Mathematics Model for 6-DOF Joints Manipulation Robots
Oleg Krakhmalev,
Nikita Krakhmalev,
Sergey Gataullin,
Irina Makarenko,
Petr Nikitin,
Denis Serdechnyy,
Kang Liang,
Sergey Korchagin
Affiliations
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
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.
