Numerical Method for Determining the Operating Area of a Robot with Relative Manipulation Mechanisms

Abstract: In this paper, we consider the application of optimization algorithms to solve the problem of determining the operating area of a robot with mechanisms of relative manipulation based on a plane 3-RPR mechanism and a tripod mechanism. A method for approximating the set of solutions to a system of nonlinear inequalities describing constraints on the geometric parameters of the robot is considered. Algorithms for constructing the operating areas of individual mechanisms were synthesized. The orientation effect of the output link on the size and shape of the operating area of each mechanism is analyzed. The operating area of the robot is obtained taking into account the constraints on the geometric parameters of the workpiece being in a moving coordinate system located in the center of the flat 3-RPR mechanism, as well as taking into account design constraints, intersections of links, and special positions.