METROLOGICAL SUBSTANTIATION OF THE EMBEDDED OPTICAL-INERTIAL BALANCE MEASUREMENT PRINCIPLE AND ITS EXTENSION TO MUSCULOSKELETAL REHABILITATION SYSTEMS

Abstract

The problem of metrological substantiation of a generalized balance-measurement principle based on sensors embedded directly in the support object, without external motion-capture systems, is considered. It is formally shown that two functionally different measurement channels the Single-Finger Dynamic Balance Test (SFDBT) based on smartphone inertial sensors, and Optical Correlation Grip Dot-Pattern Gripometry (OCGdP) based on digital speckle photography realize the same measurement-transformation operator, differing only in the physical nature of the measured object. A complete measurement equation and uncertainty budget for the OCGdP channel were constructed under the GUM methodology, in accordance with ISO/IEC Guide 98-3 and VIM terminology, comprising five error components (Type B evaluation) together with a sensitivity analysis of the combined uncertainty with respect to each component. A combined standard uncertainty of uc = 0.035 mm and an expanded uncertainty of U = 0.07 mm (k = 2, P = 0.95) were obtained, consistent with the experimentally established resolution of 0.04 mm. Technical feasibility of the SFDBT protocol was demonstrated, revealing substantial inter-effector variation in the Visual Dependency Index (VDI, 0.23 to 18.44). Based on the formalized generalization of the measurement transformation, an engineering model extending the embedded-measurement principle to musculoskeletal rehabilitation systems analytical insoles and prosthetic support apparatus was developed, including a quantitative estimate of the expected uncertainty budget of the new channel and an analysis of its applicability limits.