Graphical Interpretation of the Solution to the Redundant Problem in Biomechanics

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.