## 2 Methods
### Fall Simulation  
#### 2.2.1 Model and Physical Limits  
The fall simulator was constructed using MATLAB's Simulink toolbox and Simscape Multibody (MathWorks, Inc., Natick, MA, USA). The human model consisted of 14 rigid  
Figure 1: Overview of fall experiment.  
body links, including the and right limbs for the foot, lower leg, thigh, hand, forearm, and upper arm, as well as pelvis and trunk. Head and neck were incorporated into the trunk link. The model's size, mass, and inertia were scaled based on the participants' height and weight [19; 20]. The parameter of the simulation model is shown in Table 1. This model comprised 11 joints, including left and right ankles, knee, hip, shoulder, and elbow joints, and lumbar spine. The hip, shoulder, and lumbar joints have three degrees of freedom (DOFs), while the remaining joints have one DOF. The foot link of the supporting leg and the floor surface were connected via a virtual six-DOF joint.  
To consider human physical limitations, constraints were imposed on joint torque and the rate of joint torque change. The torque and torque change rate were determined based on values from the literature [21; 22; 23; 24; 25; 26; 27]. The torque and rate of torque change for each condition are shown in Table 2.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Segment** & **Mass** & **Length** & **Mass Center Position [\%]** & **Inertia [kg\_cm2]** \\ \hline Head and Neck & 0.069 M & 0.140 H & 59.8 (from top) & 1.43 M + 1.73 H \(-\) 112 \\  & & & & 1.17 M + 1.52 H \(-\) 78 \\  & & & & 1.72 M + 0.08 H + 61.6 \\ \hline Trunk & 0.160 M & 0.139 H & 50.7 (from neck) & 18.30 M \(-\) 5.73 H + 367 \\  & & & & 36.03 M \(-\) 9.98 H + 561 \\  & & & & 36.73 M \(-\) 5.97 H + 81.2 \\ \hline Abdomen & 0.163 M & 0.124 H & 45.0 (from trunk) & 26.70 M \(-\) 8.00 H + 263 \\  & & & & 43.14 M \(-\) 19.80 H + 1501 \\  & & & & 39.80 M \(-\) 12.87 H + 618.5 \\ \hline Pelvis & 0.112 M & 0.084 H & 61.1 (from abdomen) & 11.80 M + 3.44 H \(-\) 934 \\  & & & & 14.70 M + 1.69 H \(-\) 775 \\  & & & & 12.00 M + 7.74 H \(-\) 1568 \\ \hline Upper arm & 0.027 M & 0.162 H & 57.7 (from shoulder) & 1.53 M + 1.34 H \(-\) 232 \\  & & & & 1.56 M + 1.51 H \(-\) 250.7 \\  & & & & 0.55 M + 0.04 H \(-\) 16.9 \\ \hline Forearm & 0.016 M & 0.154 H & 45.7 (from elbow) & 0.86 M + 0.38 H \(-\) 67.9 \\  & & & & 0.95 M + 0.34 H \(-\) 64 \\  & & & & 0.31 M + 0.09 H + 5.66 \\ \hline Hand & 0.006 M & 0.050 H & 79.0 (from wrist) & 0.08 M + 0.03 H \(-\) 6.26 \\  & & & & 0.09 M + 0.09 H \(-\) 13.68 \\  & & & & 0.17 M + 0.12 H \(-\) 19.5 \\ \hline Thigh & 0.142 M & 0.243 H & 41.0 (from hip) & 32.02 M + 19.24 H \(-\) 3690 \\  & & & & 31.70 M + 18.61 H \(-\) 3557 \\  & & & & 11.30 M \(-\) 2.28 H \(-\) 13.5 \\ \hline Shank & 0.043 M & 0.249 H & 44.6 (from knee) & 4.59 M + 6.82 H \(-\) 1152 \\  & & & & 4.59 M + 6.63 H \(-\) 1105 \\  & & & & 1.13 M + 0.30 H \(-\) 70.5 \\ \hline Foot & 0.013 M & 0.148 H & 44.2 (from heel) & 0.41 M + 0.61 H \(-\) 97.09 \\  & & & & 0.14 M + 0.09 H \(-\) 15.48 \\  & & & & 0.48 M + 0.63 H \(-\) 100 \\ \hline \hline \end{tabular} The moments of inertia are presented in the following order: mediolateral axis, anterior–posterior axis, and vertical axis. The units for mass (M) and height (H) in the context of inertia are kilograms (kg) and centimeters (cm), respectively.  
\end{table}
Table 1: Parameters of the simulation model (M: body mass, H: height) [19; 20].