## 3 Experiments and Results
### Verification of Active Generation of Angular Momentum as Large as that of a Human  
We conducted an experiment using the humanoid upper body developed in this study to evaluate its capability to generate large angular momentum with human-like motion. We implemented the \begin{table}
\begin{tabular}{c c c c} \hline
**Links** & \(\mathbf{I_{xx}}\) **(Roll) kgm\({}^{2}\)** & \(\mathbf{I_{yy}}\) **(Pitch) kgm\({}^{2}\)** & \(\mathbf{I_{zz}}\) **(Yaw) kgm\({}^{2}\)** \\ \hline Trunk & 1.4 \(\times\)\(10^{-1}\) & 1.3 \(\times\)\(10^{-1}\) & 0.60 \(\times\)\(10^{-1}\) \\ Upper arm & 7.3 \(\times\)\(10^{-3}\) & 7.4 \(\times\)\(10^{-3}\) & 1.1 \(\times\)\(10^{-3}\) \\ Forearm & 4.5 \(\times\)\(10^{-3}\) & 4.4 \(\times\)\(10^{-3}\) & 4.4 \(\times\)\(10^{-4}\) \\ \hline \end{tabular}
\end{table} 
Table 6: Moment of Inertia of the upper body of the humanoid. Figure 5: Whole-body running robot. The blue joint is the roll axis, the red joint is the pitch axis, and the yellow joint is the yaw axis. In the knee and ankle joints, a variable joint stiffness mechanism is implemented for storing jumping energy. (**a**) Humanoid robot; (**b**) DOF (degrees-of-freedom) configuration. \begin{table}
\begin{tabular}{c c c c} \hline
**Links** & **Mass (S.D.) kg** & **COM Position (S.D.) mm** & **Link Length (S.D.) mm** \\ \hline Trunk & 16 & 130 & 270 \\ Upper arm & 1.6 & 140 & 260 \\ Forearm & 0.90 & 90 & 210 \\ \hline \end{tabular}
\end{table} 
Table 5: Upper-body specifications of the humanoid. upper body on a six-axis force sensor for measuring the moment which the upper body applies to the lower part such as the waist of the robot. We calculated the angular momentum generated by the upper body of the robot integrating the moment data measured by the six-axis force sensor. The motion of the upper body was the same as that of human running motion obtained in our previous research [25]. The motion of each joint of human can be expressed as an approximate sine wave as Equation (9). \[\theta_{JOINT}=\theta_{JOINT\_INITIAL}-A_{JOINT}\text{sin}(\omega t) \tag{9}\]  
where, \(\theta_{JOINT\_INITIAL}\) is the initial joint angle, \(A_{JOINT}\) is the amplitude of the joint motion, \(\omega\) is the natural frequency of the joint motion, and \(t\) is the elapsed time from the start of the experiment. Therefore, we determined the motion of the upper body of the robot as Equation (9). The experimental parameters and their value of each joint are listed in Table 7.  
Moreover, we calculated the angular momentum generated by the human upper body and the simulation model with a 300 g lighter forearm at the same motion for evaluating the influence of the difference of the weight of the link on the generated angular momentum. After that, we compared the angular momentum generated by the upper body of the developed robot with that of human. The angular momentum of a human's upper body was calculated with the human motion data and body parameters in Tables 2 and 3. Table 8 summarizes the results for angular momentum generated in the experiment, in simulation, and in human running. The results confirm that the upper-body mechanism developed in this study can generate angular momentum as large as in human motion. In addition, we calculated the angular momentum in the yaw direction with the upper-body model, which has a forearm 300 g lighter than a robot forearm. The maximum angular momentum generated with the upper-body model was 1.7 kgm\({}^{2}\)/s. On the other hand, a maximum angular momentum of 1.5 kgm\({}^{2}\)/s was generated with the lighter forearm model. The total weight of the lighter forearm model decreased by only 2.3%; however, the angular momentum in the yaw direction decreased by 12%. We confirmed the developed upper body can be used for active angular momentum control as human.