Keywords: energy storage and return, finite element analysis, gait, product design, prosthetic

foot, rehabilitation, roll-over shape
A prosthetic foot is a lower limb assistive device utilized to replicate the function of the
human ankle-foot complex. Ideally, a prosthetic foot should facilitate the kinematics, kinetics,
muscle activation patterns and metabolic cost as that of able-bodied human walking. On the
contrary, shortcomings on the aforementioned aspects have been presented and its
enhancement has been sought after. Generally, prosthetic feet have been designed
experimentally through a trial and error route. Such a design approach may not yield optimal
solutions for achieving enhanced gait characteristics. Moreover, experimental evaluation of a
prosthetic foot at each of its design iterations would be highly expensive in terms of time, cost
and manpower. Therefore, a lacuna lies in the absence of a numerical design model for the a
priori evaluation of the performance characteristics of a prosthetic foot to aid in its systematic
design.

Prior numerical investigations of prosthetic feet have involved several approximations in
the employment of material models, geometry and contact mechanics of the device, largely
excluding its non-linear mechanical behaviour. In addition, key performance parameters that
strongly influence prosthesis user’s gait have not been evaluated using an a priori numerical
model. Therefore, the objective of this work is to present a novel framework for the systematic
evaluation of a series of critical performance parameters of a prosthetic foot, viz., roll-over
characteristics, centre of pressure trajectory, ankle range of motion, ankle flexion moment arm
and energy storage and stress-strain characteristics using non-linear finite element analysis to
aid in its methodical design. A finite element model of the highly complex Solid Ankle Cushioned Heel (SACH)
prosthetic foot was developed after incorporating its non-linear mechanical characteristics. The

model encompassed the Augmented Lagrangian contact formulation, the hyperelastic Neo-
Hookean material model and a higher-order strain definition for an accurate evaluation.

Boundary conditions replicating the rocker-based inverted pendulum model were employed for
the a priori evaluation. The nodal and elemental kinematics and kinetics were utilized to
evaluate the performance characteristics of the foot numerically.

In order to verify the credibility of the proposed design model, experimental validation of
the finite element outcomes was conducted. An experimental setup was designed and fabricated
for the improved determination of the roll-over shape (ROS). The novelty of the setup lies in
the appropriate incorporation of the moment arm due to the weight acting on the foot and a
mechanism for the application of variable loading. Additionally, an inverted pendulum-like
apparatus previously utilized to evaluate the roll-over characteristics of prosthetic feet was
replicated in this work. The apparatus were used to experimentally evaluate the technical
criterion in a gait analysis facility to validate the numerical approach. Overall, a good
agreement was obtained between the numerical and the experimentally obtained results of all
the specified performance characteristics, exempting the instantaneous radius of curvature of
the ROS. For example, the radius of curvature of the numerically derived ROS deviated from
the experimental ROS by 0.1%.

The experimentally validated numerical model proposed may greatly assist during the
design phase of a prosthetic foot. Comprehensive a priori insights on the influence of a foot
design over gait symmetry, stability, centre of mass progression, metabolic cost, ground
reaction force characteristics, knee mechanics, ankle power and the structural integrity may
be obtained reliably using the non-linear finite element approach. Moreover, the application of a numerical approach is a first towards the systematic evaluation of energy storage
characteristics of a complete prosthetic foot unit. Such a credible a priori understanding of a
prosthetic foot’s performance during its design can pave the way towards arriving at improved
design solutions. As an application, the globally prescribed SACH foot was redesigned using
the numerical design model. Significant improvements in the effective foot length ratio and
centre of pressure trajectory of the foot were obtained after the procedure. In addition, the
numerical approach can be employed for the alignment and prescription of prosthetic feet.
Utilizing the ROS alignment theory, the finite element model can be employed to evaluate the
foot’s ROS and match with the ideal ROS to provide an enhanced walking experience. The
comprehensive performance insights provided by the finite element evaluation may be used to
credibly prescribe a suitable prosthetic foot for a potential user.

Given the vast advancements in computational technology, a non-linear finite element
approach towards the design and analysis of customized prosthetic feet presents substantial
advantages. Multiple design tools can assist in the efficient development of complex
geometries of prosthetic feet. Behavioural characteristics of materials commonly used with
prosthetic feet can be represented precisely with existing material models into the numerical
analysis. Hence, the design framework’s versatility would make it convenient for a product
designer to systematically arrive at a customised prosthetic foot with specified performance
characteristics effectively and economically. More importantly, the design model could serve
the multitude of prosthesis users living in developing countries towards the design of highly
functional and affordable prosthetic feet.