It is the object of the present study to develop a mathematical model for the study of the relative motions and forces in the human knee joint. The primary aim is to obtain better insight into some mechanical aspects.

In this model, two rigid bodies, representing the femur and the tibia, are connected by a number of nonlinear elastic springs, representing the ligaments and the capsule.

The geometrical parameters, that is the geometry of the articular surfaces and the locations of the insertion areas of ligaments and capsule, have been measured on joint specimens, while material properties were estimated on the basis of data in literature. The articular surfaces are represented by polynomials in space and the friction between these surfaces is neglected. The patella and the menisci are not included in the model. Forces induced by muscles and weight, for instance, can be accounted for as constant external loads acting on the femur.

The relative joint position can be calculated for a given load as a function of the flexion-extension angle. In addition contact forces, location of contact points and strain in ligaments and capsule, for instance, result from these calculations. The model is suitable for evaluating, for example, internal-external rotation, antero-posterior displacement and the stiffness of the joint.

In this work special attention is given to the definitions for the various relative motions in the joint, since in medical literature a rather confusing terminology is often used.

It is found that many aspects of the mechanical behaviour are described realistically, such as the location of contact points, the final rotation, the strain in ligaments and capsule as a function of the flexion-extension angle and the relative motions in the anteroposterior direction. The internal-external range of motion predicted by the model is found to be greater than average data in literature, which could be explained in part by the absence of menisci in the model.

On account of the variability between specimens and since the conditions of experiments described in literature are only partially known, such a comparison between model results and data in literature must be rough. To eliminate these effects, it is proposed to conduct validation experiments with specimens whose geometrical data will be used as input for the model.

The influence of a number of changes in parameters characterizing the ligaments and capsule has been evaluated. On the basis of this study those parameters can be indicated which require a more detailed study, for instance by experiment.

Although the present model has been developed for the human knee joint, the method used can be generalized to develop similar models for other joints.

Some objects of research in which the present model can be applied, are indicated.