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Technical Briefs

Novel Method to Evaluate Angular Stiffness of Prosthetic Feet From Linear Compression Tests

[+] Author and Article Information
Peter G Adamczyk

Intelligent Prosthetic Systems, LLC,
Ann Arbor, MI 48104
Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109

Michael E. Hahn

Department of Veterans Affairs,
RR&D Center of Excellence,
Seattle, WA 98108
Department of Human Physiology,
University of Oregon,
Eugene, OR 97403

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received December 10, 2012; final manuscript received July 2, 2013; accepted manuscript posted July 29, 2013; published online September 17, 2013. Assoc. Editor: Kenneth Fischer.

J Biomech Eng 135(10), 104502 (Sep 17, 2013) (5 pages) Paper No: BIO-12-1605; doi: 10.1115/1.4025104 History: Received December 10, 2012; Revised July 02, 2013; Accepted July 29, 2013

Lower limb amputee gait during stance phase is related to the angular stiffness of the prosthetic foot, which describes the dependence of ankle torque on angular progression of the shank. However, there is little data on angular stiffness of prosthetic feet, and no method to directly measure it has been described. The objective of this study was to derive and evaluate a method to estimate the angular stiffness of prosthetic feet using a simple linear compression test. Linear vertical compression tests were performed on nine configurations of an experimental multicomponent foot (with known component stiffness properties and geometry), which allowed for parametric adjustment of hindfoot and forefoot stiffness properties and geometries. Each configuration was loaded under displacement control at distinct pylon test angles. Angular stiffness was calculated as a function of the pylon angle, normal force, and center of pressure (COP) rate of change with respect to linear displacement. Population root mean square error (RMSE) between the measured and predicted angular stiffness values for each configuration of the multicomponent foot was calculated to be 4.1 N-m/deg, dominated by a bias of the estimated values above the predicted values of 3.8 ± 1.6 N-m/deg. The best-fit line to estimated values was approximately parallel to the prediction, with R2 = 0.95. This method should be accessible for a variety of laboratories to estimate angular stiffness of experimental and commercially available prosthetic feet with minimal equipment.

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References

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Figures

Grahic Jump Location
Fig. 1

Two-phase loading demonstrates superposition of linear and angular terms in determining the force and deflection of the hindfoot and forefoot. (a) Pure vertical compression results in equal deflections of the forefoot and hindfoot, each with a force proportional to its linear component stiffness. The resultant equals the applied force (Fz), acting at a COP that remains constant as load increases (Eq. (2)). The moment supported by the ankle constraint is M=yCOP-compressionFz. (b) The angle constraint can be replaced by its equivalent moment. Adding a differential moment (dM) shifts the load, moving the COP and changing the forefoot and hindfoot forces by ±dF. The accompanying deflection changes in each component result in an angular rotation . The overall angular stiffness relates this angle to the moment: dM=Kangulardα. The final state is equivalent to rotating first and then compressing, as in the proposed test method. This equivalence is used to derive an expression for angular stiffness based on measured changes in Fz and yCOP (Eq. (6)).

Grahic Jump Location
Fig. 2

Test setup for vertical compression tests. The test foot is rigidly mounted to the ground such that the pylon is normal to surface of the force plate while the foot is in a foot-flat orientation. The force plate, which is mounted to a 6-DOF parallel robot, is rotated to test angle, α, and displaced along the axis of the pylon. Force, COP, and displacement data are recorded while the foot is compressed at 5 mm/s.

Grahic Jump Location
Fig. 3

Example data plots from one compression test (–4 deg angle, heel-first contact): (a) normal force versus displacement and (b) center of pressure (COP) versus displacement. The sections shown in bold represent the data used to calculate the inputs for Eq. (4): Fz, dFz/dz, and dyCOP/dz.

Grahic Jump Location
Fig. 4

Measured (Eq. (6)) versus predicted (Eq. (4)) angular stiffness. The best fit line (solid) between the predicted and measured values has R2 = 0.95. The dashed line represents the identity, to visualize prediction errors. Measured values exceeded predicted values by an average of 3.8 ± 1.6 N-m/deg, with RMSE (from predicted) of 4.1 N-m/deg.

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