Woltring H J
University of Nijmegen, The Netherlands.
J Biomech. 1994 Dec;27(12):1399-414. doi: 10.1016/0021-9290(94)90191-0.
In view of the singularities, asymmetries and other adverse properties of existing, three-dimensional definitions for joint and segment angles, the present paper proposes a new convention for unambiguous and easily interpretable, 3-D joint angles, based on the concept of the attitude 'vector' as derived from Euler's theorem. The suggested standard can be easily explained to non-mathematically trained clinicians, is readily implemented in software, and can be simply related to classical Cardanic/Eulerian angles. For 'planar' rotations about a coordinate system's axes, the proposed convention coincides with the Cardanic convention. The attitude vector dispenses with the 'gimbal-lock' and non-orthogonality disadvantages of Cardanic/Eulerian conventions; therefore, its components have better metrical properties, and they are less sensitive to measurement errors and to coordinate system uncertainties than Cardanic/Eulerian angles. A sensitivity analysis and a physical interpretation of the proposed standard are given, and some experimental results that demonstrate its advantages.
鉴于现有关节和节段角度的三维定义存在奇异性、不对称性及其他不良特性，本文基于由欧拉定理推导得出的姿态“向量”概念，提出了一种用于明确且易于解释的三维关节角度的新约定。所建议的标准可以很容易地向未经过数学训练的临床医生解释，易于在软件中实现，并且可以简单地与经典的卡丹/欧拉角相关联。对于围绕坐标系轴的“平面”旋转，所提出的约定与卡丹约定一致。姿态向量消除了卡丹/欧拉约定的“万向节锁”和非正交性缺点；因此，其分量具有更好的度量特性，并且它们对测量误差和坐标系不确定性的敏感度低于卡丹/欧拉角。给出了对所提出标准的敏感性分析和物理解释，并给出了一些证明其优势的实验结果。
