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Multiple Solutions of Direct Kinematics of 3-RPR Parallel Manipulators

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Advances in Mechanism and Machine Science (IFToMM WC 2023)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 147))

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Abstract

It is well known that the direct kinematics of planar 3-RPR parallel manipulators has six solutions. In this paper conditions for multiple solutions are derived and linked to the notions of shakiness and flexes of these mechanisms existing in the literature.

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Notes

  1. 1.

    Note that homogeneous coordinates in this chapter are written in the European notation, with homogenizing coordinate on first place.

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Author information

Authors and Affiliations

  1. University Innsbruck, Technikerstr. 13, Innsbruck, Austria

    Manfred Husty

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  1. Manfred Husty
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Correspondence to Manfred Husty .

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Editors and Affiliations

  1. Department of Mechanical Eng, Tokyo Institute of Technology, Meguro-ku, Tokyo, Japan

    Masafumi Okada

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Husty, M. (2023). Multiple Solutions of Direct Kinematics of 3-RPR Parallel Manipulators. In: Okada, M. (eds) Advances in Mechanism and Machine Science. IFToMM WC 2023. Mechanisms and Machine Science, vol 147. Springer, Cham. https://doi.org/10.1007/978-3-031-45705-0_58

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