## 3 Methods
### Selection of Exercise Tasks  
In this study, six training protocols tailored for individuals with lower limb amputations were developed from approximately 300 body movements available within the UINCARE system. These protocols encompassed pre-prosthetic training, post-prosthetic training, basic left-right stepping training, center of mass transfer training, balance training, and flexibility training.  
For the purpose of this experiment, eight specific test movements were selected from the post-prosthetic training protocol. These movements were categorized by their balance demand into three difficulty levels: high (4 movements), medium (2 movements), and low (2 movements). The details of the selected exercise movements and their difficulty criteria are presented in Table 1.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Difficulty** & **Exercise Movement** & **Analyzed Motion** & **Criteria for Difficulty Level Selection** \\ \hline \multirow{2}{*}{Low} & Standing arm abduction & Shoulder abduction & Exercise movement involving only the upper limbs while standing with weight supported on both feet, requiring a low level of balance ability. \\ \cline{2-4}  & Standing arm flexion & Shoulder flexion & \\ \hline \multirow{3}{*}{Medium} & Standing trunk lateral flexion & Trunk lateral flexion & Standing with weight supported on both feet, bending the torso to the side; requires a moderate level of balance ability. \\ \cline{2-4}  & Standing diagonal medicine ball & Trunk rotation & Standing with weight supported on both feet, rotating the torso diagonally; requires a moderate level of balance ability. \\ \hline \multirow{3}{*}{High} & Standing forward dumbbell & \multirow{3}{*}{Knee flexion} \\  & lumge & & \\ \cline{1-1} \cline{2-4}  & Standing single-leg lateral raise & Hip abduction & Exercise movement involving supporting weight on the prosthesis and moving the intact leg, requiring both weight-bearing capacity of the prosthesis and balance ability; a high-difficulty exercise. \\ \cline{1-1} \cline{2-4}  & Standing maximal knee raise & Hip flexion & Exercise movement involving supporting weight on the prosthesis and moving the intact leg, requiring both weight-bearing capacity of the prosthesis and balance ability; a high-difficulty exercise. \\ \cline{1-1} \cline{2-4}  & Standing lateral step with arm & \multirow{2}{*}{Knee flexion} \\  & extension & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Exercise movements used in the experiment and criteria for difficulty level selection.  
Figure 1: Overview of the AR training system used in the experiment.  
For each exercise movement, the range of motion of the primary involved joint was measured. Specifically, the shoulder abduction angle was measured for the standing arm raise to the side, the shoulder flexion angle for the standing arm raise overhead, the trunk lateral flexion angle for the standing trunk lateral flexion, the trunk rotation angle for the standing diagonal medicine ball lift, the knee flexion angle for the standing dumbbell forward lunge, the hip abduction angle for the standing leg raise to the side, the hip flexion angle for the standing knee flexion to maximum height, and the knee flexion angle for the standing step out to the side with arm extension.