Equivalent spatial mechanism for modelling passive motion of the human knee

Recent literature demonstrated that the three-dimensional motion of the human knee joint in virtually unloaded conditions (passive motion) is guided in a mono-dimensional complex path by the passive structures of the joint, i.e. the two condylar contacts and isometric fibres at ACL, PCL, MCL ligaments. Thus, it was deduced that the joint behaves as a single degree of freedom mechanism. Based on experimental observations, the knee was modelled by means of equivalent parallel spatial mechanisms. A few possible solutions were considered, which featured two members (i.e. the tibia and femur) interconnected by three rigid links (i.e. the ligaments’ isometric fibres) and two separated rigid contacts (i.e. the condylar contacts). Three different models, M2, M3, and M4, having condylar surfaces with increasing approximation were analyzed. Model M2 features tibial and femoral condyle surfaces modelled by planes and spheres respectively. Differently, in model M3 and M4 both the tibial and femoral condylar surfaces are modelled by spheres or B-Spline surfaces respectively. A further model, SW, features two members (i.e. the tibia and femur) interconnected by a spherical joint (i.e. the medial condylar contact) and two rigid links (i.e. the cruciate’s isometric fibres): the low number of members makes the SW geometrically simpler than the M-type models. This paper summarizes potentialities and limits of the studied models.