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Kinematic Analysis for a Planar Redundant Serial Manipulator

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Part of the Mechanisms and Machine Science book series (Mechan. Machine Science,volume 54)

Abstract

A planar serial manipulator with three rotational joints (planar 3R) can be seen to be a kinematically redundant system if only the position of the end-effector is taken into account. Configuration sets of serial manipulators of planar 3R will be considered in this work in detail. The configuration set is the solution set of all rotational joint angles (actually, we use the tangent of the half-angle) fulfilling the kinematic mapping. Then the configuration set will be an algebraic set if we fix the end-effector or the end-effector follows algebraic motions (for instance, algebraic curves in the special Euclidean group). We show the characteristic of configuration curves among the workspace in terms of the number of real connected components. The configuration curve has either one connected component or two connected components. Furthermore, we also studied the torque variation among the real connected components of the configuration set.

Keywords

  • Planar 3R
  • Torque
  • Gröbner Basis
  • Real connected components
  • Discriminant

This research was funded by the Austrian Ministry for Transport, Innovation and Technology (BMVIT) within the framework of the sponsorship agreement formed for 2015–2018 under the project RedRobCo.

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Acknowledgements

We would like to thank Andrés Kecskeméthy (University of Duisburg-Essen), Josef Schicho (University of Linz) and Hans-Peter Schröcker (University Innsbruck) for the fruitful discussions.

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Correspondence to Zijia Li .

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Li, Z., Brandstötter, M., Hofbaur, M. (2018). Kinematic Analysis for a Planar Redundant Serial Manipulator. In: Carvalho, J., Martins, D., Simoni, R., Simas, H. (eds) Multibody Mechatronic Systems. MuSMe 2017. Mechanisms and Machine Science, vol 54. Springer, Cham. https://doi.org/10.1007/978-3-319-67567-1_9

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  • DOI: https://doi.org/10.1007/978-3-319-67567-1_9

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