A constraint-based approach to modelling the mobility of the human knee joint

A model of knee mobility able to predict the range and pattern of movement in the unloaded joint was proposed by Wilson et al. (J. Biomech. 31 (1998) 1127-1136). The articular surfaces in the lateral and medial compartments and isometric fascicles in three of the knee ligaments were represented as five constraints on motion between the femur and tibia in a single degree-of-freedom parallel spatial mechanism. The path of movement of the bones during passive flexion was found by solving the forward kinematics of the mechanism using an iterative method. The present paper shows that such a mechanism-based solution approach can lead to an underestimation of the flexion range. This is due to the mechanism reaching a 'stationary configuration' and 'locking'. A new, constraint-based approach to the solution of the model joint displacement is proposed. It avoids the representation of ligaments and articular surfaces by kinematically equivalent chains of one degree-of-freedom pairs which are prone to singularities. It relies instead on a numerical solution of five non-linear constraint equations to find the relative positions of the bones at a series of flexion angles. The method is successful both in its ability to predict motion through a physiological range and in its efficiency with a solution rate forty times faster than the original algorithm. The new approach may be extended to include more complex joint surface geometry, allowing a study of the effects of articular surface shape and ligament arrangement on joint kinematics.