Mathematical models of passive motion at the human ankle joint by equivalent spatial parallel mechanisms

The paper presents a theoretical model of the ankle joint, i.e. tibio-talar articulation, which shows how the articular surfaces and the ligaments, acting together as a mechanism, can control the passive kinematics of the joint. The authors had previously shown that, in virtually unloaded conditions, the ankle behaves as a single degree-of-freedom system, and that two ligament fibres remain nearly isometric throughout the flexion arc. Two different equivalent spatial parallel mechanisms together with corresponding kinematic models were formulated. These assumed isometricity of fibres within the calcaneal-fibular and tibio-calcaneal ligaments and rigidity of the articulating surfaces, taken as three sphere-plane contacts in one model, and as a single spherical pair in the other. Geometry parameters for the models were obtained from three specimens. Motion predictions compare quite well with the measured motion of the specimens. The differences are accounted for by the simplifications adopted to represent the complex anatomical structures, and might be reduced by future more realistic representations of the natural articular surfaces.