## 2 Materials and Methods
### Kinematic Analysis of the Positioning of the Mechanical Actuator System  
To analyse the kinematics of the CPM device, a scenario corresponding to the real use of the device was assumed. After defining the kinematic pairs in each link joint (link 5 is permanently fixed to the ground and is a fixed link; a rotational kinematic pair \(A^{\prime}\) is defined between links 5 and 3; links 3 and 4 form a rotating pair \(D^{\prime}\); a rotating pair \(E^{\prime}\) is defined between links 4 and 6; the linear guide car 6 together with the guide form a translational pair \(F^{\prime}\); between the linear electric actuator 9 and the calf support 8, a fixed stationary connection \(G^{\prime}\) is defined; similarly, connections are defined between links 9 and 11, i.e., the actuator and the link of the Delta robot--\(H^{\prime}\) and between 10 and 11, i.e., the link of the robot and the platform supporting the patient's foot--kinematic pair \(I^{\prime}\)--as these kinematic pairs are excluded from further analysis; link 1 forms a rotating pair \(B^{\prime}\) with the ground and is connected on the other side to link 2, forming a rotating pair \(C^{\prime}\) with it; link 2 is connected to links 3 and 4 by a rotating pair \(D^{\prime}\); the thigh and calf supports are permanently attached to links 3 and 4 and this connection is defined as fixed); all components of the combined mechanism are positioned in the configuration shown in Figure 2B. The starting position defined in this way allows the lower limb to be positioned and fixed to the movement apparatus of the CPM device. The mechanism analyses did not include the mass and impact of the elastic bands used to attach and secure the limb to the thigh, calf, and foot supports (Figure 1, Detail 10). The actuator is attached to link 1 and forms with it a rotating pair \(B^{\prime}\). The operating mode of the device includes the speed of the actuator, which can be set to 4, 2, or 1 rpm. For the analysis, a variant of actuator movement was assumed with a maximum speed of 4 rpm (i.e., 24\({}^{\circ}\)/s), in the angle range 0\({}^{\circ}\)\(\rightarrow\) 157\({}^{\circ}\)\(\rightarrow\) 0\({}^{\circ}\)\(\rightarrow\) -3\({}^{\circ}\)\(\rightarrow\) 0\({}^{\circ}\). For the most part, this covers a regular range of motion of the knee (from \(-\)10\({}^{\circ}\) to 155\({}^{\circ}\)) [38], with the imposition of the restriction that the motion after the phase of complete knee extension \(-\)0\({}^{\circ}\) is still only deepened by a value of 30, rather than the maximum value of 10\({}^{\circ}\) assumed for the healthy knee. The motion in the maximum range was increased by 2\({}^{\circ}\), to a value of 157\({}^{\circ}\), to compensate for the effect of structural clearances on the accuracy of the displacements. The CPM allows fully programmable actuator control within specifiedincomplete ranges of motion with specified speed and acceleration parameters. This is due to the need for targeted rehabilitation, individually defined by the therapist for each patient, with specific requirements depending on the type of disease entity.  
Displacements of the Delta robot's end effector (the platform that supports the patient's foot) were not included in the analysis. During the robot's motion phase, the support platform is assumed to be in a fixed position throughout the motion and is therefore not considered further. The finite element mesh required for numerical analysis is automatically generated by the CAE tool. For this type of study, this is of little importance as the final result does not depend on the accuracy and type of mesh chosen.