## 4 Discussion
Figure 4: Evolution of the norm of the distance between minimal moment axis and COM (\(d_{\text{COM-A}}\)) dashed line and the absolute value of the anterior-posterior component (\(d_{AP}\)) full-line, during the gait cycle, for the average of healthy subjects (**a**) and one person with amputation (**b**). MMA is always inclined forward when \(\mathbf{d_{AP}}\) is negative and conversely inclined backward when \(\mathbf{d_{AP}}\) is positive. Despite using different prostheses, amputees showed similar characteristics. The pattern of the distance is asymmetrical. The MMA is further behind the body when the prosthetic limb is in the stance phase than when it is in the swing phase. This can be related to the limited inclination of the axis towards the COM, which may result in more instability and less comfort when the stance is on the prosthesis. This agrees with previous studies that state that the sound limb has higher dynamic stability [19]. The event heel strike also ensures a drop in the distance; however, the sound limb stance results in a much higher drop than the prosthetic one. The MMA is now in front of the body. It is further in front after the event toe off of the sound limb than the event toe off of the prosthetic limb. Therefore, as long as the sound limb is on the ground supporting the body, it can correct any instability [19; 20]. The sound limb is much more active in amputee gait, especially in producing the stabilizing and compensatory effects. The parameters that play a significant role in the distance are the GRF&M (anterior-posterior force, vertical force) and the COM position. The plot of the 3D distance and the anterior-posterior distance in Figure 4 shows that due to the prominent value of \(\mathbf{F_{V}}\) the 3D distance can be approximated to be:  
\[d_{com-\Delta}\approx d_{AP}\approx\frac{F_{V}M_{ML}}{\left|\left|F\right| \right|^{2}}, \tag{11}\]  
\[M_{ML}=\left(r_{y}F_{V}-r_{z}F_{AP}\right), \tag{12}\]  
[PERSON] et al. [21] showed that the ground reaction forces produced by the prosthetic side are less than those produced by the sound side. Most importantly, the prosthetic side is not able to produce an adequate amount of push and break (\(F_{AP}\)). This means that the subject's COM is not able to gain the normal acceleration and deceleration when the prosthetic limb is in stance phase. This is consistent with the lower MMA inclination. The height of COM \(\mathrm{r_{z}}\) is also lower during prosthetic foot stance phase [22]. The term \(\mathrm{r_{y}}\) is the foot forward placement (FFP). It is the distance between the COM and the leading foot as defined by [PERSON] et al. [23]. They proved that the asymmetry in amputees' step length is due to the asymmetry in the FFP. It has been mentioned by previous studies that amputees' step asymmetry helps in preserving stability. The above-mentioned parameters, shown schematically in Figure 5: the FFP, the COM height, the external forces and moments are all wrapped up in one significant parameter: the distance. The control of any mentioned parameter contributes to the control of the distance. Finally, the distance describes the angular momentum because the external moment is equal to the derivate of the angular momentum Equation (6). Our results are consistent with the ones of [PERSON] et al. who have proposed that the healthy subjects control the variation of the angular momentum [9]. Surprisingly, the walking speed of subjects with amputation was higher than the speed of healthy subjects. This result can be attributed to the different laboratory setup and arrangement of force plates. However, this difference is not significant and its impact on the distance can be neglected. When the speed effect was studied by [PERSON] et al. a much higher speed difference between groups was taken into consideration [5]. The classic limitations of studies involving people with amputation include low subject numbers, heterogeneity of levels of amputation, of prosthetic types and walking speeds.