One-degree-of-freedom spherical model for the passive motion of the human ankle joint

Mathematical modelling of mobility at the human ankle joint is essential for prosthetics and orthotic design. The scope of this study is to show that the ankle joint passive motion can be represented by a one-degree-of-freedom spherical motion. Moreover, this motion is modelled by a one-degree-of-freedom spherical parallel mechanism model, and the optimal pivot-point position is determined. Passive motion and anatomical data were taken from in vitro experiments in nine lower limb specimens. For each of these, a spherical mechanism, including the tibiofibular and talocalcaneal segments connected by a spherical pair and by the calcaneofibular and tibiocalcaneal ligament links, was defined from the corresponding experimental kinematics and geometry. An iterative procedure was used to optimize the geometry of the model, able to predict original experimental motion. The results of the simulations showed a good replication of the original natural motion, despite the numerous model assumptions and simplifications, with mean differences between experiments and predictions smaller than 1.3 mm (average 0.33 mm) for the three joint position components and smaller than 0.7° (average 0.32°) for the two out-of-sagittal plane rotations, once plotted versus the full flexion arc. The relevant pivot-point position after model optimization was found within the tibial mortise, but not exactly in a central location. The present combined experimental and modelling analysis of passive motion at the human ankle joint shows that a one degree-of-freedom spherical mechanism predicts well what is observed in real joints, although its computational complexity is comparable to the standard hinge joint model.