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

Abstract

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.

Musculoskeletal modelling of human ankle complex: Estimation of ankle joint moments

“…Ankle complex kinematics have also been modelled using four-bar linkages and spatial parallel mechanisms [15,25]. Parameter identification for a biaxial kinematic model for ankle joint has been investigated in an in vivo manner [23,26].…”

“…In the present work, the muscle path is made to pass though certain intermediate points before finally joining the insertion point. In order to determine length of each force element, suitable equations (24,25) can be used where is the length of the force element, is the total number of attachment points, is an index representing the attachment point being considered, is an identifier for the joint coordinate frame which corresponds to the th attachment point (where , and are respectively used to denote the dataset frame, the ankle frame and the subtalar frame), is the homogeneous transformation matrix which transform the dataset coordinate frame to the corresponding joint coordinate frame; and is the position vector of the attachment point for the th force element, expressed in the local coordinates of the frame.…”

Helical axis calculation based on Burmester theory: experimental comparison with traditional techniques for human tibiotalar joint motion

“…At the tibiotalar joint, despite its known complex pattern of motion [11,25,30,44], it has been shown in in vitro experiments [25,30] that the instantaneous helical axes are near, i.e. have a small angular and position dispersion, to a MHA located approximately through the tips of the malleoli, so that the natural joint can also be approximated by a hinge in certain research contexts.…”

“…Comparison of the techniques was obtained also in terms of robustness, by adding known artificial errors to the original experimental data. In this study, the motion between the tibia and the talus was analysed, as taken from previous experiments on the entire human ankle joint complex [8,11]. Absolute and relative such motion was taken in virtually unloaded conditions on two fresh-frozen skeleto-ligamentous lower leg preparations from amputation (specimen A and B), explained fully elsewhere [8,11,47].…”

“…In this study, the motion between the tibia and the talus was analysed, as taken from previous experiments on the entire human ankle joint complex [8,11]. Absolute and relative such motion was taken in virtually unloaded conditions on two fresh-frozen skeleto-ligamentous lower leg preparations from amputation (specimen A and B), explained fully elsewhere [8,11,47]. A ''flexing rig'' [25] allowed fixation of the tibia to a workbench and pure passive flexion of the entire joint complex performed by means of a long pin protruding from calcaneous posterior surface.…”