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

This paper describes a new method of determining the axial rotation angle o f a limb segment during three-dimensional movement. Instead of describing t he 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 lon g axis of the limb segment about a specific axis passing through the proxim al 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 det ailed derivation of some important equations (Appendices), comparison with Euler/Cardan angles and a simple experimental demonstration are given in th is paper. A method of solving the gimbal-lock problem when using this metho d is also proposed. (C) 2000 Elsevier Science Ltd. All rights reserved.