Abstract
We give a detailed study of planar Stewart Gough platforms, which possess a quadratic singularity surface in the space of translations for any orientation of the platform. These manipulators were already characterized by a rank condition of a \(5\times 6\) matrix, but a geometric interpretation is still missing until now. We give this geometric criterion based on the useful existence result, that every non-architecturally singular Stewart Gough platform has corresponding triples of anchor points, where the triangles in the platform and the base are not degenerated. Moreover, we present a rational parametrization of the 5-dimensional singularity locus and give an upper bound for the number of solutions of the direct kinematics problem. Finally we remark special properties of the locus of anchor points for singular-invariant leg-replacements.
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Acknowledgments
This research is supported by Grant No. P 24927-N25 of the Austrian Science Fund FWF within the project “Stewart Gough platforms with self-motions”. The authors want to thank the reviewers for their useful suggestions and comments, which have helped to improve the quality of the paper.
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Aigner, B., Nawratil, G. (2017). Planar Stewart Gough Platforms with Quadratic Singularity Surface. In: Wenger, P., Flores, P. (eds) New Trends in Mechanism and Machine Science. Mechanisms and Machine Science, vol 43. Springer, Cham. https://doi.org/10.1007/978-3-319-44156-6_10
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DOI: https://doi.org/10.1007/978-3-319-44156-6_10
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