  Background: Kinematics is studied by practitioners and researchers in
different fields of practice. It is therefore critically important to adhere to
a taxonomy that explicitly describes positions and movements. However, current
representation methods such as cardan and Euler angles fail to report shoulder
angles in a way that is easily and correctly interpreted by practitioners, and
that is free from numerical instability such as gimbal lock. Methods: In this
paper, we comprehensively describe the recent Tilt-and-Torsion method and
compare it to the Euler YXY method currently recommended by the International
Society of Biomechanics. While using the same three rotations (plane of
elevation, elevation, humeral rotation), the Tilt-and-Torsion method reports
humeral rotation independently from the plane of elevation. We assess how it
can be used to describe shoulder angles (1) in a simulated assessment of
humeral rotation with the arm at the side, which constitutes a gimbal lock
position, and (2) during an experimental functional task, with 10 wheelchair
basketball athletes who sprint in straight line using a sports wheelchair.
Findings: In the simulated gimbal lock experiment, the Tilt-and-Torsion method
provided both humeral elevation and rotation measurements, contrary to the
Euler YXY method. During the wheelchair sprints, humeral rotation ranged from
14{\deg} (externally) to 13{\deg} (internally), which is consistent with
typical maximal ranges of humeral rotation, compared to 65{\deg} to 50{\deg}
with the Euler YXY method. Interpretation: Based on our results, we recommend
that shoulder angles be expressed using Tilt-and-Torsion angles instead of
Euler YXY.
