基于机构条件数的30m望远镜三镜Stewart平台

从误差传递的角度研究了30 m望远镜（TMT）三镜大型Stewart平台的转动精度。首先，利用奇异值分析Stewart平台速度雅克比矩阵，得出机构条件数与支腿伸长量的关系。利用条件数与系统误差传递系数的关系推导出TMT三镜特殊运动形式下支腿伸长量误差与平台姿态误差的关系，并使用MATLAB优化平台结构参数得出一组优化解。然后，利用ADAMS对之前的理论推导进行仿真验证。最后，利用已知误差传递模型结合精度实验数据进行实验，辨识得出Stewart支腿伸长误差为均匀分布、动平台转动误差向量模为双峰分布。利用MATLAB进行模拟，模拟结果显示：假设支腿伸长误差为0到1之间均匀分布，动平台转动误差向量模的期望会由优化前的5.345 4×10^-4变为优化后的4.272 1×10^-4，优化量约为20%；转动误差分布的两个肩峰相互靠拢且向0点移动。

Third mirror Stewart platform of TMT based on mechanism condition number

The rotation accuracy of large Stewart platform of a three mirror system in a 30 m telescopy was explored based on the error transfer. Firstly, the singular value method was used to analyze the Stewart platform velocity Jacob matrix, and to obtain the relationship between mechanism condition number and leg elongation. Then, using condition number and system error transfer function, the relationship between the leg elongation error and the platform attitude error was discussed in TMT special kinematical forms, and a group of optimal solution was given out by the MATLAB optimization. After using the ADAMS to validate the theoretical derivation, the known error transfer model combined with precision experiment was used to identify the leg elongation error for evenly distribution and the mobile platform rotation error for bimodal distribution. The MATLAB simulation indicates when the leg elongation error is distributed from 0 to 1 evenly, the expectation of mobile platform rotation error vector norm has reduced from 5.345 4×10^-4 to 4.272 1×10^-4 with optimizing quantity by 20%. It concludes that the error distributions of the two shoulder peaks are close to each other and move to 0 point integratively.