This contribution mathematically formalizes Codman's idea of conjunct rotation, a term he used in 1934 to describe a paradoxical phenomenon arising from a closed-loop arm movement. Real (axial) rotation is distinguished from conjunct rotation. For characterizing the latter, the idea of reference vector fields is developed to define the neutral axial position of the humerus for any given orientation of its long axis. This concept largely avoids typical coordinate singularities arising from decomposition of 3D joint motion and therefore can be used for postural (axial) assessment of the shoulder joint both clinically and in sports science in almost the complete accessible range of motion. The concept, even though algebraic rather complex, might help to get an easier and more intuitive understanding of axial rotation of the shoulder in complex movements present in daily life and in sports.