Mathematical model of the lower extremity joint reaction forces using Kane’s method of dynamics

This report describes a new mathematical model for defining the joint reaction forces of the lower extremity using Kane’s method of dynamics. Our model utilized average lower extremity joint motion and force/plate data from one healthy female patient during gait. From a cadaver specimen, the anatomical mass centers of the pelvis, femur, tibia, and foot were determined. Joint angular motion during the normal gait cycle was computed using Cardan angles for each distal segment relative to the proximal segment. Fluoroscopy of four normal knees determined average femorotibial and patellofemoral contact positions throughout flexion. A three dimensional model of the lower extremity was defined in weight-bearing motion by 30 differential equations. During normal walking, the joint reaction forces for the subject tested ranged from 1.9 to 2.6 times body weight at the hip joint and 1.7–2.3 times body weight at the knee joint, depending primarily on gait speed. The method correlates well with known in vivo telemetrically measured forces at the hip joint.