Modeling the boundaries of the working space of a planar three-link manipulator

• Published in: Omskij naučnyj vestnik Vol. 3 (191); pp. 73 - 81
• Main Authors: Sheveleva, T. A., Lyashkov, A. A.
• Format: Journal Article
• Language: English
• Published: Omsk State Technical University, Federal State Budgetary Educational Institution of Higher Education 01.09.2024
• Subjects: computer model; discriminant; geometric modeling; gripper center; hypersurface; manipulator; manipulator workspace; three-link planar manipulator
• ISSN: 1813-8225; 2541-7541
• DOI: 10.25206/1813-8225-2024-191-73-81

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.