A one-degree-of-freedom spherical mechanism for human knee joint modelling

In-depth comprehension of human knee kinematics is necessary in prosthesis and orthosis design and in surgical planning but requires complex mathematical models. Models based on one-degree-of-freedom equivalent mechanisms have replicated well the passive relative motion between the femur and tibia, i.e. the knee joint motion in virtually unloaded conditions. In these mechanisms, fibres within the anterior and posterior cruciate and medial collateral ligaments were taken as isometric and anatomical articulating surfaces as rigid. A new one-degree-of-freedom mechanism is analysed in the present study, which includes isometric fibres within the two cruciates and a spherical pair at the pivot point of the nearly spherical motion as measured for this joint. Bounded optimization was applied to the mechanism to refine parameter first estimates from experimental measurements on four lower-limb specimens and to best-fit the experimental motion of these knees. Relevant results from computer simulations were compared with those from one previous equivalent mechanism, which proved to be very accurate in a former investigation. The spherical mechanism represented knee motion with good accuracy, despite its simple structure. With respect to the previous more complex mechanism, the less satisfactory results in terms of replication of natural motion were counterbalanced by a reduction of computational costs, by an improvement in numerical stability of the mathematical model, and by a reduction of the overall mechanical complexity of the mechanism. These advantages can make the new mechanism preferable to the previous ones in certain applications, such as the design of prostheses, orthoses, and exoskeletons, and musculoskeletal modelling of the lower limb.