Nowadays, lower-limb orthoses facilitate various locomotion tasks for rehabilitation therapies that are repetitive and constant. Therefore, this research presents the kinematic analysis of a 4 DoF orthosis for knee and ankle rehabilitation. To obtain the kinematics of the axes, an analysis was performed from the biomechanical point of view, consequently, the Denavit-Hartenberg (D-H) method was used, which consisted of finding a homogeneous transformation matrix, followed by the orientation, position, and Euler angles; furthermore, the open-source software Jupiter (Phyton) was used as a testing tool. The homogeneous transformation matrix was obtained as a result and the simplification of the direct kinematic matrices was achieved. Finally, the direct kinematic analysis for a 4 DoF orthosis was established using the method of position (D-H), orientation, and Euler angles, which were very useful for the research.