Faber M J, Schamhardt H C, van Weeren P R
Department of Equine Sciences, Faculty of Veterinary Medicine, Utrecht, University, Netherlands.
J Biomech. 1999 Dec;32(12):1355-8. doi: 10.1016/s0021-9290(99)00131-1.
In this paper a method is presented to calculate Euler's angles of rotation of a body segment during locomotion without a priori defining the location of the center of rotation, and without defining a local vertebral coordinate system. The method was applied to in vivo spinal kinematics. In this method, the orientation of each segment is identified by a set of three markers. The orientation of the axes of rotation is calculated based on the average position of the markers during one stride cycle. Some restrictions and assumptions should be made. The approach is viable only when the average orientation of the anatomical axes of rotation of each spinal segment during a stride cycle coincides with the three axes of the laboratory coordinate system. Furthermore, the rotations should be symmetrical with respect to both sides of the plane of symmetry of the spinal segment, and the subject should move parallel to one axis of the laboratory coordinate system. Since in experimental conditions these assumptions will only be met approximately, errors will be introduced in the calculated angles of rotation. The magnitude of the introduced errors was investigated in a computer simulation experiment. Since the maximal errors did not exceed 0.7 degrees in a range of misalignments up to 10 degrees between the two coordinate systems, the approach proved to be a valid method for the estimation of spinal kinematics.
本文提出了一种计算身体节段在运动过程中欧拉旋转角的方法，无需事先定义旋转中心的位置，也无需定义局部椎体坐标系。该方法应用于活体脊柱运动学。在这种方法中，每个节段的方向由一组三个标记点确定。旋转轴的方向基于一个步幅周期内标记点的平均位置来计算。需要做出一些限制和假设。仅当每个脊柱节段在一个步幅周期内解剖学旋转轴的平均方向与实验室坐标系的三个轴重合时，该方法才可行。此外，旋转应相对于脊柱节段对称平面的两侧对称，并且受试者应平行于实验室坐标系的一个轴移动。由于在实验条件下这些假设只能近似满足，因此在计算的旋转角度中会引入误差。在计算机模拟实验中研究了引入误差的大小。由于在两个坐标系之间高达10度的错位范围内，最大误差不超过0.7度，因此该方法被证明是一种估计脊柱运动学的有效方法。
