A motion-decomposition approach to address gimbal lock in the 3-cylinder open chain mechanism description of a joint coordinate system at the glenohumeral joint

Abstract

In this study, the standard-sequence properties of a joint coordinate system were implemented for the glenohumeral joint by the use of a set of instantaneous geometrical planes. These are: a plane that is bound by the humeral long axis and an orthogonal axis that is the cross product of the scapular anterior axis and this long axis, and a plane that is bounded by the long axis of the humerus and the cross product of the scapular lateral axis and this long axis. The relevant axes are updated after every decomposition of a motion component of a humeral position. Flexion, abduction and rotation are then implemented upon three of these axes and are applied in a step-wise uncoupling of an acquired humeral motion to extract the joint coordinate system angles. This technique was numerically applied to physiological kinematics data from the literature to convert them to the joint coordinate system and to visually reconstruct the motion on a set of glenohumeral bones for validation.