Data for: A coordinate-system-independent method for comparing joint rotational mobilities

Three-dimensional studies of range of motion currently plot joint poses in
an "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 comparisons 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 comparisons of joint rotational
mobilities. When tested with data from a bird hip joint, cosine-corrected
Euler space demonstrated a ten-fold reduction in variation among
mobilities measured from three joint coordinate systems. This new
quantitative framework enables previously intractable, comparative studies
of articular function.