Three-dimensional studies of range of motion currently plot joint poses in a `Euler space` whose axes are angles measured in the joint's three rotational degrees of freedom. Researchers then compute the volume of a pose cloud to measure rotational mobility. However, pairs of poses that are equally different from one another in orientation are not always plotted equally far apart in Euler space. This distortion causes a single joint's mobility to change when measured based on different joint coordinate systems and precludes fair comparison among joints. Here, we present two alternative spaces inspired by a 16th century map projection - cosine-corrected and sine-corrected Euler spaces - that allow coordinate-system-independent comparison of joint rotational mobility. When tested with data from a bird hip joint, cosine-corrected Euler space demonstrated a 10-fold reduction in variation among mobilities measured from three joint coordinate systems. This new quantitative framework enables previously intractable, comparative studies of articular function.
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