New Mathematical Definition and Calculation of Axial Rotation of Anatomical Joints

[+] Author and Article Information
Shinji Miyazaki, Akimasa Ishida

Institute for Medical and Dental Engineering, Tokyo Medical and Dental University, Tokyo, 101 Japan

J Biomech Eng 113(3), 270-275 (Aug 01, 1991) (6 pages) doi:10.1115/1.2894884 History: Received June 01, 1990; Revised January 15, 1991; Online March 17, 2008


In the field of joint kinematics, clinical terms such as internal-external, or medical-lateral, rotations are commonly used to express the rotation of a body segment about its own long axis. However, these terms are not defined in a strict mathematical sense. In this paper, a new mathematical definition of axial rotation is proposed and methods to calculate it from the measured Euler angles are given. The definition is based on the integration of the component of the angular velocity vector projected onto the long axis of the body segment. First, the absolute axial rotation of a body segment with respect to the stationary coordinate system is defined. This definition is then generalized to give the relative axial rotation of one body segment with respect to the other body segment where the two segments are moving in the three-dimensional space. The well-known Codman’s paradox is cited as an example to make clear the difference between the definition so far proposed by other researchers and the new one.

Copyright © 1991 by The American Society of Mechanical Engineers
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