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Oscillations of Double Mathematical Pendulum with Noncollinear Joints

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Advances in Mechanical Engineering (MMESE 2020)

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Abstract

This paper considers the dynamics of a double mathematical pendulum whose cylindrical joints axes are not collinear to each other and form a certain acute angle between them. Such system is the simplest scheme of spatial two-link manipulator and can also be a component of various multi-link robotic devices. Basic geometric and kinematic characteristics of a double pendulum are given, which are necessary for deriving the equations of its motion. Small oscillations of the system near the lower equilibrium position are studied. As a result, formulas for the natural frequencies and modes of small oscillations are obtained. The dependence of frequencies and modes on the angle between the pendulum joints is revealed using a qualitative and graphical analysis of found expressions. The obtained results are both of theoretical interest and important practical value.

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Authors and Affiliations

  1. Peter the Great St. Petersburg Polytechnic University, Saint Petersburg, Russia

    Alexey S. Smirnov & Boris A. Smolnikov

  2. Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, St. Petersburg, Russia

    Alexey S. Smirnov & Boris A. Smolnikov

Authors
  1. Alexey S. Smirnov
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  2. Boris A. Smolnikov
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Corresponding author

Correspondence to Alexey S. Smirnov .

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Editors and Affiliations

  1. Saint Petersburg Polytechnic University, Saint Petersburg, Russia

    Alexander N. Evgrafov

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Smirnov, A.S., Smolnikov, B.A. (2021). Oscillations of Double Mathematical Pendulum with Noncollinear Joints. In: Evgrafov, A.N. (eds) Advances in Mechanical Engineering. MMESE 2020. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-62062-2_18

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  • DOI: https://doi.org/10.1007/978-3-030-62062-2_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-62061-5

  • Online ISBN: 978-3-030-62062-2

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