An, K.N.

Force analysis of musculoskeletal joint systems is a redundant problem since the number of unknowns exceeds the number of equilibrium and constraint equations. Such a problem has been analyzed previously by the method of permutation/combination and by optimization technique. This paper combines both methods and discusses the results in the light of a graphical presentation from which unique and nonunique solutions to the problem are elaborated. When the applied load is nominal, multiple solutions are possible to meet the functional requirements. However, under maximum strength, unique solution exists because the redundant muscles reach their physiological limits.

Analytic determination of muscle force across human joints encounters an indeterminate problem. A new optimization approach, based on minimizing the upper bound of muscle stress, is introduced to obtain a unique solution. Mathematical and physiological justification of this new approach distinguishes it from previously described methods. A complex joint, the elbow, was studied. The results of muscle forces in resisting the elbow flexion moment were obtained and compared with electromyographic observation, as well as with solution from other optimizing techniques. The resultant humero-ulnar joint forces at various elbow joint positions are calculated. In normal daily activities, resultant joint forces of 0.3–0.5 times body weight are commonly encountered.

In muscle force analysis, orientations and moment arms of the muscles about a joint provide essential coefficients in the equilibrium equations. For the determination of these parameters, several experimental techniques, including geometric measurement, tendon-joint displacement measurement and direct load measurement, are available. Advantages and disadvantages associated with each of the techniques are reviewed and compared based on our extensive experience.