One degree-of-freedom spherical mechanism models for kinematic analysis of the human knee and ankle joints

Kinematic models based on one-degree-of-freedom equivalent spatial mechanisms replicated well natural motion of the knee and ankle joints by direct representations of their anatomical structures. However, these mechanisms are limited by high computational costs, overall mechanical complexity and numerical instability. Spherical parallel mechanisms based both on anatomy and kinematics are here analysed to overcome these problems. These models include isometric fibres within two ligaments (the cruciates for the knee, the calcaneal-fibular and tibio-calcaneal for the ankle) and a spherical pair at the pivot point of the nearly-spherical motion observed for these joints. Spherical mechanisms were defined from experimental data obtained from several knee and ankle specimens. Model predictions were compared with original measurements, and with those from a previous equivalent mechanism that proved to be very accurate. The spherical models replicated natural motion with a comparable accuracy with respect to previous more complex mechanisms. The slightly lower precision was observed to be counterbalanced by a reduction of computational costs and of overall mechanical complexity, and by an improvement of numerical stability. All these aspects are very important for dynamic analysis and also design of prostheses and orthoses of these joints, and for musculo-skeletal modelling of the lower limb as well.