Geometric method for researching the robot service area under the obstacles for the limitations on links movement

The work is devoted to solving one of the problems of robot motion virtual simulation using computer graphics. The paper offers a method for studying the shape and position of the work envelop of manipulator mechanisms in the presence of restricted work envelopes in the workspace. The method for determining the work envelope is based on the construction of allowed configuration of robot mechanisms. A parameter describing the structure and maneuverability index in different parts of the work envelope is proposed. The construction of cross sections of service areas for different positions of restricted work envelopes allows determining the areas where the output link centers of various mechanisms can not be located. The conducted research makes it possible to place the trajectories of the output link in solving motion problems, which reduce the probability of deadlocks in the automated motion synthesis along the velocity vector.