## 3 Results  
The comparison between our data and the reference data showed that our tibo-femoral contact force in the \"All muscles\" condition was larger than the reference one (see Figure 6, up). The main features of the two curves, however, were similar: two peaks in the stance phase, the second higher than the first one, and a third peak at the end of the swing phase. The root mean square (RMS) of the difference was 429 N. Downscaling the contact force by a factor 0.7 reduced the RMS to a minimum of 318 N. The lower panels of Figure 6 report the knee joint kinematics as measured by our G&S mechanism in the two loading conditions: \"All muscles\", in which all external loads and muscle forces were applied to the model, and \"No muscles\", in which the knee joint was moved without muscle forces (ground reactions and moments were also removed). In this condition, the rotations and the displacements were determined by the only contact surfaces and by the ligaments' tensions. Their amplitudes were in the range described in the literature, both for the loaded and the unloaded conditions [45; 46]. The amplitude of the internal/external rotations, anterior/posterior displacements and medial/lateral displacements were slightly increased when loads, and muscle forces were applied, although the general time course was not very different. No appreciable difference appeared concerning the adduction/abduction and the proximal/distal movements. Some oscillations were observed all along the stride cycle, more pronounced in the \"No muscles\" condition. They could have been triggered by the residual roughness of the contact surfaces. Nevertheless, the physiological screw-home mechanism (knee external rotation associated with knee extension and vice versa) was evident either in the unloaded and in the loaded condition. As to the displacements, a forward displacement of the tibia was observed during both knee flexion phases (the first during stance and the second associated with the swing phase). The medial/lateral displacement was also in relation to the two flexion phases of the knee. The forces supported by the cruciate ligaments and the collateral ligaments are reported in Figure 7. As to the cruciate ligaments, it appears that the muscle activity produces a much higher tension (continuous lines) than in the \"No muscles\" condition (dashed lines). This does not happen for the collateral ligaments, where the tensions in the two conditions are not very different. The ACL is loaded in two phases along the stride cycle, the first in correspondence with the load acceptance phase and the second in correspondence with the initiation of the unloading phase, when the knee starts flexing. The PCL presents a mild tension in the stance phase, in correspondence with the knee extension movement, and considerably high tension in the second half of the swing phase, in correspondence with the large knee extension movement. For both cruciate ligaments, there seems to be no specific engagement angle but rather a strong dependence on loading conditions. Figure 6: Up: comparison of tibio-femoral contact forces between our result (**blue**) and reference data (**black**), taken from the Grand Challenge competition (see text). The orange curve represents our contact force after downscaling by a factor of 0.7. Mid and lower panels: rotations and displacements of the tibia in relation to the femur as measured by our “Grood&Suntary” mechanism (G&S). Flexion/extension was imposed, all other movements resulted from the dynamic equilibrium of forces and by the geometry of the contact surfaces. Two conditions are reported: “All muscles” refers to the application of muscular forces simulating a normal loading condition, and “No muscles” refers to the absence of muscle forces and ground reactions. The two collateral ligaments (Figure 7, lower panel) present a baseline tension around 20-25 N. The MCL is recruited in three phases: early stance, late stance, early swing. In the second half of the swing, its tension drops below the baseline.