Analysis of Rollover Shape and Energy Storage and Return in Cantilever Beam-type Prosthetic Feet

This paper presents an analysis of the rollover shape and energy storage and return in a prosthetic foot made from a compliant cantilevered beam. The rollover shape of a prosthetic foot is defined as the path of the center of pressure along the bottom of the foot during stance phase of gait, from heel strike to toe off. This path is rotated into the reference frame of the ankle-knee segment of the leg, which is held fixed. In order to achieve correct limb loading and gait kinematics, it is important that a prosthetic foot both mimic the physiological rollover shape and maximize energy storage and return. The majority of prosthetic feet available on the market are cantilever beam-type feet that emulate ankle dorsiflexion through beam bending. In this study, we show analytically that a prosthetic foot consisting of a beam with constant or monotonically decreasing cross-section cannot replicate physiological rollover shape; the foot is either too stiff when the ground reaction force (GRF) acts near the ankle, or too compliant when the GRF acts near the toe. A rigid constraint is required to prevent the foot from over-deflecting. Using finite element analysis (FEA), we investigated how closely a cantilever beam with constrained maximum deflection could mimic physiological rollover shape and energy storage/return during stance phase. A constrained beam with constant cross-section is able to replicate physiological rollover shape with R = 0.86. The ratio of the strain energy stored and returned by the beam compared to the ideal energy storage and return is 0.504. This paper determines that there is a trade off between rollover shape and energy storage and return in cantilever beam-type prosthetic feet. The method and results presented in this paper demonstrate a useful tool in early stage prosthetic foot design that can be used to predict the rollover shape and energy storage of any type of prosthetic foot.