# The Analysis of Mechanical Structure of a Robotic Leg in Running for Impact Mitigation
## 5 Discussion and Conclusions  
This study was motivated by the fact that impact weakens the controllability and durability of the leg of legged robots while running. Since the previous research had been limited to the component-level approach in order to mitigate the impact, the approach needed to move up to the structure-level approach, as proposed. However, in order to evaluate the impact by the mechanical structure, a measure that can quantify the impact was required, and the measure, i.e., CI, could be \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Experimental Set** & \multicolumn{2}{c}{**(1)**} & \multicolumn{2}{c}{**(2)**} & \multicolumn{2}{c}{**(3)**} \\ \hline Configuration & B & F & B & F & B & F \\ \hline Average \(x\)-force (kN) & 0.1964 & 0.0781 & 0.1949 & 0.0759 & 0.1006 & 0.1063 \\ \hline Average \(z\)-force (kN) & 0.7895 & 0.3664 & 0.7896 & 0.4411 & 0.5050 & 0.5863 \\ \hline Average net force (kN) & 0.8145 & 0.3751 & 0.8141 & 0.4479 & 0.5156 & 0.5960 \\ \hline Experimental rCI & \multicolumn{2}{c}{0.4605} & \multicolumn{2}{c}{0.5501} & \multicolumn{2}{c}{1.156} \\ \hline Simulated rCI & \multicolumn{2}{c}{0.4742} & \multicolumn{2}{c}{0.5523} & \multicolumn{2}{c}{1.155} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Impact forces and rCIs for backward (B)/forward (F) flexion. Figure 16: rCIs (\(\lambda_{r}\)) in the case of **(a,b)**: hollow circles and gray lines represent the experimental and simulated rCIs, respectively. derived from the impact dynamics of the leg. Based on the hypothesis that the impact could be represented by CI and in turn, CI was affected by mechanical structures, CI was verified to play a crucial role in the impact and vary on mechanical structures by simulations and experiments. It could be easily inferred from this paper that smaller CIs were effective for impact mitigation. Since CI varies on the impact direction even if the impact directions were bounded as shown in Figure 11, however, CI, which still can have many different values with respect to a combination of mechanical structures, would not be a good measure of the impact to select mechanical structures effective for impact mitigation. Alternatively, the maximum of CIs can be a good measure of impact. The optimal mechanical structures can be found by minimizing the maximum CI. The average or variance of CIs can also be good measures if the average impact should be mitigated or if the impact is desired such that it should be not sensitive to the impact direction. Depending on the applications, the set range for the possible impact directions can be narrower, wider, or shifted such that the applicable combination of mechanical structures will have more variety. Interestingly, most legged robots, introduced in Section 1, have their legs flexed backward. This trend might be due to the fact that the forward flexed legs often interfere with stairs or a wide variety of terrains that those robots should overcome. Since the flexion direction was intensively dealt with as one of the mechanical structures in this paper, this study could help to analyze and further improve the mechanical structures of the aforementioned legs in terms of impact. Technically, running legs require two more properties besides effective impact mitigation: great force production and fast swing recovery. Although the paper focused on the effect of mechanical structures on impact mitigation, the mechanical structures are also supposed to affect force production and swing speed, as previously investigated in [26]. Accordingly, this study, which focused on impact mitigation only, should be extended to define measures to evaluate those three properties and, thus, to comprehensively analyze the mechanical structures, not individually. A subsequent paper will deal with the analysis in the near future. Conceptualization, J.C. and K.K. ; methodology, J.C.; software, J.C.; validation, J.C.; formal analysis, J.C.; investigation, J.C.; resources, K.K.