Globographic visualisation of three dimensional joint angles

Three different methods for describing three dimensional joint angles are commonly used in biomechanics. The joint coordinate system and Cardan/Euler angles are conceptually quite different but are known to represent the same underlying mathematics. More recently the globographic method has been suggested as an alternative and this has proved particularly attractive for the shoulder joint. All three methods can be implemented in a number of ways leading to a choice of angle definitions. Very recently Rab has demonstrated that the globographic method is equivalent to one implementation of the joint coordinate system. This paper presents a rigorous analysis of the three different methods and proves their mathematical equivalence. The well known sequence dependence of Cardan/Euler is presented as equivalent to configuration dependence of the joint coordinate system and orientation dependence of globographic angles. The precise definition of different angle sets can be easily visualised using the globographic method using analogues of longitude, latitude and surface bearings with which most users will already be familiar. The method implicitly requires one axis of the moving segment to be identified as its principal axis and this can be extremely useful in helping define the most appropriate angle set to describe the orientation of any particular joint. Using this technique different angle sets are considered to be most appropriate for different joints and examples of this for the hip, knee, ankle, pelvis and axial skeleton are outlined.