotically-optimal path planning on manifolds, in Robotics: Science and Systems (2012)
L. Campos, F. Bourbonnais, I.A. Bonev, P. Bigras, Development of a five-bar parallel robot with large workspace, in Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE (Montreal, Canada) (2010)
F. Bourbonnais, Utilisation optimale de l’espace de travail des robots parallèles en affrontant certains types de singularités,” Master’s thesis, École de Technologie Supérieure, Université du Québec (2012)
J. Coulombe, I.A. Bonev, A new rotary hexapod for micropositioning, in Proceedings of the IEEE International Conference on Robotics and Automation, ICRA (Karlsruhe, Germany) (2013), pp. 877–880
M. Zoppi, D. Zlatanov, R. Molfino, On the velocity analysis of interconnected chain mechanisms. Mech. Mach. Theory 41(11), 1346–1358 (2006)
A. Müller, On the terminology and geometric aspects of redundant parallel manipulators. Robotica 31(1), 137–147 (2013)
F. Bourbonnais, P. Bigras, I. Bonev, Minimum-time trajectory planning and control of a pick-and-place five-bar parallel robot. IEEE/ASME Trans. Mechatron. 20(2), 740–749 (2015)
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Bohigas, O., Manubens, M., Ros, L. (2017). Conclusions. In: Singularities of Robot Mechanisms. Mechanisms and Machine Science, vol 41. Springer, Cham. https://doi.org/10.1007/978-3-319-32922-2_7
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DOI: https://doi.org/10.1007/978-3-319-32922-2_7
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