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Classification of higher mobility closed-loop linkages

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Abstract

We provide a complete classification of paradoxical closed-loop n-linkages, where \(n\ge 6\), of mobility \(n-4\) or higher, containing revolute, prismatic or helical joints. We also explicitly write down strong necessary conditions for nR-linkages of mobility \(n-5\). Our main new tool is a geometric relation between a linkage L and another linkage \(L'\) resulting from adding equations to the configuration space of L. We then lift known classification results for \(L'\) to L using this relation.

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Acknowledgements

The first author would also like to express his gratitute to Hamid Abban for his encouragement and for putting him in contact with the research group led by Josef Schicho. He was supported by EPSRC Grant ref. EP/V048619/1 and by the Austrian Science Fund (FWF): W1214-N15, Project DK9 while staying at RICAM. This research was partially supported by the Austrian Science Fund (FWF): W1214-N15, project DK9. The research was funded by the Austrian Science Fund (FWF): P 31061.

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Author notes

  1. Tiago Duarte Guerreiro, Zijia Li and Josef Schicho have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK

    Tiago Duarte Guerreiro

  2. KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, No. 55, Zhongguancun East Road, Haidian District, Beijing, 100190, China

    Zijia Li

  3. Research Institute for Symbolic Computation, Johannes Kepler University Linz, Altenberger Strasse 69, 4040, Linz, Austria

    Josef Schicho

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  1. Tiago Duarte Guerreiro
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  2. Zijia Li
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  3. Josef Schicho
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Correspondence to Zijia Li.

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Duarte Guerreiro, T., Li, Z. & Schicho, J. Classification of higher mobility closed-loop linkages. Annali di Matematica 202, 737–762 (2023). https://doi.org/10.1007/s10231-022-01258-y

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