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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Autores principales:	Oleg Krakhmalev, Nikita Krakhmalev, Sergey Gataullin, Irina Makarenko, Petr Nikitin, Denis Serdechnyy, Kang Liang, Sergey Korchagin
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	mathematics model dynamic model manipulation robots 6-DOF joints Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/2167813f2b4643dcbdc0a67d540a6d68
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id	oai:doaj.org-article:2167813f2b4643dcbdc0a67d540a6d68
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spelling	oai:doaj.org-article:2167813f2b4643dcbdc0a67d540a6d682021-11-11T18:21:19ZMathematics Model for 6-DOF Joints Manipulation Robots10.3390/math92128282227-7390https://doaj.org/article/2167813f2b4643dcbdc0a67d540a6d682021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2828https://doaj.org/toc/2227-7390A 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.Oleg KrakhmalevNikita KrakhmalevSergey GataullinIrina MakarenkoPetr NikitinDenis SerdechnyyKang LiangSergey KorchaginMDPI AGarticlemathematics modeldynamic modelmanipulation robots6-DOF jointsMathematicsQA1-939ENMathematics, Vol 9, Iss 2828, p 2828 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	mathematics model dynamic model manipulation robots 6-DOF joints Mathematics QA1-939
spellingShingle	mathematics model dynamic model manipulation robots 6-DOF joints Mathematics QA1-939 Oleg Krakhmalev Nikita Krakhmalev Sergey Gataullin Irina Makarenko Petr Nikitin Denis Serdechnyy Kang Liang Sergey Korchagin Mathematics Model for 6-DOF Joints Manipulation Robots
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.
format	article
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
title	Mathematics Model for 6-DOF Joints Manipulation Robots
title_short	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_sort	mathematics model for 6-dof joints manipulation robots
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/2167813f2b4643dcbdc0a67d540a6d68
work_keys_str_mv	AT olegkrakhmalev mathematicsmodelfor6dofjointsmanipulationrobots AT nikitakrakhmalev mathematicsmodelfor6dofjointsmanipulationrobots AT sergeygataullin mathematicsmodelfor6dofjointsmanipulationrobots AT irinamakarenko mathematicsmodelfor6dofjointsmanipulationrobots AT petrnikitin mathematicsmodelfor6dofjointsmanipulationrobots AT denisserdechnyy mathematicsmodelfor6dofjointsmanipulationrobots AT kangliang mathematicsmodelfor6dofjointsmanipulationrobots AT sergeykorchagin mathematicsmodelfor6dofjointsmanipulationrobots
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Mathematics Model for 6-DOF Joints Manipulation Robots

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