Mathematical model of a planar four-link mechanism for motion of the cruciate ligaments of the knee joint; and validation of the model using video analysis

The mathematical model of four linkages for knee joint requires the joint components to establish a “kind” of a linkage. The linkage was a “cruciate” linkage, besides of the anatomical geometry of cruciate ligaments, the cruciate linkage was established because of the efficiency of motion and force transmission. The joint components make motions of: flexion, extension, abduction, adduction and internal and external rotation. This present paper focused in the flexion and extension motions on the sagittal plane. The Freudenstein's equation was determined and from that equation was possible obtain the real value of the bond angle and real value of the output angle. Applying the least squares technique to Freudenstein's equation the lengths of the links were optimized to “n” positions. For the optimization was necessary obtain the smallest error between the desired value of the angle of the coupling link and the experimental. The standard deviation was 0.6340. Newton Raphson method was used to figure out the non-lineal equations system. Finally, the video analysis technique was used to validate the model that was developed. The percentage errors were between 4 and 16. The mathematical model obtained can be used in PIMI 1504 Project. PIMI 1504 Project is being developed between Escuela Politécnica Nacional and Universidad Politécnica de Valencia.