Algorithm for Automatic Generation of Systems of Equations for Determining the Workspace of a Class of 3-DOF Planar Parallel Robots

The article considers the problem of automatically obtaining a system of equations for determining the workspace of a class of 3-DOF planar parallel robots. The patterns of influence of the robot structure features on the system of equations are revealed. The revealed patterns are used to synthesize an algorithm for automatically generating a system of equations based on a typical symbolic description of the robot structure. The algorithm provides for the introduction of equations of various types into the general system depending on the type of constraints. It is shown that the algorithm can be scaled for other classes of robots, and the resulting systems can be used both to determine the workspace and to solve the forward and inverse kinematics using numerical methods. The synthesized algorithm is implemented in the Python programming language. A comparison of the automatically obtained systems of equations with the systems of equations obtained manually is performed.