Interpreting the tilt-and-torsion method to express shoulder joint kinematics

  • Félix Chénier
    Corresponding author at: Department of Physical Activity Science, UQAM, Biological Sciences Building, Office SB-4455, Université du Québec à Montréal, P.O. Box 8888, Station Centreville, Montreal, Quebec H3C 3P8, Canada.
    Mobility and Adaptive Sports Research Lab, Department of Physical Activity Sciences, Faculty of Sciences, Université du Québec à Montréal, Montreal, Canada

    Centre for Interdisciplinary Research in Rehabilitation of Greater Montreal (CRIR), Montreal, Canada
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  • Ilona Alberca
    Université de Toulon, Impact de l'Activité Physique sur la Santé (UR IAPS n°201723207F), Campus de La Garde, CS60584, F-83041 Toulon, France
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  • Arnaud Faupin
    Université de Toulon, Impact de l'Activité Physique sur la Santé (UR IAPS n°201723207F), Campus de La Garde, CS60584, F-83041 Toulon, France
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  • Dany H. Gagnon
    Centre for Interdisciplinary Research in Rehabilitation of Greater Montreal (CRIR), Montreal, Canada

    School of Rehabilitation, Faculty of Medicine, Université de Montréal, Montreal, Canada
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      • The ISB advises reporting shoulder orientation using an Euler YXY angle sequence.
      • Euler YXY has a humeral rotation bias and fails in non-elevated shoulder.
      • The Tilt-and-Torsion method is simpler to understand and may solve these problems.
      • We confirm that Tilt-and-Torsion angles are coherent in sports wheelchair propulsion.
      • We confirm that Tilt-and-Torsion correctly reports rotation in gimbal lock position.



      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.


      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.


      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° (externally) to 13° (internally), which is consistent with typical maximal ranges of humeral rotation, compared to 65° to 50° with the Euler YXY method.


      Based on our results, we recommend that shoulder angles be expressed using Tilt-and-Torsion angles instead of Euler YXY.


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