Simplified representation of 3D angular position with least singularity for an anatomical movement

In this study, a novel method is proposed to represent the three dimensional angular position of the body segment in space with least singularity adopting the new definition of the axial rotation. Firstly, the orientation of the axis of the body segment is defined by the geographical coordinate system (ISO 31-11). Secondly, the axial rotation of the body segment is defined by the rotation offset from the geodesic movement of the body segment from the zero position. To minimize the possibility of the singularity, the posture in the womb is preferred as the zero position of the human body in contrast to the clinical definition of the standing posture. In addition, the North Pole is defined along the z-axis to match to the clinical definition. However, it would be better if the Pole be taken along the y-axis to avoid the singularity at the Pole. In this way of defining the three dimensional position of the human body, we can reduce singularities in an anatomical movement. Also, the angular position becomes vector additive as the representation of the position is path independent by the introduction of the new axial rotation definition.