Towards Estimating Normal and Shear Interface Pressures in Prosthetic Sockets via Least Squares and Mechanics Modeling

2026-06-02

AI Summary

This study addresses the lack of objective assessment methods for prosthetic socket fit, where existing sensors struggle to simultaneously capture long-term, decoupled normal and shear interface stresses. To overcome this limitation, the authors propose a two-stage convex optimization framework that integrates global six-degree-of-freedom wrench measurements with local multi-channel capacitive pressure sensing. By identifying parameters of a quasi-static spring-mass contact model, the method jointly estimates both normal and shear stresses at the residual limb–socket interface. A constant bias term is introduced to effectively mitigate steady-state errors in wrench measurements, substantially improving agreement between estimated and experimentally measured local stresses. Experimental results demonstrate the framework’s validity and superior accuracy under static loading conditions.

Abstract

Prosthetic socket fitting remains largely manual and iterative, and objective fit metrics are still limited. Part of the challenge is the lack of long-term real-life pressure data at the residual limb--socket interface. Traditional pressure sensors are prone to drift over time, and capture only normal pressures at sparse locations within the socket, missing a critical component for biomechanical analysis: shear. Although some sensors can report both normal and shear interface stresses, these components are often difficult to decouple because of measurement crosstalk. One potential path forward is to develop models that can augment available measurements. This work introduces a testbed to evaluate model performance under sparse pressure sensing using two complementary validation signals: (i) the global wrench (\ie, total forces and moments expressed in an orthonormal frame) transmitted through the socket, by an artificial residual-limb, and (ii) local interface loads (\ie, decoupled normal and shear pressure components in a right-hand-rule orthogonal frame that lives in each instrumented location) measured by sparse sensing clusters, each composed of four capacitance-sensing channels. Rather than presenting full-field pressure estimates, the focus is on an analysis sequence that quantifies how well candidate mechanical models explain both global and local measurements under controlled conditions. A quasi-static spring--mass contact model is evaluated, and its parameters are identified via a two-stage convex least-squares problem. Validation under static loading shows that estimating constant bias terms reduces steady offsets in the wrench channels and improves agreement with local measurements. A Pareto-front sensitivity analysis further illustrates how the trade-off between global and local objectives changes when bias terms are included.

Problem

• prosthetic socket
• interface pressure
• shear stress
• normal pressure
• biomechanical modeling

Innovation

• interface pressure estimation
• shear stress decoupling
• mechanics-informed modeling
• convex least-squares identification
• prosthetic socket validation