关于刚体位移矩阵

本文比较深入地探讨了机构分析与综合中应用广泛的刚体位移矩阵。从刚体运动分解的基本概念出发．阐明了它的由来，明确指出该矩阵中所有元素之值与刚体位移的确定关系，与所取刚体上参考点的位置无关；证明了其末列列向量恒等于刚体上初始位置与坐标原点重合之点的位移向量。据此．进一步阐明了刚体位移矩阵与螺旋矩阵的同一性及其与坐标变换矩阵的关系。文末有一数字实例说明应用刚体位移矩阵计算刚体空间位移的螺旋运动参数。

On the Rigid Body Displacement Matrix

The rigid body displacement matrix, which has been widely applied to analysis and synthesis of mechanisms, is thoroughly studied in this paper. Based on the basic concept of resolution of the general displacement of a rigid body, the rigid body displacement matrix is concisely derived and it is proved that the values of all the elements of the matrix depend only on the rigid body displacement, regardless of the chosen reference point in the rigid body, and the last column vector in the matrix always represents the displacement vector of the point in the rigid body which is originally coincident with the origin of the reference frame. The identity of the rigid body displacement matrix and the screw matrix, and the relationship between the displacement matrix and the coordinate transformation matrix are expounded as well. A num- erical example is provided at the end of the paper to demonstrate the application.