Interpreting the Tilt-and-Torsion Method to Express Shoulder Joint Kinematics

TL;DR

This paper advocates for using the Tilt-and-Torsion method over Euler angles to accurately and reliably describe shoulder joint kinematics, especially in positions prone to gimbal lock, demonstrated through simulations and athlete data.

Contribution

It provides a comprehensive explanation of the Tilt-and-Torsion method and compares it to Euler YXY, highlighting its advantages in reporting shoulder angles without numerical instability.

Findings

Tilt-and-Torsion reports shoulder angles accurately in gimbal lock positions.

In athlete sprints, Tilt-and-Torsion yields realistic humeral rotation ranges.

Euler YXY overestimates rotation ranges due to instability.

Abstract

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.