The article describes the structure of the lower limb rehabilitation system based on serial RRRR mechanism as a passive orthosis and an active parallel 3-PRRR mechanism. A mathematical model of the kinematics of the RRRR mechanism is presented. A description of a numerical method for determining the workspace of the RRRR mechanism based on the approximation of solutions of nonlinear inequalities systems to provide the required rotation angles in joints for rehabilitation is considered. A calculation algorithm, a software, and a visualization system for export the three-dimensional workspaces in STL format are synthesized. The results of mathematical modeling and analysis of the results are presented. © 2020, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.