Modeling the boundaries of the working space of a planar three-link manipulator
A study of the boundaries of the working space of a three-link planar manipulator, specified by analytical equations, is carried out. A new geometric interpretation of these samples is proposed. On its basis, it is established that outer space consists of two-parameter volumes of eccentric and co...
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| Format: | Article |
| Language: | English |
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Omsk State Technical University, Federal State Autonoumos Educational Institution of Higher Education
2024-09-01
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| Series: | Омский научный вестник |
| Subjects: | |
| Online Access: | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2024/%E2%84%963%20(191)%20(%D0%9E%D0%9D%D0%92)/73-81%20%D0%A8%D0%B5%D0%B2%D0%B5%D0%BB%D0%B5%D0%B2%D0%B0%20%D0%A2.%20%D0%90.,%20%D0%9B%D1%8F%D1%88%D0%BA%D0%BE%D0%B2%20%D0%90.%20%D0%90..pdf |
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| _version_ | 1832543207450214400 |
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| author | T. A. Sheveleva A. A. Lyashkov |
| author_facet | T. A. Sheveleva A. A. Lyashkov |
| author_sort | T. A. Sheveleva |
| collection | DOAJ |
| description | A study of the boundaries of the working space of a three-link planar manipulator,
specified by analytical equations, is carried out. A new geometric interpretation of
these samples is proposed. On its basis, it is established that outer space consists
of two-parameter volumes of eccentric and concentric circles. When transforming
such environments into four-dimensional space, two types of hypersurfaces are
obtained, which represent a geometric model of the manipulator's workspace. The
discriminants of these hypersurfaces on the hyperplane are two two-dimensional
surfaces. Both an analytical description of these surfaces and their computer models
are obtained. As a result, it is established that the boundaries of the working space
on the plane of the mechanism are the discriminants of such surfaces. To confirm
the reliability of the results obtained, as an example, an inverse kinematics problem
is solved on discriminant surfaces — the values of generalized coordinates at the
boundary points of the manipulator’s workspace are determined for their given
Cartesian coordinates. |
| format | Article |
| id | doaj-art-2f56af4d007e43c88d071db082f230e7 |
| institution | Kabale University |
| issn | 1813-8225 2541-7541 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | Omsk State Technical University, Federal State Autonoumos Educational Institution of Higher Education |
| record_format | Article |
| series | Омский научный вестник |
| spelling | doaj-art-2f56af4d007e43c88d071db082f230e72025-02-03T11:51:36ZengOmsk State Technical University, Federal State Autonoumos Educational Institution of Higher EducationОмский научный вестник1813-82252541-75412024-09-013 (191)738110.25206/1813-8225-2024-191-73-81Modeling the boundaries of the working space of a planar three-link manipulatorT. A. Sheveleva0https://orcid.org/0009-0002-2577-8348A. A. Lyashkov1https://orcid.org/0000-0003-0100-8584Omsk State Technical UniversityOmsk State Technical UniversityA study of the boundaries of the working space of a three-link planar manipulator, specified by analytical equations, is carried out. A new geometric interpretation of these samples is proposed. On its basis, it is established that outer space consists of two-parameter volumes of eccentric and concentric circles. When transforming such environments into four-dimensional space, two types of hypersurfaces are obtained, which represent a geometric model of the manipulator's workspace. The discriminants of these hypersurfaces on the hyperplane are two two-dimensional surfaces. Both an analytical description of these surfaces and their computer models are obtained. As a result, it is established that the boundaries of the working space on the plane of the mechanism are the discriminants of such surfaces. To confirm the reliability of the results obtained, as an example, an inverse kinematics problem is solved on discriminant surfaces — the values of generalized coordinates at the boundary points of the manipulator’s workspace are determined for their given Cartesian coordinates.https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2024/%E2%84%963%20(191)%20(%D0%9E%D0%9D%D0%92)/73-81%20%D0%A8%D0%B5%D0%B2%D0%B5%D0%BB%D0%B5%D0%B2%D0%B0%20%D0%A2.%20%D0%90.,%20%D0%9B%D1%8F%D1%88%D0%BA%D0%BE%D0%B2%20%D0%90.%20%D0%90..pdfgeometric modelingcomputer modelmanipulatorgripper centermanipulator workspacehypersurfacediscriminantthree-link planar manipulator |
| spellingShingle | T. A. Sheveleva A. A. Lyashkov Modeling the boundaries of the working space of a planar three-link manipulator Омский научный вестник geometric modeling computer model manipulator gripper center manipulator workspace hypersurface discriminant three-link planar manipulator |
| title | Modeling the boundaries of the working space of a planar three-link manipulator |
| title_full | Modeling the boundaries of the working space of a planar three-link manipulator |
| title_fullStr | Modeling the boundaries of the working space of a planar three-link manipulator |
| title_full_unstemmed | Modeling the boundaries of the working space of a planar three-link manipulator |
| title_short | Modeling the boundaries of the working space of a planar three-link manipulator |
| title_sort | modeling the boundaries of the working space of a planar three link manipulator |
| topic | geometric modeling computer model manipulator gripper center manipulator workspace hypersurface discriminant three-link planar manipulator |
| url | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2024/%E2%84%963%20(191)%20(%D0%9E%D0%9D%D0%92)/73-81%20%D0%A8%D0%B5%D0%B2%D0%B5%D0%BB%D0%B5%D0%B2%D0%B0%20%D0%A2.%20%D0%90.,%20%D0%9B%D1%8F%D1%88%D0%BA%D0%BE%D0%B2%20%D0%90.%20%D0%90..pdf |
| work_keys_str_mv | AT tasheveleva modelingtheboundariesoftheworkingspaceofaplanarthreelinkmanipulator AT aalyashkov modelingtheboundariesoftheworkingspaceofaplanarthreelinkmanipulator |