## 2 Materials and Methods
### Methodology Used in the Present Research  
In order to be able to approach the problem of optimising the positioner design according to the criterion of reducing the mass of the links forming the structure of the kinematic chain using Generative Design methods, a preliminary numerical study was carried out for this purpose in the ANSYS Workbench 2022R2--Rigid Dynamics toolbox [36]. This allowed the kinematic and dynamic parameters of the main positioner to be determined. Based on the results of the kinematic and dynamic analysis, the parameters that have a significant influence on the control of the CPM positioner actuator were evaluated. For the CPM numerical analyses, a simplified test model was prepared based on the geometry previously modelled in SolidWorks 2022, which was the basis for further analyses in ANSYS Workbench 2022. Simplifications were made to the computer model by removing process chamfers and roundings, eliminating holes for connecting elements that attach the motion apparatus to the structure's support frame, and replacing bolted connections with fixed mates. These modifications were duly justified so as not to compromise the quality of the final test result while at the same time speeding up the numerical calculations. Figure 2 shows the kinematic structure of the single-limb positioner. Figure 2 also shows the components of the positioner. We can distinguish between them: (a) links (1), (2), and (3) form the articulated quadrilateral mechanism; (b) links (3), (4), and (6), form the crank-slider mechanism; (c) (5) indicates the fixed attachment to the device frame forming a rotating kinematic pair with link (3); (d) (6) is the translational car of the linear guide, and forms a rotating kinematic pair with link (4); (e) (11) is the Delta robot articulated joint connecting the electric actuators to the patient's foot support platform (10), via spherical joints; (f) (12) is the linear guide track. Major changes to the geometry from the original 3D virtual model in SolidWorks include (a) removal of any chamfers and small holes for connectors; (b) removal of the screws connecting the kinematic chain components; (c) removal of bearings and shafts from rotating pairs; (d) replacing the mass of individual electric linear actuators by masses concentrated at a point, to obtain a representation of the real mass of a commercial solution (9); (e) adding a mass points loading of the thigh, calf, and foot supports to model the impact of the patient's lower limb at points of direct contact with the CPM device positioning system (7), (8), and (10). A summary of the masses of each joint and element is highlighted in Figure 1 and an indication of the material of manufacture of the joints is given in Table 1.  
The study of the design of the motion apparatus to optimise the solution for reducing the mass of the main components that make up the positioner of the CPM device, and finally the selection of a new actuator for the positioner drive system, was divided into several stages. In the first stage, a kinematic analysis of the motion apparatus mechanism of the CPM positioner will be performed, using the Rigid Dynamics toolbox of ANSYS Workbench 2022R2. This allows the determination of displacement, velocity, and acceleration values in specific kinematic pairs. These parameters will be defined for the geometry of the virtual