Viscoelasticity Estimation of Sports Prosthesis by Energy-minimizing Inverse Kinematics and Its Validation by Forward Dynamics

Abstract

In this study, we present a method for estimating the viscoelasticity of a leaf-spring sports prosthesis using advanced energy minimizing inverse kinematics based on the Piece-wise Constant Strain (PCS) model to reconstruct the three-dimensional dynamic behavior. Dynamic motion analysis of the athlete and prosthesis is important to clarify the effect of prosthesis characteristics on foot function. However, three-dimensional deformation calculations of the prosthesis and viscoelasticity have rarely been investigated. In this letter, we apply the PCS model to a prosthesis deformation, which can calculate flexible deformation with low computational cost and handle kinematics and dynamics. In addition, we propose an inverse kinematics calculation method that is consistent with the material properties of the prosthesis by considering the minimization of elastic energy. Furthermore, we propose a method to estimate the viscoelasticity by solving a quadratic programming based on the measured motion capture data. The calculated strains are more reasonable than the results obtained by conventional inverse kinematics calculation. From the result of the viscoelasticity estimation, we simulate the prosthetic motion by forward dynamics calculation and confirm that this result corresponds to the measured motion. These results indicate that our approach adequately models the dynamic phenomena, including the viscoelasticity of the prosthesis.

Figures (9)

• Figure 1: (a) The sports prosthesis (Sprinter 1E90, Ottobock). (b) Schematic illustration of the PCS model of the sports prosthesis.
• Figure 2: (a) Measuring jig used in the experiment. The prosthesis was loaded in four different directions to investigate different deformations. (b) Marker array attached to the prosthesis. Twenty-two retro-reflective optical markers were attached. (c) Experimental procedure.
• Figure 3: Results of the strain calculated by the inverse kinematics: The red line is the result of the proposed approach and the black line is the result of the conventional inverse kinematics calculation.
• Figure 4: The PCS model of the prosthesis deformed according to the result of the strain: In the first segment, the conventional inverse kinematics has an inconsistent strain, while the result of the proposed inverse kinematics is more reasonable.
• Figure 5: Comparison of ground reaction force values in the backward horizontal direction: The red line represents the estimated value $\widehat{\bm{f}}$ based on the equation of motion, and the black line represents the measured value $\bm{f}$. The shaded area is magnified view of the one second period.