# The Analysis of Mechanical Structure of a Robotic Leg in Running for Impact Mitigation
## 4 Experiments
### Impact Experiment  
As described in Figure 13, the three sets of experiments are as follows: (1) backward/forward flexion with \(l_{n}=0.75\), \(\theta=0^{\circ}\), and \(\angle\mathbf{v}=\sim 30^{\circ}\), (2) backward/forward flexion with \(l_{n}=0.75\), \(\theta=8^{\circ}\), and \(\angle\mathbf{v}=\sim 30^{\circ}\), and (3) backward/forward flexion with \(l_{n}=0.75\), \(\theta=8^{\circ}\), and \(\angle\mathbf{v}=\sim 0^{\circ}\). In the experiments, the virtual stiffness of the leg was regulated to the given extension ratio and attack angle. In the first and second sets, where the attack angle was regulated to \(0^{\circ}\) and \(8^{\circ}\), respectively, the leg was thrown at about 1 m/s from 0.2 m high, which would reach 2 m/s downward when in contact with the ground, such that the impact direction could be estimated around \(30^{\circ}\), as shown in Figure 14a,b. In the third set, the leg was just dropped from the same height such that only the downward velocity was generated, as shown in Figure 14c. In each set, the flexion direction was controlled backward and forward, and each set was repeated 20 times.  
The first peak forces were logged and averaged as shown in Figure 15, where the squares represent the experimental data while the bold and dotted lines represent the mean and standard deviation of the data, respectively. In the sets of (1) and (2), the peak forces of backward flexion were higher than those of the forward flexion, and in the set of (3), the peak forces of forward flexion were higher than those of the backward flexion. This corresponded to Figure 13 because CI of backward flexion was larger than that of forward flexion in (1) and (2), and CI of forward flexion was larger than that of backward flexion in (3).  
The experimental result could be organized as in Table 2. In the third and fourth row, the average net force in \(x\)- and \(z\)-directions, calculated from the measurements, are shown. In the fifth row, the average net force was derived by averaging the magnitudes of the vectors that consisted of the two forces, i.e., the square root of the sum of squares of the \(x\)- and \(z\)-forces. Again, the impact force, described as the average net force in the experiment, was dominated by CI and thus proportional to CI, as discussed in (17). Therefore, the experimental relative CI (rCI) in the sixth row was calculated by dividing the average net force of forward flexion (F) by that of backward flexion (B) and consequently eliminated the need for a proportional constant. At last, the simulated rCIs were derived by dividing CIs of forward flexion by those of backward flexion such that the experimental ones could be directly compared with the simulated ones. Table 2 shows that the experimental and simulated rCIs matched about 98% and that CI could represent the impact force. The result of each set also showed that mechanical structures affected the impact mitigation because rCI was not unity. The experimental and simulated rCIs in Table 2 are visualized in Figure 16, where hollow circles describe the experimental rCIs marked with the set number and gray lines represent all the simulated rCIs, obtained from the data shown in Figure 13, including the simulated rCIs marked with the set number. Figure 16 reconfirms that the experimental and simulated rCIs were almost identical.