## 3 Results  
The reaction forces and moments of knee joints that did not undergo TKA and did or did not exhibit VM impairment for the flexion angle are shown in Figure 3. Within 0-30\({}^{\circ}\) flexion angles, the dominant vector of the medial-lateral reaction forces was altered from lateral to medial secondary to VM impairment (\(p\) < 0.05). Here, the medial-lateral reaction forces on quadriceps with/without VM impairment were significantly different  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **VM Impairment** & **Repetition Count** & **Total Test Count (m \(\ast\) n)** \\ \hline TKA not performed & With 3 (m 1 = 4) & n 2 = 3 & 12 \\ (m 1 = 4) & Without 4 (m 1 = 4) & n 2 = 3 & 12 \\ \hline TKA performed & With 3 (m 1 = 4) & n 2 = 3 & 12 \\ (m 1 = 4) & Without 4 (m 1 = 4) & n 2 = 3 & 12 \\ \hline \hline \end{tabular}  
* m = number of specimens. 2 n = repetition count of the test for each specimen. 3 Vastus medialis (VM) muscle force was set to zero (VM: 0 N; RF/VL: 49 N; VL: 45 N). 4 VM muscle force was set to normal muscle force (VM: 31 N; RF/VL: 49 N; VL: 45 N).  
\end{table}
Table 1: Test conditions and total test count performed in the current study.  
Figure 2: Test configurations for muscle forces and directions (RF: rectus femoris; VI: vastus intermedius; VL: vastus lateralis; VM: vastus medialis) applied to the knee joint and the coordinate system (Fx: anterior–posterior reaction force; Fy: medial–lateral reaction force; Fz: proximal–distal reaction force; Tx: varus–valgus moment; Ty: flexion–extension moment; Tz: internal–external moment) on the knee joint and their degrees of freedom (T1: proximal–distal displacement on the femur; R2: flexion–extension rotation on the femur; R4: flexion–extension rotation on the tibia): (**a**) frontal view; (**b**) sagittal view for each flexion angle (0\({}^{\circ}\), 30\({}^{\circ}\), 60\({}^{\circ}\), and 90\({}^{\circ}\)).  
at 10\({}^{\circ}\) (13.8 \(\pm\) 3.0 N) and 20\({}^{\circ}\) (9.2 \(\pm\) 0.2 N) flexion angles (\(p\) < 0.05). The other reaction forces and moments with/without VM impairment were not significantly different (\(p\) > 0.05). Nevertheless, the vectors of the varus-valgus and internal-external moments showed tendencies for alteration from valgus and external to varus and internal. These tendencies were evident in 6 cases in 12 total test pairs (with and without VM impairment). Within 40-90\({}^{\circ}\) flexion angles, all reaction forces and moments with/without VM impairment were not significantly different (\(p\) > 0.05). For knee joints that had undergone TKA, the joint reaction forces and moments are shown in Figure 4. The joint reaction forces and moments with/without VM impairment were not significantly different for all flexion angles (\(p\) > 0.05). Nevertheless, the vectors of internal-external moments mostly showed a tendency for alteration from external to internal due to VM impairment. This tendency was evident in 9 cases in 12 total test pairs (with and without VM impairment) (Figure A1). Furthermore, the vectors of the anterior-posterior reaction forces mostly showed a tendency for anterior increase due to VM impairment. This tendency was evident in 9 cases in 12 total test pairs (with and without VM impairment) (Figure A1).  
Figure 3: _Cont._  
Figure 4: _Cont._  
Figure 3: Knee–joint reaction forces and moments in native knee joints with/without VM impairment during knee–joint flexion: (**a**) anterior–posterior reaction force (Fx); (**b**) varus–valgus moment (Tx); (**c**) medial–lateral reaction force (Fy); (**d**) flexion–extension moment (Ty); (**e**) proximal–distal reaction force (Fz); (**f**) internal–external moment (Tz). * \(p\) < 0.05.