## 2 LI Device Design for Fast Motion
### Design of Actuation System for Desired Performance  
When a human try to run or stop quickly during straight walking, a maximum acceleration of 3 m/s\({}^{2}\) is generated [22]. Thus, the target performance of velocity and acceleration of the ODT were set to 3 m/s and 3 m/s\({}^{2}\), respectively, to simulate running and stopping. To validate the target performance, dynamic analysis was performed using a commercial multibody dynamics software (ADAMS), as shown in Figure 6. To obtain realistic analysis results, the boundary conditions, including the mass and inertia, were set based on 3D modeling, gravity, the initial X-axis drive chain tension (3000 N) and the Coulomb friction due to contact between the segment belt and the Teflon-coated segment structure [19]. The X-axis motion simulation was done by actuating all 64 unit segments (total weight: 576 kg) and human mass (150 kg) through the rotation of the chain and sprocket, and Y-axis motion was performed with one segment among the 27 segment belts on the active surface loaded with 150 kg to simulate a human mass. The additional information of  
Figure 5: (**a**) Drive chain of segment treadmills for X-axis motion, (**b**) Design and operation of the synchronizer mechanism. Figure 6: Dynamics simulation for X and Y axes. the proposed ODT is summarized in Table 1, which is used to determine the actuator power. The X-axis and Y-axis motor instantaneous powers required to maintain a speed of 3 m/s were determined to be 28 kW and 8 kW, with average values of 8.8 kW and 4.2 kW, respectively. Table 2 summarizes the power requirements for each axis actuation. In the presented system, 3-rows of GOP shafts were installed to connect 6 GOPS per one segment, as shown in Figure 7a, to secure the performance of the geared-coupling between the segment and GOPS. Thus, this mechanism reduces the power concentration on the contacted teeth of a segment belt by increasing the number of the contacted teeth by 3 times. Therefore, it can guarantee the power transmission performance because the generated motor torque required to drive the segment belt is distributed over the 3-row GOP shaft. The motors (Motor1Y, Motor2Y) actuate the power transmission belts, which in turn drive the gearboxes. The gearboxes actuate timing belts for rotation of the 3 GOP shafts simultaneously as a mechanically coupled power transmission system. The actuation mechanism for the X-axis also uses a distributed power design, in which the four drive chains are mechanically coupled. In Figure 7b, Motor1X and Motor2X simultaneously actuate the drive chains by actuating the sprockets. \begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Specifications** \\ \hline System frame dimensions & 2780 mm \(\times\) 3310 mm \(\times\) 640 mm \\ Active surface area & 2.5 m \(\times\) 2.5 m \\ Unit segment dimensions & 100 mm \(\times\) 2577 mm \(\times\) 70.5 mm \\ Unit segment weight & 9 kg \\ Number of segments & 64 units \\ Number of active segments & 27 units \\ Number of GOPS in 1 GOP shaft & 54 units per 1 GOP shaft \\ \hline Chain and timing belt & X-axis drive chain & Y-axis segment belt \\ Pitch & 18.875 mm & 10 mm \\ Width & 9.4 mm & 96 mm \\ Actuation part specification & Sprocket & GOP shaft \\ Pitch diameter & 396.375 mm & 114.59 mm \\ The number of teeth & 21 & 36 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The ODT Specifications for Dynamic Simulation. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Axis** & **Required Pulley Torque** &
\begin{tabular}{c} **Required Pulley** \\ **Angular Velocity** \\ \end{tabular} & **Power** \\ \hline X & 1768 Nm (max.) & 15.63 rad/s & 28 kW (peak) \\ \cline{2-4}  & 563 Nm (avg.) & & 8.8 kW (nominal) \\ \hline Y & 148.5 Nm (max.) & & 8 kW (peak) \\ \cline{2-4}  & 81 Nm (avg.) & & 4.2 kW (nominal) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Power Requirements.