Determination of axial rotation angles of limb segments — a new method

This paper describes a new method of determining the axial rotation angle of a limb segment during three-dimensional movement. Instead of describing the three-dimensional rotation by a three-step rotation (Euler/Cardan angles), a one-step rotation (instantaneous screw axis), or a non-step rotation (floating axis method), the new method uses a two-step rotation to describe the three-dimensional rotation of the limb segment: the rotation of the long axis of the limb segment about a specific axis passing through the proximal joint centre and perpendicular to the long axis of the limb segment, and the axial rotation about the long axis. A short review of previous methods followed by a full description of the principle of the new method with detailed derivation of some important equations (Appendices), comparison with Euler/Cardan angles and a simple experimental demonstration are given in this paper. A method of solving the gimbal-lock problem when using this method is also proposed.