Perturbation Analysis of Kinematic Trajectories Using Fractal Dynamics for the Detection of Experimental Errors in Patients With Rheumatoid Arthritis

In the context of finger biomechanics and the development of biomechatronic systems, joint motion trajectories exhibit nonlinear variations and local instabilities that cannot always be adequately described by classical deterministic models; therefore, this study proposes a mathematical framework based on the introduction of controlled fractal perturbations generated through Mandelbrot-type iterative dynamics. The time series of MCP, PIP, and DIP joint angles were processed using a graphical user interface developed in MATLAB, designed for the kinematic analysis of the index finger, modeled as a serial kinematic chain with three degrees of freedom, allowing the reconstruction of the distal phalanx trajectory and its comparison with a reference trajectory derived from healthy-subject data. Through the automatic computation of Cartesian errors, normal deviations, and discrepancies in the joint space, the proposed method highlights motion variability and local instabilities, contributing to data validation and to the optimization of objective biomechanical assessment in rheumatoid arthritis.