## 3 Results  
### Lower Limb Operating Conditions during a Gait Cycle at a Medium Speed  
The angular relationships, angular velocities, resulting moments, and reaction forces of joints presented in the following figures are plotted vs. the cycle of human motion to determine the positions in the gait cycle where greater angular relationships, angular speeds, resulting moments, and reaction forces are achieved. Such values are considered for the analytical design of prostheses. Figure 14 shows the angular relationships in knee and ankle joints from triangular geometric relationships (law of cosines).  
Figure 14: Analysis of knee flexion in the gait cycle using the Tracker® software. (**A**) Flexion angles of the knee joint. (**B**) Flexion angles of the ankle joint.  
Figure 13: Case 3: Critical support phases for ANSYS® prosthesis analysis.  
Figure 15 shows the vertical displacements obtained from coordinates and distances between joints; a maximum vertical displacement of 7.755 cm (hip), 7.476 cm (knee), and 12.009 cm (ankle) can be observed. Although the test subject mass center does not follow a straight line during the gait cycle, the mean point of this vertical displacement in the male adult is, on average, 8 cm, causing the center of gravity to have a very smooth movement without abrupt deflection changes, minimizing the spent energy.  
The parameters obtained from both knee and ankle flexion angles are shown in Figure 16. In this work, a knee joint flexion between 4.7\({}^{\circ}\) and 50.5\({}^{\circ}\) was determined, while, for the ankle joint, it lied between 10\({}^{\circ}\) and 19.7\({}^{\circ}\). Furthermore, it ought to be remarked that the obtained graphical behavior of angles during the gait cycle is consistent with previous work [12; 13; 14; 15; 16; 17; 18; 19; 20]. The fact that the minimum flexion angle at the ankle joint is slightly above the average reported values might be because the employed camera has a lower resolution with respect to those used in other works. As for the moments of reaction and resulting forces, the literature reports that moments resulting from the knee have a maximum of 0.5-0.45 nm and a minimum of 0.01-0.05 nm [12; 13; 14], while, for the ankle, they have a maximum of 0.9-0.70 Nm and a minimum of 0.01-0.03 Nm [15; 16; 17; 18]. In this work, the resulting moments for knee joint of 0.035 nm and 0.487 nm were obtained as minimum and maximum values, respectively, while for the ankle joint, values of 0.0164 nm and 0.703 nm were obtained analogously. These values are in good agreement with previously published results. With respect to the reaction forces, the knee joint was the only considered joint, because this work is focused on the design of a transtibial prosthesis. In Figure 8, the reaction forces, generated in the knee, can be particularly observed in the tibiofemoral joint. This is mainly because the prosthesis under design is focused on working during low-medium impact activities, such as climbing stairs, smooth jogging, or even a fall, which do not entail double support. Therefore, the values obtained due to reaction forces in this work and double values are published elsewhere. Figure 16 shows the resulting moments obtained from Equation (7), in knee and ankle joints, where the ankle angle is represented with a red line and the ankle reaction moment is represented with a blue line for Figure 16A,B, while Figure 17 shows the reaction forces in such joints.  
Figure 15: Vertical displacements of foot joints during the gait cycle.