State variable approach to the function of the muscular system supporting the hip joint during normal walking

In Figures 6 and 7, the results of the forces Fk and Fm are analytically represented. The signs of these forces show the direction of the corresponding moment which emanates from this force, since this sign is stable throughout the entire duration of the interval. The resultant moment, included in the equation 7 or 8, is expressed as Fkdk or Fmdm respectively. The direction of this moment is positive if F1 or F3 is operational, and negative if F2 or F4 is operational, therefore the sign attached to this force must follow the sign of the corresponding moment. The results show that this is satisfied for all values, except for those at the 65 and 75% point of the period. This is probably because the value of the corresponding moment is very small, about 0.1, and the resultant force is primarily due to the effect of the moment Mx. In this work, the flexion-extension and abduction-adduction forces, Fk, Fm respectively, were found to take their maximum and minimum values at times which are proximal to those found by Paul and other authors. On the other side there is a difference in values which fluctuates between 15 and 35% at various points; this divergence should be generally acceptable, given that it concerns models describing biological systems. These results seem to lend encouraging support to our method and suggest that the model should be reliable and effective and could be further enhanced if the time intervals were shorter but more numerous.