The paper presents the method of optimal geometric parameters synthesis for a robotic rehabilitation system of the lower limbs as based on a passive orthosis in the form of a serial RRRR mechanism and an active parallel 3-PRRR mechanism. A mathematical model of the kinematics of the RRRR mechanism is formulated. A numerical method is worked out for determining the workspace of the RRRR mechanism. The workspace description is based on the approximation of many solutions of systems of nonlinear inequalities to provide the required rotation angle of rotation in the joints. Effective numerical methods and algorithms are developed and tested. The paves the way for determining the minimum geometric parameters of an active parallel mechanism that ensure movements of a passive orthosis within the workspace under clinical data constrains when simulating walking. In order to implement the developed methods, an effective algorithm, software package and visualization system are synthesized for exported three-dimensional workspaces in STL. © 2021, Springer Nature Switzerland AG.