## 2 Angular Momentum Compensation
### Design of the Upper-Body Mechanism  
To fulfill the above requirements of an upper-body robot mechanism, we developed an upper-body mechanism that has human-like mass properties and can perform the motions observed during human running (see Figure 1). Some studies have been conducted using humanoid robots with upper-body mechanisms [7; 10; 11; 35], but it is difficult to achieve human-like size, mass properties and motion. The reason for this is that human-like motion requires a high-power output, but high-power actuators are too heavy to mimic a human mass properties. For example, the mass of the upper arm of a human may be 1600 g. Three actuators are required in the upper arm for the shoulder and elbow joints. However, the mass of each actuator, including the gear, is approximately 400 g. We considered the use of brushless direct-current (DC) motors as actuators, because they are small and light and can output high power. Based on the upper body motion during human running shown in Table 4, the maximum joint power of the shoulder pitch and trunk joints is around 150 W, and that of other joints is even smaller. Implementation of such actuators requires that the mass of the other parts,such as the frames connecting each joint and the electric parts, be less than 400 g. We must save the weight of frames; however, the frames must bear the load derived from large angular momentum for preventing yaw rotation. Therefore, we considered the material properties required for the structural members of the humanoid robot to best mimic the size and mass properties of a human. Aluminum is typically used for the structural members of a robot. The structure of the upper body of most humanoid robots are exoskeleton structures, wherein the frame shapes the body, and every component, such as motors and electrical parts, is stored in the frame. It is difficult to save the weight of the upper body because the amount of aluminum parts for shaping the body are increased. For weight saving in the links, we used carbon-fiber-reinforced plastic (CFRP), which is extremely strong yet also light. The density of CFRP (1.5 g/cm\({}^{3}\)) is much lower than that of aluminum (2.7 g/cm\({}^{3}\)). CFRP pipes were used in the center of each link, similar to the inner skeleton structure based on the human structure, with actuators, motor controllers and cables placed around the pipes (see Figures 2 and 3). In the torso link, a large twisting moment is loaded for generating angular momentum in yaw direction. To stand the twisting moment, two pipes were implemented instead of one big pipe (Figure 3). Consequently, the size of each link was close to that of a human's, and the mass of each link was approximately 11% less than if it were made of aluminum. Figure 1: Computer-aided design (CAD) of the developed humanoid. Figure 2: CAD of the humanoid robot arm. The green line is the rotational axis. CFRP: carbon-fiber-reinforced plastic. Achieving a human-like COM position and inertial moment requires axial symmetry of the structure of the torso. Some humanoids have a torso mechanism actuated by a motor and a gear implemented on only one side (see Figure 4a). In this type of mechanism, the COM position of the torso is inclined from the center in the frontal plane and is thus different from that of a human. It therefore produces an angular momentum that is different from that of a human. A humanoid robot developed using this type of mechanism cannot mimic human-like motion by generating the same angular momentum. A counterweight can be used to shift the COM position, but the total mass of the mechanism may still be too large compared with that of a human. To solve this problem, we implemented a symmetrical joint mechanism with two of the same actuators and gears (see Figure 4b). The COM position was thus shifted to the center of the torso, as in a human. With two actuators in parallel, each actuator and gear required less power when only one actuator was used, which made it possible to decrease the size and weight of the actuator.