## 2 Methods
### Data Processing  
Both the motion and GRF data were recorded at 120 Hz, and the motion data were smoothed using a 6 Hz Butterworth filter [23; 27]. Trials in which tripping occurred during the wrong gait phase, the reaction motion was off target, or the recorded parameters included errors were not used in the analysis. The joint angle and posture of the subject were calculated by fitting a human model to the position of the markers using the least-squares method. The biomechanical analysis software, SIMM (MulsculoGraphics Inc., Evanston, IL, USA), was used for this process [26]. The timing of the HC and toe off (TO) of each foot was determined based on the GRF. The threshold force for a gait event was set to 80 N of vertical force. This threshold value was tuned to neglect the detection of foot contact during the swing phase. The effects of contact side differences were disregarded. Therefore, the recorded data of trials where the right leg was tripped was mirrored to the motion of the left leg trip. An elevating strategy was expected based on the gait phase during which tripping occurred [3; 5]. According to this expected recovery motion, three gait events and two motion phases were defined. The hit time (HT) was defined as the time when tripping occurred. Then, the first step (FS) was defined as the time when the subject stepped over the tripping bar with the tripped leg. The subsequent step performed by the recovery leg was defined as the second step (SS). The intervals between HT and FS, and between FS and SS, were determined to be the first and second recovery phases, respectively. The stride time and step length of non-tripped strides were calculated and compared to the normal gait parameters. The parameters used to evaluate the recovery motion are shown in Table 1 and Figure 3. The outliers, which were higher or lower than the range of 1.5 times the range between the first and third interquartile range, were omitted from the analysis. Then, the mean and standard deviation of each parameter were calculated. We considered the \(p\)-value of 0.05 to be the threshold of statistical significance. To compensate for individual differences, certain parameters were normalized by the height, weight, and walking speed of each subject and trial. The margin of stability (MoS) is an index for evaluating the kinematic stability of motion which is based on the inverted pendulum model [28]. The extrapolated center of mass (XCoM) was determined by extending the center of mass (CoM) position, considering the CoM velocity. The safety margin from the fall was quantified as the distance between XCoM and the edge of the support foot, which was determined as the position of the toe marker [29]. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Definition** \\ \hline \(Stlength\) & Distance covered by each step (heel–heel) normalized by the subject’s height \\ \hline \(Sttime\) & Time duration of each step \\ \hline \(Kang\) & Maximum knee flexion angle during each phase \\ \hline \(Hang\) & Maximum hip flexion angle during each phase \\ \hline \(CoMVt\) & Center of Mass (CoM) speed at the FS and SS \\ \(CoMVv\) & in the traveling (Vt) and vertical (Vv) directions \\ \hline \(MoSt\) & Margin of stability (MoS) at FS and SS in the traveling direction normalized by the subject’s height \\ \hline \(GRFt\) & Maximum deceleration force in the traveling direction exerted on the stepping foot after the FS and SS normalized to the subject’s weight \\ \hline \(GRFv\) & Maximum GRF of the stance leg in the vertical direction during each recovery phase normalized to the subject’s weight \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Definitions of the recovery motion parameters. The correlation coefficients of the reaction motion parameters were calculated to evaluate the relationship between parameters. All parameters were \(z\)-scored, following which principal component analysis (PCA) [30] was performed to determine the factors that represent the reaction motion.