The spatial gross motion of the foot with respect to the shank is modelled as rotations about two fixed ankle axes: the upper ankle rotation axis (plantar flexion/dorsiflexion) and the subtalar rotation axis (inversion/eversion). The positions of the axes are determined by externally visible bony landmarks of the lower leg, and are measured for a living subject. The model input data are the plantar flexion/dorsiflexion and inversion/eversion rotation angles; the model output is a 4 X 4 transformation matrix which quantitatively describes the relative position of a foot coordinate system with respect to a shank coordinate system.

The use of optimization techniques to predict individual muscle forces in redundant biomechanical systems implies the formulation of a criterion for load sharing between the muscles. In part I of this paper, the characteristics and performance of several linear and non-linear criteria reported in the literature have been compared for static-isometric knee flexion. The results show that linear criteria inherently predict discrete muscle action (orderly recruitment of muscles) whereas non-linear criteria can predict synergistic action. All criteria predict that relatively more force is allocated to muscles with large moment arms. When muscle stresses (or ratios of muscle force to maximum muscle force) are used as the decision variables in the objective function, then relatively more force is allocated to muscles with large maximum possible force as well. Future formulations of the optimization should consider the differences in fiber type composition among the muscles. Such an approach is presented in part II of the paper.