中文摘要：

针对光电子封装中超精密平台运动控制困难，末端坐标系与各轴运动关系复杂等问题，对串联机构的几何结构以及单自由度运动轴与末端姿态变换的关系进行研究。其步骤是：首先，基于串联机构的D—H方程，分析运动轴与其位姿的坐标变换并建立各运动轴和末端阵列光纤的位姿运动方程；然后，以末端点为原点，由位姿运动方程导出保持末端点不动的轴运动约束方程；最后，由约束方程导出旋转轴运动条件下移动轴的运动补偿方程。研究结果表明：在微小行程下，通过旋转轴行程的均匀细分和移动轴的运动补偿，末端原点的运动范围大大减少，减少的比例与细分系数近似呈正比。

英文摘要：

Based on the fact that there are many difficulties to control the movement of ultraprecise platform used widely in optoelectronic packaging and to analyze the complex relationship between the end coordinate and those motion axis, the geometry of the serial mechanism and the relationships between single-DOF motion axis and the attitude and position of the end coordinate were studied. The main procedures were as follows. At first, based on the D-H equation applied in serial mechanism, coordinate transformation that revealed relations of axis of motion on its position and attitude was analyzed, the equation of motion that connected the movement axis and the position and orientation of the fiber array was established. Then, axis motion constraint equation was derived from that motion equation regarding the terminal spot as the zero point. At last, the movement compensation equation of translation axis was obtained from the eonstraint equation under the condition that only rotation axis was activated. The results show that the space range of the origin spot movement is significantly reduced and the proportion of the reducing is approximate to the subdivision, by subdividing the travel of rotational axis uniformly and eompensating to adjust the translation axis travel accordingly.