A planar model of the knee joint to characterize the knee extensor mechanism

A simple planar static model of the knee joint was developed to calculate effective moment arms for the quadriceps muscle. A pathway for the instantaneous center of rotation was chosen that gives realistic orientations of the femur relative to the tibia. Using the model, nonlinear force and moment equilibrium equations were solved at one degree increments for knee flexion angles from 0 (full extension) to 90 degrees, yielding patellar orientation, patellofemoral contact force and patellar ligament force and direction with respect to both the tibial insertion point and the tibiofemoral contact point. The computer-derived results from this two-dimensional model agree with results from more complex models developed previously from experimentally obtained data. Due to our model's simplicity, however, the operation of the patellar mechanism as a lever as well as a spacer is clearly illustrated. Specifically, the thickness of the patella was found to increase the effective moment arm significantly only at flexions below 35 degrees even though the actual moment arm exhibited an increase throughout the flexion range. Lengthening either the patella or the patellar ligament altered the force transmitted from the quadriceps to the patellar ligament, significantly increasing the effective moment arm at flexions greater than 25 degrees. We conclude that the levering action of the patella is an essential mechanism of knee joint operation at moderate to high flexion angles.