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Sbornik: Mathematics, 2022, Volume 213, Issue 4, Pages 512–533
DOI: https://doi.org/10.1070/SM9542 (Mi sm9542) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Configuration spaces of hinged mechanisms, and their projections

M. D. Kovalev

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
English version PDF (604 kB) Citations (1)
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DOI: https://doi.org/10.1070/SM9542
Abstract: Our subject is the geometry of planar hinged mechanisms. The article contains a formalization of basic concepts of the theory of hinged-lever constructions, as well as some information from real algebraic geometry needed for their study. We consider mechanisms with variable number of degrees of freedom and mechanisms that have more than one degree of freedom but each hinge of which moves with one degree of freedom. For the last type we find the dimension of the configuration space. We give a number of examples of mechanisms with unusual geometric properties and formulate open questions.
Bibliography: 17 titles.
Keywords: hinged mechanism, configuration space, reducibility, dimension.
Received: 25.12.2020 and 16.12.2021
Russian version:
Matematicheskii Sbornik, 2022, Volume 213, Number 4, Pages 74–99
DOI: https://doi.org/10.4213/sm9542
Bibliographic databases:
Document Type: Article
MSC: 70B15
Language: English
Original paper language: Russian
Citation: M. D. Kovalev, “Configuration spaces of hinged mechanisms, and their projections”, Mat. Sb., 213:4 (2022), 74–99; Sb. Math., 213:4 (2022), 512–533
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm9542
  • https://doi.org/10.1070/SM9542
  • https://www.mathnet.ru/eng/sm/v213/i4/p74
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник Sbornik: Mathematics
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    Abstract page:249
    Russian version PDF:52
    English version PDF:36
    Russian version HTML:145
    References:39
    First page:8
     
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