Abstract
Cuspidal robots can travel from one inverse kinematic solution (IKS) to another without meeting a singularity. This property can be analyzed by understanding the inverse kinematic model (IKM) as well as the singularities in the joint space and in the workspace. In this article, we revisit the geometrical interpretation of the IKM with conics. The conditions of getting different conics and their implication on singularities are discussed and the observations regarding the nature of the conics are presented. Further, a sufficient condition for a 3R robot to be binary (i.e. with up to 2 IKS) as well as quaternary (i.e. with up to 4 IKS) is put forth by analyzing the geometrical interpretation of the IKM. The possibility to derive a necessary and sufficient condition is presented too.
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References
Wenger, P.: A new general formalism for the kinematic analysis of all non-redundant manipulators. In: Proceedings of the 1992 IEEE International Conference on Robotics and Automation, Nice, France, pp. 442–447 (1992)
Wenger, P.: Uniqueness domains and regions of feasible paths for cuspidal manipulators. IEEE Trans. Rob. 20(4), 745–750 (2004)
Wenger, P., Chablat, D., Baili, M.: A DH-parameter based condition for 3R orthogonal manipulators to have 4 distinct inverse kinematic solutions. J. Mech. Des. 127, 150–155 (2005)
Salunkhe, D.H., Spartalis, C., Capco, J., Chablat, D., Wenger, P.: Necessary and sufficient condition for a generic 3R serial manipulator to be cuspidal. Mech. Mach. Theory 171, 104729 (2022)
Pieper, D.L.: The kinematics of manipulators under computer control. Ph.D. thesis, Stanford University, USA, October 1968
Kohli, D., Spanos, J.: Workspace analysis of mechanical manipulators using polynomial discriminants. J. Mech. Transm. Autom. Des. 107(2), 209–215 (1985)
Acknowledgements
The authors are supported by the joint French and Austrian ECARP project: ANR-19-CE48-0015, FWF I4452-N. The authors also thank Christoforos Spartalis for his contribution in the initial stages of the work.
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Salunkhe, D., Capco, J., Chablat, D., Wenger, P. (2022). Geometry Based Analysis of 3R Serial Robots. In: Altuzarra, O., Kecskeméthy, A. (eds) Advances in Robot Kinematics 2022. ARK 2022. Springer Proceedings in Advanced Robotics, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-031-08140-8_8
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DOI: https://doi.org/10.1007/978-3-031-08140-8_8
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