Modeling the boundaries of the working space of a planar three-link manipulator
https://doi.org/10.25206/1813-8225-2024-191-73-81
EDN: PBNXWQ
Abstract
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.
About the Authors
T. A. Sheveleva
Omsk State Technical University
Russian Federation
Russian Federation
Sheveleva Tatyana Anatolyevna - Graduate Student of Engineering Geometry and CAD Department, OmSTU.
Omsk
A. A. Lyashkov
Omsk State Technical University
Russian Federation
Russian Federation
Lyashkov Aleksey Anufriyevich - Doctor of Technical Sciences, Associate Professor, Professor of Engineering Geometry and CAD Department, OmSTU, SPIN-code: 2377-7912. AuthorID (SCOPUS): 55237710400. ResearcherID: C-2426-2017.
Omsk
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For citations:
Sheveleva T.A., Lyashkov A.A. Modeling the boundaries of the working space of a planar three-link manipulator. Omsk Scientific Bulletin. 2024;(3):73-81. (In Russ.) https://doi.org/10.25206/1813-8225-2024-191-73-81. EDN: PBNXWQ
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