Three-dimensional analyses of the human knee were performed using mathematical surface analysis, cadaveric experimental methods, and mathematical computer models. Surface anatomy, kinematics and contact areas of the knee, as well as their influence on each other, were investigated. Both patellofemoral and tibiofemoral compartments were examined as they are affected by different muscle forces, pathological conditions, and surgical treatments. For each method used, rigorous calibration was performed to establish the accuracy of the method.

Surface curvature theory was employed to characterize the complex topography of the retro-patellar and disto-femoral cartilage surfaces. Many of previously reported surface features were confirmed, and new features were identified. The analysis also related how the surface anatomy may influence the tracking and contact area of the patellofemoral joint.

A custom knee testing machine was designed and built to experimentally investigate the knee. Both the kinematics and contact areas of patellofemoral and tibiofemoral joints were quantified. Using the machine, it was found that the hamstrings force and the iliotibial band force significantly altered the kinematics and contact areas of the knee joint. Also, when patellar tendon adhered to the anterior tibia, a common pathology following knee surgery, the adhesion significantly affected the normal knee mechanics. To report the experimental results, coordinate systems based on the knee anatomy were used, which produced a more consistent kinematic representation between different knees than previous methods.

Finally, a 3D multibody mathematical computer model of diarthrodial joints was developed to predict the kinematics, contact areas, and internal forces of the joint. The model converged rapidly by using efficient analytical Jacobian formulation and contact calculation. It also provided a sophisticated interactive graphics to view and manipulate the 3D model. The multibody mathematical model was first applied and validated for patellofemoral joints by comparing model predictions to actual experimental results. The model was also applied to demonstrate its capability to predict surgical outcomes.

The mathematical model offers opportunities to further investigate the diarthrodial joints beyond the scope of this dissertation. Although the knee is investigated as an example of complex diarthrodial joints, the methods developed and described here can be readily applied to investigate other joints.