Mathematical modelling of the effect of sole elasticity distribution on pronation

A coronal plane model of a distributed elastic sole has been proposed and analyzed with respect to the effects of different medial-lateral elasticity distribution on pronation under quasi-static conditions. The distributed model consists of an array of linear vertical line springs. Under minimum energy assumption, the behavior of the top surface of the interface under resultant force and moment loading was shown to be equivalent to that of a rigid-body mechanism under the same loading. The model was then combined with a rigid-link model of the lower limb. Expressions that describe the relationship of the interface aggregate parameters with pronation and the center of pressure were obtained. These expressions were confirmed by an experiment in which the elastic distribution in the interface was systematically varied and the pronation angle and the center of pressure measured. The model has the potential of being a useful analytical tool in the design of elastic soles in running shoes.