Automated Modeling of the Workspace of a Two-Link Planar Manipulator

Abstract

A study was carried out on the plane of a cloud of points specified by analytical equations that determine the position of the grip center of a two-dimensional manipulator. It has been established that a cloud of points can be represented by two families of circles: eccentric and concentric. The completed mapping of these circles into space made it possible to obtain two U and V surfaces. It has been established that the boundaries of the working space of the mechanism, in this case, are the discriminants of the U and V surfaces. The analysis of such surfaces and their discriminants provided the opportunity to develop algorithms and programs for automated modeling of the manipulator's workspace. The fundamental difference between the results obtained and the known ones is that the proposed algorithms and programs solve both the direct and inverse problems of the kinematics of a given mechanism. All modeling stages are performed with the required accuracy and visualized.