# Hardware-in-the-Loop Test of a Prosthetic Foot
## 4 Experimental Results
### Results of One Gait Cycle  
Firstly, the trajectory of the CoM was analyzed. The results of the HiL test are shown in Figure 7. The CoM trajectory exhibited a sinusoidal shape in \(y\) direction. The maxima were when the CoM was above one leg (midstance). For the left left leg, this was at \(x=0\) m and \(x\approx 0.6\) m, and right midstance occurred at \(x\approx 0.3\) m. The oscillation magnitude was \(\approx 0.04\) m, which corresponds well with the observations made in human walking (\(0.032\pm 0.008\) m [14]). In continuous human walking (and also for stable walking models), the motion trajectory oscillates with a constant magnitude. In this HiL test, the magnitude increased, or in other words, the CoM was lifted excessively for \(x>0.45\) m. In this phase, the prosthetic foot rolled over the forefoot. Since the ankle joint is not flexible, the CoM needed to be lifted. Next, the orientation of the trunk was analyzed. The results are visualized in Figure 8a. The figure reveals that the trunk rotated backwards throughout the whole GC. For contin  
Figure 7: CoM trajectory of the modeled amputee during one GC in the HiL test. uous walking, an oscillations of the trunk about 0\({}^{\circ}\) was expected. This suggests that the model is about to fall backwards and that the parameters used for the simulation do not lead to a continuous gait pattern. The duration of the GC was 0.67 s, which corresponds to the duration of the GC in a pure simulation of the VPP model with the same biomechanical parameters and initial conditions. The proportion of the stance phase of the right leg in the GC was 85%. In normal human walking, this is only 60%. The single support phase of the right leg was relatively short with 17% of the GC. The reason might lie in the relatively slow forward velocity of the model that was selected to meet the hardware limitations of the Stewart Platform: when humans walk slowly, the stance time, as well as the double-stance phase increase, because the body needs to be balanced more [14]. The modeled amputee, as shown in Figure 8b, initially walked at a speed of 0.98 m/s (the preferred walking speed of able-bodied people is 1.36 m/s). During the GC, the forward velocity decreased to 0.78 m/s. Together with Figure 8a (backward movement of the trunk, \(\phi_{\text{VPP}}<0\)\({}^{\circ}\)), this revealed that the model lost energy and could not walk stably with the selected parameters and initial conditions. There are several reasons for this: The initial values of the gait model were found based on an optimization of the VPP model that did not include the CoP shift. Due to this forward shift, the time span where the CoM was behind the foot point (in \(x\) direction) was prolonged. Since the CoM decelerated as long as the CoM was behind the foot, the system energy decreased. A further reason why energy was lost is the added damper. The amount of dissipated energy was not compensated. With respect to the system energy, this energy dissipation was small (\(\approx\)5%). Due to the three-dimensional foot, the CoM was lifted in the second half of the right leg's stance phase (cf. Figure 7). The conversion of kinetic energy into potential energy is a further reason why the CoM velocity decreased. Furthermore, there was energy lost in the foot impact and by the deformation of the prosthetic foot. Based on these results, one can assume that the model would not be able to complete a second stride and would tip over backwards. Another important characteristic of human gait is the GRFs, as illustrated in Figure 9a. The GRFs in the vertical direction (\(GRF_{\text{R,y}}\)) represent the typical m-shape with two maxima and one minimum in between. Similar to observations made in human walking, the maximum values featured a magnitude of approximately 110% of the body weight.