About kinematic consistency in the inverse dynamics problem in biomechanics

Abstract

The inverse dynamic analysis is used in the study of the human gait to evaluate the reaction forces transmitted between anatomical segments and to calculate the net joint moments resulting from the muscle activity in each joint. There are two approaches well defined. In the clinical field reconstruction techniques are often applied. The errors caused, mainly, by the relative movement of the skin over the bones make that the joint centres localized in two adjacent segments do not place the same position in the space. Velocities and accelerations are obtained through numerical derivation of the position. Finally, joint moment are calculated to balance the equilibrium equations. On the other hand, the engineers employ multibody models. They apply techniques to reduce the measurement errors and to obtain kinematically consistent data up to the acceleration level and calculate reaction and driving actions by means of the Lagrange multipliers. There is no agreement about which approach provides better results. The first procedure presents errors due to the skin motion which are avoid in the second method introducing errors inherent to the model. In this work, the two approaches were compared. Dynamic residuals defined to balance the Newton's equations were used as a measure of the model goodness. A discussion about the effect of the kinematically inconsistent data on the second approach was carried out. Results highlighted that the addition to the recorded motion of kinematic constrains according to a multibody model could lead to worse results in the inverse dynamic problem.