Numerical Stability of Two Classes of Mechanisms for the Kinematic Modelling of the Knee

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 particular, two mechanisms revealed particularly interesting in previous investigations. The first model proved to be able to replicate the knee passive motion with a high accuracy; the second model was slightly less accurate, but mechanical complexity of the mechanism is much lower. In this paper, numerical stability of these two mechanisms is analysed. Both mechanisms are identified on four relevant specimens and numerical stability is quantitatively assessed for all models. The results prove that for all specimens the second simpler mechanism is less sensitive to geometrical parameter variations, generates a smoother, more stable motion and gives rise to less singularity problems than the first more complex model. All these features, low mechanical complexity included, makes the simpler mechanism an interesting tool in the field of rehabilitation and prosthesis and orthosis design.