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Mathematics Model for 6-DOF Joints Manipulation Robots

Author

Listed:
  • Oleg Krakhmalev

    (Department of Data Analysis and Machine Learning, Financial University under the Government of the Russian Federation, Shcherbakovskaya, 38, 105187 Moscow, Russia)

  • Nikita Krakhmalev

    (Department of Engineering Graphics, Moscow State University of Technology “STANKIN”, Vadkovsky Lane, 3a, 127055 Moscow, Russia)

  • Sergey Gataullin

    (Department of Data Analysis and Machine Learning, Financial University under the Government of the Russian Federation, Shcherbakovskaya, 38, 105187 Moscow, Russia)

  • Irina Makarenko

    (Department of Data Analysis and Machine Learning, Financial University under the Government of the Russian Federation, Shcherbakovskaya, 38, 105187 Moscow, Russia)

  • Petr Nikitin

    (Department of Applied Informatics, Russian State Agrarian University—Moscow Timiryazev Agricultural Academy, Timiryazevskaya str., 49, 127550 Moscow, Russia)

  • Denis Serdechnyy

    (Department of Innovation Management, State University of Management, Ryazansky Pr., 99, 109542 Moscow, Russia)

  • Kang Liang

    (School of Electronic and Electrical Engineering, Shanghai Polytechnic University, 2360 Jin Hai Road, Pudong District, Shanghai 201209, China)

  • Sergey Korchagin

    (Department of Data Analysis and Machine Learning, Financial University under the Government of the Russian Federation, Shcherbakovskaya, 38, 105187 Moscow, Russia)

Abstract

A universal solution to an applied problem related to the study of deviations occurring in the joints of manipulation robots, for example, due to elastic deformations or gaps in them, is proposed. A mathematical (dynamic) model obtained by the Lagrange–Euler method is presented, making it possible to investigate such deviations. Six generalized coordinates, three linear and three angulars, were used to describe the variations of each joint in the dynamic model. This made it possible to introduce into consideration joints with six degrees of freedom (6-DOF joints). In addition, mathematical models for external forces acting on the links of manipulation robots are presented. When composing matrices of coefficients of equations of motion, elements identically equal to zero were excluded, which significantly increased the computational efficiency of these equations. The dynamic model based on the obtained equations can be used in the computer simulation of manipulation robots.

Suggested Citation

  • Oleg Krakhmalev & Nikita Krakhmalev & Sergey Gataullin & Irina Makarenko & Petr Nikitin & Denis Serdechnyy & Kang Liang & Sergey Korchagin, 2021. "Mathematics Model for 6-DOF Joints Manipulation Robots," Mathematics, MDPI, vol. 9(21), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2828-:d:674315
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    References listed on IDEAS

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    1. Vera Ivanyuk, 2021. "Formulating the Concept of an Investment Strategy Adaptable to Changes in the Market Situation," Economies, MDPI, vol. 9(3), pages 1-19, June.
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    Cited by:

    1. Sandi Baressi Šegota & Nikola Anđelić & Mario Šercer & Hrvoje Meštrić, 2022. "Dynamics Modeling of Industrial Robotic Manipulators: A Machine Learning Approach Based on Synthetic Data," Mathematics, MDPI, vol. 10(7), pages 1-17, April.

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