Since the advent of X-ray Reconstruction of Moving Morphology, studies of joint range of motion (ROM) have become increasingly common in comparative biomechanics. These 3-D ROM studies have typically plotted poses measured from a joint coordinate system in “Euler space.” The axes of Euler space are angles measured in each of the joint’s three rotational degrees of freedom (for example, flexion-extension, abduction-abduction, and long-axis rotation). Researchers then virtually shrinkwrap the pose cloud with an alpha shape and compute its volume 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 — rather, they are plotted farther and farther apart as the magnitude of the second rotation approaches +/- 90 degrees. 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 our work on two alternative spaces, both inspired by a 16th century map projection: cosine-corrected and sine-corrected Euler spaces. Plotting 3-D joint poses in these spaces allows coordinate-system-independent comparisons of joint rotational mobilities. When tested with data from a Helmeted Guineafowl (Numida meleagris) hip joint, cosine-corrected Euler space demonstrated a ten-fold reduction in variation among mobilities measured from three different joint coordinate systems. This new quantitative framework enables previously intractable, comparative studies of articular function, and can also be applied to other research questions involving 3-D orientation.