## 4 Discussion
At the end of the swing phase, the hamstrings are the muscles required to reduce the forward velocity of the limb, and this is achieved by producing an extensor moment at the hip and a simultaneous knee flexion moment. The gastrocnemius muscles force dominates most of the stance phase since the major role of this muscle is to produce the plantar flexion moment at the ankle, synergistically with the soleus. When these muscle forces and the ground reaction forces were applied to the knee, the kinematics changed with respect to the unloaded condition, but still preserved its basic features, as represented in Figure 6. A notable difference was observed in the backward displacement of the femur, which was interrupted at about 75% of the stride cycle in the loaded condition. This is the effect of the activity of the hamstrings that brake the forward movement of the shank and so produce a rear displacement of the proximal tibia in relation to the femur. The hamstrings activity is also responsible for the increase of tibio-femoral contact force that is observed at the end of the swing phase, both in our data and in the reference data (Figure 6). The adduction/abduction rotation and the distal/proximal displacement were relatively unaffected by the muscle contractions. The changes in the knee kinematics had as a counterpart a different loading of the ligaments. Considerable was the effect on the cruciate ligaments. The total force of the ACL increased, in the first phase, corresponding to early stance phase, from 20 N to about 200 N, as well as in the second phase, corresponding to late stance-early swing the force changed from 0 N to about 100 N. The maximum PCL force was about 150 N in the unloaded condition and occurred at around the 80% of the stride cycle. In the loaded condition, the PCL tension increased up to 670 N with a peak at approximately 90% of the stride cycle. The relation between the increase of tension in this phase and the presence of hamstrings force, which produce a rear displacement of the tibia is evident. It is interesting to note that in the unloaded condition the ACL was recruited at around knee maximum extension (about 15\({}^{\circ}\) of knee engagement angle) and the PCL had a maximum tension in correspondence with maximum knee flexion, while in the loaded condition the engagement of the cruciate ligaments was not closely related to the knee angle, but it was strictly dependent on the forces applied. The different components of the collateral ligaments were less affected by the application of the muscular forces, and this is consistent with their longitudinal arrangement in relation to the long axis of the limb. Actually, the distal/proximal displacement and the adduction/abduction movements could only have been changed if the femoral condyles and tibia surfaces detached from each other, in one or both knee joint compartments, which did not occur. Therefore, the small increase of the strain (and consequently the change in ligament tension) was in this case mainly due to the increase of internal/external rotation. Both anterolateral (CAP-Ant-L) and posterior capsule (Cap-Post-L and Cap-Post-M) were affected by muscle contractions and almost doubled their tension. This is evidently associated to the increased internal/external rotation and anterior slide of tibia produced by the quadriceps contraction in the same phase of the walking cycle. The effect of the muscle contractions on the tension of the ligaments became more evident when the single muscle groups were removed in our simulations. The most affected ligaments were again the cruciate ligaments. ACL tension dropped dramatically when quadriceps was eliminated, thus revealing that quadriceps was responsible for ACL loading. PCL force instead increased with quadriceps force removal, which indicates that the remaining forces applied to the knee produced a tendency for the proximal tibia to slide backwards. Removal of the hamstrings produced an increase of the ACL tension at the end of the swing phase and a reduction of the tension in the PCL.