The Geometry of the Knee in the Sagittal Plane

A geometric model of the tibio-femoral joint in the sagittal plane has been developed which demonstrates the relationship between the geometry of the cruciate ligaments and the geometry of the articular surfaces. The cruciate ligaments are represented as two inextensible fibres which, with the femur and the tibia, are analysed as a crossed four-bar linkage. The directions of the ligaments at each position of flexion are calculated. The instant centre, where the flexion axis crosses the parasagittal plane through the joint, lies at the intersection of the cruciates. It moves relative to each of the bones during flexion and extension. The successive positions of the flexion axis relative to a fixed femur and to a fixed tibia are deduced. The shapes of articular surfaces which would allow the bones to flex and extend while maintaining the ligaments each at constant length are calculated and are found to agree closely with the shapes of the natural articular surfaces. The calculated movements of the contact point between the femur and the tibia during flexion also agree well with measurements made on cadaver specimens. The outcome is a geometric simulation of the tibio-femoral joint in the sagittal plane which illustrates the central role played by the cruciate ligaments in the kinematics of the knee and which can be used for the analysis of ligament and contact forces.