Miyazaki S, Ishida A
Institute for Medical and Dental Engineering, Tokyo Medical and Dental University, Japan.
J Biomech Eng. 1991 Aug;113(3):270-5. doi: 10.1115/1.2894884.
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 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.
在关节运动学领域，诸如内-外旋转或医学-外侧旋转等临床术语通常用于表示身体节段绕其自身长轴的旋转。然而，这些术语在严格的数学意义上并未得到定义。本文提出了轴向旋转的新数学定义，并给出了根据测量的欧拉角计算轴向旋转的方法。给出了根据测量的欧拉角计算轴向旋转的定义和方法。该定义基于角速度矢量投影到身体节段长轴上的分量的积分。首先，定义了身体节段相对于静止坐标系的绝对轴向旋转。然后将该定义推广，以给出一个身体节段相对于另一个在三维空间中运动的身体节段的相对轴向旋转。引用了著名的科德曼悖论作为例子，以阐明其他研究人员迄今提出的定义与新定义之间的差异。
