多环闭链机构偏差传递分析及几何精度建模

Deviation Propagation Analysis and Accuracy Modeling for Multi-closed-loop Mechanism

要实现对多环闭链机构的精度预测和反演设计,建立其几何精度模型至关重要。由于存在闭环耦合、结构复杂等不利因素,多环闭链机构精度建模相比开链机构更加困难。为了解决上述问题,提出一种适应于任意多环闭链机构的几何精度建模方法。首先对多环闭链机构中的误差源进行分析和建模,利用提出的两个新概念——独立环和耦合环来描述机构中存在的所有闭环类型。然后通过首次定义的新算子——低层环算子和新序列——低层环序列来表征多环闭链机构中的环与环邻接关系,并以此获得多环闭链机构误差传递规律。在此基础上,利用多环闭链几何位置方程建立精度计算模型,并基于该精度模型和误差源概率分布函数实现多环闭链误差空间分析。最后以平面SAR天线可展支撑机构作为算例,验证了上述方法和理论的有效性。

Establishing geometric accuracy model is essential to conduct the accuracy prediction and inverse design of multi-closed-loop mechanism. Compared with the open-loop mechanism, accuracy modeling for multi-closed-loop mechanism is much more difficult due to the existence of negative factors like coupling and complex structure. In order to solve the above problems, a novel method of accuracy modeling is developed. First of all, the error sources are analyzed and modeled, and then two new concepts of independent loop and coupled loop are proposed to describe the loop types involved in multi-closed-loop mechanisms. Then, the relationship between loops is illustrated by the new low-layer-loop operator and sequence. Additionally, the deviation propagation principle is obtained according to the relationship. Based on the deviation propagation principle, the geometric accuracy model is built by the positional equation of the multi-closed-loop mechanism and the error space is calculated accordingly by combining the above model with the probability distribution of error sources. Eventually, the method is verified by the extendible support structure of planar SAR antenna.