## 3 Materials and Method
### Design Phase
#### 3.1.1 Geometry Optimization: 2D FE Model  
In this first step of the _design phase_, geometry optimization was carried out through a 2D FEA. For example, this step can be used to optimize the profile shapes of an already defined configuration of elastic elements, to configure the energy-storing parts of a new ESR foot, or to investigate the behavior of an existing prosthetic device after modifications or additions of other functional components, such as dampers and actuators. Optimizing the geometry of a foot prosthesis is very important, especially with regard to ESR feet and their elastic components. Although the result of the 2D FE model in terms of stiffness is not definitive, this model is essential to optimize the shapes of the various elastic components to ensure the full range of motion needed to walk. A non-optimization of the shapes of the elastic components can bring a range of motion too reduced or too wide. Regardless of the stiffness of the elastic components, if the range of motion is too  
Figure 3: Flowchart of the design methodology: _design phase_, _validation phase_ and _functional verification phase_. small, the foot rotates around the ankle joint up to a certain angle and then, a sudden sensation of increase in the equivalent rotational stiffness around the ankle joint follows. Due to this sudden increase in stiffness of the ankle joint, the foot no longer rotates around the ankle and the heel comes off the ground before the desired moment. This situation can be perceived by the user as a sudden disappearance of the support, which can cause discomfort or even a fall of the user. If the range of motion is too wide, the foot may continue to rotate in dorsiflexion beyond the desired limit by delaying the hell-off. Even this situation can generate discomfort or even a fall of the user. For MyFlex-\(\gamma\), geometry optimization was focused on the profile shape of the middle blade and the upper blade, aiming to meet the biomechanical requirements previously defined (Section 2.4). The lower blade used for the present application was provided by Ossur and it was already optimized for the chosen weight category. Then, an initial 2D geometry of the foot was drawn bearing in mind the dimensional parameters defined by the human anatomy such as length \(L\) of the foot, the height \(h\) of the ankle joint from the ground and the distance \(d\) of the ankle joint from the heel, which is around 1/3 of the foot length. For the present application, the length of the foot was 250 mm and the height of the ankle joint was between 80 mm and 100 mm, as shown in Figure 1.  
_Load conditions._ The CAD model was drawn in the \(x\)-\(y\) plane and imported into ANSYS Workbench. The FE model was simulated in a 2D static structural analysis. Following the ISO 10328 standard, the dorsiflexion test was simulated by loading the FE model with a platform at the forefoot. For the plantar flexion test, the FE model was loaded at the heel. The platforms were moved by imposing 10 mm of displacement for the plantar flexion test and 50 mm for the dorsiflexion test. The shank was constrained with a fixed support at the top of the tube connector. For the present application, the loads and the constraints are depicted in Figure 4.  
The geometry optimization was carried out by varying the geometric parameters. These parameters depend on the foot prosthesis architecture and the designers can choose them. For MyFlex-\(\gamma\), the parameters are depicted in Figure 5 and listed in Table 3. The upper blade was defined in the sagittal plane by 6 parameters. The parameter UB\({}_{t}\) is the thickness, while the parameters c\({}_{1}\), c\({}_{2}\), c\({}_{3}\), c\({}_{4}\) and c\({}_{5}\) define the curvatures of the curved profile of the upper blade, which was composed by 6 straight sections--starting from the metatarsus (front), c\({}_{1}\) is the relative inclination between the first and the second section, c\({}_{2}\) is the relative inclination between the second and third section, etc.