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What is a Hinge Mechanism? What did Kempe Prove?

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Abstract

For a long time, it was believed that Alfred Kempe proved (1876) a theorem about the possibility of plotting an arbitrary planar algebraic curve by parts using hinge mechanisms (linkages). However, at the end of the 20th century, specialists in algebraic geometry, having rediscovered and developed this result in modern language, began to assert that Kempe’s reasoning contained significant gaps and errors. In the author’s opinion, these claims are unfounded. In this paper, by a detailed analysis of the notions of a linkage and its configuration space, the author tries to substantiate this point of view.

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, Moscow, Russia

    M. D. Kovalev

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  1. M. D. Kovalev
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Correspondence to M. D. Kovalev.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 179, Proceedings of the International Conference “Classical and Modern Geometry” Dedicated to the 100th Anniversary of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 1, 2020.

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Kovalev, M.D. What is a Hinge Mechanism? What did Kempe Prove?. J Math Sci 276, 366–378 (2023). https://doi.org/10.1007/s10958-023-06751-0

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  • DOI: https://doi.org/10.1007/s10958-023-06751-0

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