Mathematics Model for 6-DOF Joints Manipulation Robots
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 t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/21/2828 |
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| author | Oleg Krakhmalev Nikita Krakhmalev Sergey Gataullin Irina Makarenko Petr Nikitin Denis Serdechnyy Kang Liang Sergey Korchagin |
| author_facet | Oleg Krakhmalev Nikita Krakhmalev Sergey Gataullin Irina Makarenko Petr Nikitin Denis Serdechnyy Kang Liang Sergey Korchagin |
| author_sort | Oleg Krakhmalev |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T05:56:32Z |
| format | Article |
| id | doaj.art-2167813f2b4643dcbdc0a67d540a6d68 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T05:56:32Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2167813f2b4643dcbdc0a67d540a6d682023-11-22T21:19:27ZengMDPI AGMathematics2227-73902021-11-01921282810.3390/math9212828Mathematics Model for 6-DOF Joints Manipulation RobotsOleg Krakhmalev0Nikita Krakhmalev1Sergey Gataullin2Irina Makarenko3Petr Nikitin4Denis Serdechnyy5Kang Liang6Sergey Korchagin7Department of Data Analysis and Machine Learning, Financial University under the Government of the Russian Federation, Shcherbakovskaya, 38, 105187 Moscow, RussiaDepartment of Engineering Graphics, Moscow State University of Technology “STANKIN”, Vadkovsky Lane, 3a, 127055 Moscow, RussiaDepartment of Data Analysis and Machine Learning, Financial University under the Government of the Russian Federation, Shcherbakovskaya, 38, 105187 Moscow, RussiaDepartment of Data Analysis and Machine Learning, Financial University under the Government of the Russian Federation, Shcherbakovskaya, 38, 105187 Moscow, RussiaDepartment of Applied Informatics, Russian State Agrarian University—Moscow Timiryazev Agricultural Academy, Timiryazevskaya str., 49, 127550 Moscow, RussiaDepartment of Innovation Management, State University of Management, Ryazansky Pr., 99, 109542 Moscow, RussiaSchool of Electronic and Electrical Engineering, Shanghai Polytechnic University, 2360 Jin Hai Road, Pudong District, Shanghai 201209, ChinaDepartment of Data Analysis and Machine Learning, Financial University under the Government of the Russian Federation, Shcherbakovskaya, 38, 105187 Moscow, RussiaA 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.https://www.mdpi.com/2227-7390/9/21/2828mathematics modeldynamic modelmanipulation robots6-DOF joints |
| spellingShingle | Oleg Krakhmalev Nikita Krakhmalev Sergey Gataullin Irina Makarenko Petr Nikitin Denis Serdechnyy Kang Liang Sergey Korchagin Mathematics Model for 6-DOF Joints Manipulation Robots Mathematics mathematics model dynamic model manipulation robots 6-DOF joints |
| title | Mathematics Model for 6-DOF Joints Manipulation Robots |
| title_full | Mathematics Model for 6-DOF Joints Manipulation Robots |
| title_fullStr | Mathematics Model for 6-DOF Joints Manipulation Robots |
| title_full_unstemmed | Mathematics Model for 6-DOF Joints Manipulation Robots |
| title_short | Mathematics Model for 6-DOF Joints Manipulation Robots |
| title_sort | mathematics model for 6 dof joints manipulation robots |
| topic | mathematics model dynamic model manipulation robots 6-DOF joints |
| url | https://www.mdpi.com/2227-7390/9/21/2828 |
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