assessment of anatomical frame variation effect on joint angles: a linear perturbation approach

although the interpretability and reliability of joint kinematics depends strongly on the accuracy and precision of determining the anatomical frame (af) orientation, the exact dependency of joint angle error on af misalignment is still not clear. to fully understand the behavior, this study uses linear perturbations to quantify joint angle error due to known modifications of the afs, where the joint angles are calculated according to the cardanic convention. the result is a functional representation of joint angle error with dependence on nominal joint angles and on the orientations of the alternative afs relative to the nominal afs. the results are validated using numerical analysis on knee joint angle data during walking. the derived relationship elucidates results from previous work studying this effect and allows af differences to be inferred by joint angle curves when multiple sets of joint angle curves are collected simultaneously.