## 3 Results  
The results show differences in the AP translation measured by the application between injured and non-injured legs. The range of AP translation was higher in the injured leg than in the contralateral leg for all seven subjects (S1 to S7). Interestingly, it was significantly higher for five subjects during the Lachman tests (\(p<0.001\) for S2 and S3, \(p=0.005\) for S5, \(p=0.004\) for S6 and \(p=0.001\) for S7), and for three subjects during the Pivot-Shift tests (\(p=0.036\) for S5, \(p=0.045\) for S6 and \(p=0.02\) for S7) (Figure 3). The three subjects who had significant differences consistently in both tests (S5, S6 and S7) were under anesthesia. Additionally, we measured the AP translation in one subject (gender: woman, age: 28 years old) pre and post-surgery for an ACL reconstruction while she was awake. The results show that there were significant differences in the range of AP translation of the injured knee before and after the surgery (Figure 4). The processing of one video of about 10 s takes about 5 s. The results were obtained in a regular smartphone emulator (Nexus X5 Android 9.0, API 28). We also analyzed how the camera position and orientation influence the calculation of AP translation. Figure 4 shows the dependence of the absolute AP translation (calculated as explained in Section 2.3) on the orientation of the camera with respect to the sagittal plane (with orientations from \(-60^{\circ}\) to \(60^{\circ}\), Figure 5a) and on the distance between the camera plane and the sagittal plane (with distances from 20 cm to 100 cm, Figure 5b). In those cases, a subject remained in a static position and two videos were recorded changing the orientation or the distance of the camera plane with respect to the sagittal plane. Orientations of the camera plane far from being parallel to the sagittal plane led to high AP translation deviations. The distance between the plane of the camera and the sagittal plane did not highly affect the calculation of the AP translation. Between 20 cm and 80 cm, the difference in AP translation was only 2.2 mm. Figure 3: Range of anterior–posterior translation values (mean \(\pm\) standard deviation) in the ipsilateral (injured) and contralateral (non-injured) legs of seven anterior cruciate ligament (ACL)-deficient subjects during Lachman and Pivot-Shift tests. Note that the vertical axes do not have the same range of values. The underlined subjects were under anesthesia. The star \({}^{\star}\) indicates significant differences (\(p<0.05\)). The influence of marker positions on the range of AP translation was also tested. An AP translation of 12 mm was imposed in the model configuration as shown in Figure 6a. The same translation of the tibia with respect to the femur was applied but considering \(10^{5}\) cases where markers were deviated following a normal distribution with a mean of 0 mm and a standard deviation of 10 mm (consistent with the inter-subject precision of manual palpation of main knee bony landmarks reported by [PERSON] et al. [17]). Figure 6b shows a graphical representation of the calculation of AP translations from the deviated markers (yellow ticks). The results indicated that the mean and standard deviation of the range of AP translation in those cases were \(11.1\) mm and \(1.4\) mm, respectively. Figure 4: Range of anterior–posterior translation values (mean \(\pm\) standard deviation) in the ipsilateral (injured) leg of one ACL-deficient subject before (Pre-surg) and after (Post-surg) the surgery during Lachman and Pivot-Shift tests. The differences were significant (\(p<0.05\)) in both tests. Figure 5: (**a**) AP translation as a function of the orientation angle of the camera with respect to the sagittal plane. (**b**) AP translation as a function of the distance of the camera plane. Figure 6: Graphical representation of the calculation of AP translation ranges (as mentioned in Section 2.3). (**a**) Calculation of AP translations without deviations (from green dots).