Automated Determination of the 3-DOF Planar Parallel Robots Workspace Based on a Symbolic Notations

The paper discusses the problem of determining the workspace of planar 3-DOF parallel robots. An approach is proposed for the automatic formulation of systems of equations describing the limitations of the workspace using its symbolic notation. During determination the workspace and the links interference, it is necessary to structure the variables taking into account their classification. For this purpose, the allocation and classification is carried out for variables included in the system of equations. Depending on the type of variables, they can have discrete or interval forms. The approximation of the set of solutions of the obtained systems using the performed classification allows us to determine the workspace. The coordinates of the joints are included in the number of variable equations and are used to exclude interference of links. The developed approaches are implemented in Python. The simulation results are presented.