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Research Papers: Design of Mechanisms and Robotic Systems

Passive Prosthetic Foot Shape and Size Optimization Using Lower Leg Trajectory Error

[+] Author and Article Information
Kathryn M. Olesnavage

Global Engineering and Research (GEAR)
Laboratory,
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: kolesnav@mit.edu

Victor Prost

Global Engineering and Research (GEAR)
Laboratory,
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: vprost@mit.edu

William Brett Johnson

Global Engineering and Research (GEAR)
Laboratory,
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: wbj@mit.edu

Amos G. Winter, V

Global Engineering and Research (GEAR)
Laboratory,
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: awinter@mit.edu

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 6, 2017; final manuscript received June 11, 2018; published online July 31, 2018. Assoc. Editor: Massimo Callegari.

J. Mech. Des 140(10), 102302 (Jul 31, 2018) (11 pages) Paper No: MD-17-1741; doi: 10.1115/1.4040779 History: Received November 06, 2017; Revised June 11, 2018

A method is presented to optimize the shape and size of a passive, energy-storing prosthetic foot using the lower leg trajectory error (LLTE) as the design objective. The LLTE is defined as the root-mean-square error between the lower leg trajectory calculated for a given prosthetic foot's deformed shape under typical ground reaction forces (GRFs), and a target physiological lower leg trajectory obtained from published gait data for able-bodied walking. Using the LLTE as a design objective creates a quantitative connection between the mechanical design of a prosthetic foot (stiffness and geometry) and its anticipated biomechanical performance. The authors' prior work has shown that feet with optimized, low LLTE values can accurately replicate physiological kinematics and kinetics. The size and shape of a single-part compliant prosthetic foot made out of nylon 6/6 were optimized for minimum LLTE using a wide Bezier curve to describe its geometry, with constraints to produce only shapes that could fit within a physiological foot's geometric envelope. Given its single part architecture, the foot could be cost effectively manufactured with injection molding, extrusion, or three-dimensional printing. Load testing of the foot showed that its maximum deflection was within 0.3 cm (9%) of finite element analysis (FEA) predictions, ensuring the constitutive behavior was accurately characterized. Prototypes were tested on six below-knee amputees in India—the target users for this technology—to obtain qualitative feedback, which was overall positive and confirmed the foot is ready for extended field trials.

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Figures

Grahic Jump Location
Fig. 1

Lower leg position for modeled prosthetic foot (solid line) and target physiological gait data (dotted line) at one particular time interval during a step, with variables used in Eq. (1) shown. Note that physiological data come from markers placed at anatomically relevant positions on a human subject, resulting in a gap between the marker positions and the ground.

Grahic Jump Location
Fig. 2

Three analytical prosthetic foot architectures optimized and compared using LLTE: (a) rigid model, (b) rotational ankle and metatarsal model, and (c) rotational ankle, beam forefoot model

Grahic Jump Location
Fig. 3

Prototypes designed based on the simple prosthetic foot models shown in Fig. 2. While useful tools for clinical testing, the prototypes are too heavy, large, and complicated to be used as daily prostheses: (a) prototype with rotational ankle and metatarsal joints and (b) prototype with rotational ankle, beam forefoot.

Grahic Jump Location
Fig. 4

Parameterization of the keel of the foot. The shape and size of the keel are defined with nine independent design variables shown in red.

Grahic Jump Location
Fig. 5

Various possible keel designs that fall within the defined design space

Grahic Jump Location
Fig. 6

Certain combinations of design variables result in the keel shape intersecting itself, creating a design that is not physically meaningful. Constraints were imposed to prevent cases like those shown here from being included in the optimization: (a) self-intersection constraint violation and (b) loop constraint violation.

Grahic Jump Location
Fig. 7

Of the 43 time intervals during stance included in Winter's published gait data [21] shown in gray, the foot is flat on the ground and the ankle is in dorsiflexion for 26. Of those 26, the five shown in black were found to best represent the entire step. When these five data points were used, the optimal design variable values for each of the two degree-of-freedom analytical models in Fig. 2 were each within a maximum difference of 5% of the optimal design variable values as found when all 26 available data points were used.

Grahic Jump Location
Fig. 8

Free body diagrams of the GRFs on the feet and the lower leg position during three of the five time intervals used in the finite element LLTE evaluation: (a) global reference frame and (b) ankle-knee reference frame

Grahic Jump Location
Fig. 9

Example of a deformed foot result from the FE model in the ankle-knee reference frame with the variables used in Eqs. (9)(11) labeled. The variables XAK, YAK, Xglobal, and Yglobal denote the x- and y-axes of the ankle-knee reference frame and the global reference frame, respectively.

Grahic Jump Location
Fig. 10

Deformed foot finite element results from Fig. 9 rotated into the global reference frame. The variables xknee, yknee, and θLL shown here for the modeled foot are input into Eq. (1) to compare these resulting kinematics to the target physiological data.

Grahic Jump Location
Fig. 11

Experimental setup used to measure vertical displacement of the forefoot in response to applied vertical loading up to 658 N to validate finite element model of foot

Grahic Jump Location
Fig. 12

Optimal keel designs found through the wide Bézier curve optimization method. The initial bounds resulted in a foot with an LLTE value of 0.145 (shown in green), but too large to fit within the envelope of a biological foot (shown in black). The subsequent designs, shown in blue, and finally in red, have higher LLTE values, at 0.153 and 0.186, respectively, but only the final optimal design (red) meets the size and shape requirements of a prosthetic foot that can be used in daily life. Note that in this figure, the three designs and the outline of the foot are aligned by the ankle position as defined in Sec. 2.1. The length of the pylon connecting the user's socket to the ankle of the foot would be adjusted to ensure the length of the prosthetic-side leg was equal to that of the biological leg.

Grahic Jump Location
Fig. 13

Lower leg trajectory for the final optimal compliant foot (red foot design in Fig. 12, solid line showing lower leg trajectory here) compared to the target physiological lower leg trajectory (dotted line) for each of the five loading scenarios considered. The physiological data show the position of the markers at the knee, ankle, heel, metatarsal, and toe as collected during typical, unimpaired walking. Because these markers were placed at physical locations on the subject's foot, there is space between the markers and the ground in the physiological data.

Grahic Jump Location
Fig. 14

Solid model of foot based on optimal design, with added heel and male pyramid adapter to attach the foot to the rest of the prosthesis

Grahic Jump Location
Fig. 15

Comparison of Instron-measured and FEA-calculated vertical displacements under loads applied at a horizontal distance of 13 cm from the ankle for both the supplier-provided elastic modulus, E = 2.41 GPa, and the measured elastic modulus, E = 2.54 GPa

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