Abstract
This chapter is dedicated to the so-called cuspidal robots; i.e., those robots that can move from one inverse geometric solution to another without meeting a singular configuration. This feature was discovered quite recently and has then been fascinating a lot of researchers. After a brief history of cuspidal robots, the chapter provides the main features of cuspidal robots: explanation of the non-singular change of posture, uniqueness domains, regions of feasible paths, identification and classification of cuspidal robots. The chapter focuses on 3-R orthogonal serial robots. The case of 6-dof robots and parallel robots is discussed in the end of this chapter.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M. Baili, P. Wenger, D. Chablat, Classification of one family of 3R positioning manipulators, in Proceedings of 11th International Conference on Advanced Robotics (2003)
P. Borrel, A. Liegeois, A study of manipulator inverse geometric solutions with application to trajectory planning and workspace determination, in Proceedings of IEEE International Conference Robotics and AUT, pp. 1180–1185 (1986)
J.W. Burdick, Kinematic analysis and design of redundant manipulators. Ph.D. thesis, Standford University (1988)
J.W. Burdick, A classification of 3R regional manipulator singularities and geometries. Mech. Mach. Theor. 30(1), 71–89 (1995)
S. Caro, P. Wenger, D. Chablat, Non-singular assembly mode changing trajectories of a 6-dof parallel robot, in In Proceedings of ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference (2012)
G.E. Collins, Quantifier elimination for real closed fields by cylindrical algebraic decomposition. in Spring lecture, Notes in Computer Science vol. 3, pp. 515–532 (1975)
S. Corvez, F. Rouillier, Using computer algebra tools to classify serial manipulators, in Automated Deduction in Geometry, Lectures Notes in Computer Science, pp. 31–43 (2004)
M. Coste, A simple proof that generic 3-RPR manipulators have two aspects. ASME J. Mech. Robot. 4(1) (2012)
M. Coste, D. Chablat, P. Wenger, Non-singular change of assembly mode without any cusp, in Advances in Robot Kinematics, ed. J. Lenarčič, O. Khatib (Springer, 2014)
P.S. Donelan, C.G. Gibson, Singular phenomena in kinematics, in Singularity Theory, ed. by B. Bruce, D. Mond (Cambridge University Press, 1999)
P.S. Donelan, A. Müller, Singularities of regional manipulators revisited, in Advances in Robot Kinematics, Motion in Man and Machine, ed. by J. Lenarčič, M. Staničić (Springer, 2010)
J. El Omri, Kinematic analysis of robot manipulators (in French). Ph.D. thesis, Ecole Centrale de Nantes (1996)
J. El Omri, P. Wenger, How to recognize simply a nonsingular posture changing 3-dof manipulator, in Proceedings of 7th International Conference on Advanced Robotics, pp. 215–222 (1995)
C.G. Gibson, Kinematics from the singular viewpoint, in Geometrical Foundation of Robotics, ed. J.M. Selig (World Scientific Press, 2000)
E. Hemmingson, S. Ellqvist, J. Pauxels, New Robot Improves Cost-Efficiency of Spot Welding (ABB Review, Spot Welding Robots, 1996)
M. Husty, Non-singular assembly mode change in 3-RPR parallel manipulators, in Singularity Theory, ed. A. Müller, A. Kecskemthy (Springer, 2009)
C. Innocenti, V. Parenti-Castelli, Singularity-free evolution from one configuration to another in serial and fully-parallel manipulators. ASME J. Mech. Des. 120, 73–99 (1998)
W. Khalil, J. Kleinfinger, A new geometric notation for open and closed loop robots, in Proceedings of IEEE International Conference Robotic and AUT, pp. 1174–1179 (1986)
D. Kholi, J. Spanos, Workspace analysis of mechanical manipulators using polynomial discriminant. ASME J. Mech. Transm. Autom. Des. 107, 209–215 (1985)
X. Kong, C.M. Gosselin, Determination of the uniqueness domains of 3-RPR planar parallel manipulators with similar platforms, in Proceedings of ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference (2000)
D. Lazard, F. Rouillier. Solving parametric polynomial systems. INRIA Technical Report (2004)
C. Mavroidis, B. Roth, Structural parameters which reduce the number of manipulator configurations. ASME J. Mech. Des. 116, 3–10 (1994)
P.R. McAree, R.W. Daniel, An explanation of never-special assembly changing motions for 3–3 parallel manipulators. Int. J. Robot. Res. 18(6), 556–574 (1999)
D.K. Pai, M.C. Leu, Genericity and singularities of robot manipulators. IEEE Trans. Robot. Autom. 20(4), 545–559 (1991)
C.V. Parenti, C. Innocenti, Position analysis of robot manipulators: Regions and sub-regions, in Proceedings of International Conference on Advances in Robot Kinematics, pp. 150–158 (1988)
B. Pieper. The Kinematics of Manipulators Under Computer Control. Ph.D. thesis, Stanford University (1968)
P. Wenger, A new general formalism for the kinematic analysis of all non-redundant manipulators, in Proceedings of IEEE International Conference Robotic and AUT, pp. 442–447 (1992)
P. Wenger, Design of cuspidal and noncuspidal manipulators, in Proceedings of IEEE International Conference Robotic and AUT, pp. 2172–2177 (1997)
P. Wenger, Some guidelines for the kinematic design of new manipulators. Mechanisms Mach. Theor. 35(3), 437–449 (1999)
P. Wenger, Uniqueness domains and regions of feasible paths for cuspidal manipulators. IEEE Trans. Robot. 20(4), 750–754 (2004)
P. Wenger, D. Chablat, Workspace and assembly-modes in fully parallel manipulators: a descriptive study, in Advances in Robot Kinematics, ed. by J. Lenarčič, M. Husty (Kluwer Academic Publisher, 1998)
P. Wenger, J. El Omri, Modeling kinematic properties of type-2 regional manipulators using octrees, in Proceedings of IEEE International Conference Man and Cybernetics, pp. 183–188 (1993)
H. Whitney, On singularities of mappings of euclidean spaces 1. mappings of the plane into the plane. Ann. Math. 62(3), 374–410 (1955)
M. Zein, P. Wenger, D. Chablat, An exhaustive study of the workspace topologies of all 3R orthogonal manipulators with geometric simplifications. Mechanisms Mach. Theor. 41(8), 971–986 (2006)
M. Zein, P. Wenger, D. Chablat, Singular curves in the joint space and cusp points of 3-RPR parallel manipulators. Robotica Spec. Issue Geometry Robot. Sens. 25(6), 714–724 (2007)
M. Zein, P. Wenger, D. Chablat, Non-singular assembly-mode changing motions for 3-RPR parallel manipulators. Mechanisms Mach. Theor. 43(4), 480–490 (2008)
M. Zoppi, Effective backward kinematics for an industrial 6Rrobot, in Proceedings of ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference (2002)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 CISM International Centre for Mechanical Sciences
About this chapter
Cite this chapter
Wenger, P. (2019). Cuspidal Robots. In: Müller, A., Zlatanov, D. (eds) Singular Configurations of Mechanisms and Manipulators. CISM International Centre for Mechanical Sciences, vol 589. Springer, Cham. https://doi.org/10.1007/978-3-030-05219-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-05219-5_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-05218-8
Online ISBN: 978-3-030-05219-5
eBook Packages: EngineeringEngineering (R0)