Abstract
Parallel manipulators which are singular with respect to the Sch¨onflies motion group X(a) are called Schönflies-singular, or more precisely X(a)-singular, where a denotes the rotary axis. A special class of such manipulators are architecturally singular ones because they are singular with respect to any Schönflies group. Another remarkable set of Schönflies-singular planar Stewart Gough platforms was already presented by the author in [5]. Moreover the main theorem on these manipulators was given in [6]. In this paper we give a complete discussion of the remaining special cases which also include so-called Cartesian-singular planar manipulators as byproduct.
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References
Karger, A., Singularities and self-motions of equiform platforms, Mechanism and Machine Theory, 36(7):801–815, 2001.
Karger, A., Architecture singular planar parallel manipulators, Mechanism and Machine Theory, 38(11):1149–1164, 2003.
Karger, A., Parallel manipulators with simple geometrical structure. In Proc. 2nd European Conference on Mechanism Science, M. Ceccarelli (Ed.), pp. 463–470, Springer, 2008.
Mick, S. and Röschel, O., Geometry & architecturally shaky platforms. In Advances in Robot Kinematics: Analysis and Control, J. Lenarcic and M.L. Husty (Eds.), pp. 455–464, Kluwer, 1998.
Nawratil, G., A remarkable set of Schönflies-singular planar Stewart Gough platforms, Technical Report No. 198, Geometry Preprint Series, Vienna University of Technology, 2009.
Nawratil, G., Main theorem on Schönflies-singular planar Stewart Gough platforms. In Advances in Robot Kinematics, J. Lenarcic and M.M. Stanisic (Eds.), Springer, 2010.
Nawratil, G., Special cases of Schönflies-singular planar Stewart Gough platforms, Technical Report No. 202, Geometry Preprint Series, Vienna University of Technology, 2009.
Röschel, O. and Mick, S., Characterisation of architecturally shaky platforms. In Advances in Robot Kinematics: Analysis and Control, J. Lenarcic, M. Husty (Eds.), pp. 465–474, Kluwer, 1998.
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Nawratil, G. (2010). Special Cases of Schönflies-Singular Planar Stewart Gough Platforms. In: Pisla, D., Ceccarelli, M., Husty, M., Corves, B. (eds) New Trends in Mechanism Science. Mechanisms and Machine Science, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9689-0_6
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DOI: https://doi.org/10.1007/978-90-481-9689-0_6
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