本文提出了一种机构指向误差计算方法。首先, 采用反射镜单位法向量和光束单位方向向量分别表示机构反射镜的姿态和激光束的传播方向, 接着采用坐标变换和矩阵传递求出反射镜在总体坐标系中的单位法向量, 通过向量对称计算出激光束经过两次镜面反射后的方向向量, 最后将机构各参数的理论值和实际值代入上述算法, 分别求出激光束经过两次镜面反射后的理论方向向量和实际方向向量, 两向量夹角即为机构的指向误差。在得到指向误差和部件误差的关系式后, 机构设计时即可通过机构指向误差反计算求出部件的误差值。结果表明: 机构物理样机测试指向误差值为0005 7°, 将机构部件参数测试误差值代入误差正计算算式, 得出机构的指向误差值为0006 1°, 以该指向误差通过反计算得出的参数平均误差值为0002 25°, 与测试结果相近, 可以为机构的精度设计提供参考依据。

A method of assembly error calculation is proposed in this paper. First, the posture of the mirrors and the direction of the laser beam are represented by using unit normal vector and unit direction vector. Then, using the coordinate transformation and the transfer matrix, the unit normal vector of the mirrors is obtained in the global coordinate system. The beam direction vector after twice specular reflection by the vector symmetry is calculated. Finally, taking the theoretical value and the actual value of the parameters of the assembly into the algorithm, the theoretical and actual direction vector of the laser beam reflected twice from the mirror are obtained. The intersection angle between two vectors is the pointing error of the assembly. After getting the relationship of the global pointing error and the part error, the average part error can be obtained by the pointing error back calculation. The testing pointing error of the prototype is 0005 7°, and the value of assembly pointing error which is obtained by taking the part testing error into the algorithm is 0006 1°. With this value, the average parts error is 0002 25° by back calculation. The calculation data is closed to the result of testing, and it can provide a reference for the accuracy design of the periscope pointing assembly.