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针对并联机构的精度分析中已知误差源误差变化范围(误差空间)的情况,提出一种基于集合理论的分析方法。该方法以矢量集合的形式来表示误差空间,并定义出矢量集合的加法,根据这种矢量集合的加运算,由误差源的误差空间得到机构终端的误差空间,从而把传统的精度分析中由矢量到矢量的计算模式变为矢量集合到矢量集合的计算模式,很好地解决了误差空间的分析传递问题。该方法计算量小,形象直观,可深入反映并联机构误差传递的特点,为分析机构中公差、随机误差、铰链间隙等对终端精度的影响提供了新的工具。以S tew art平台的精度分析为实例进行了仿真实验,通过矢量集合的加运算确定出终端误差空间和误差极值。结果表明:与传统的分析方法相比,该方法结果更加准确,计算效率大大提高。
Aiming at the range of error source error (error space) in the accuracy analysis of parallel mechanism, an analysis method based on set theory is proposed. In this method, the error space is expressed in the form of a set of vectors, and the addition of a set of vectors is defined. Based on the addition of such a vector set, the error space of the terminal of the error source is obtained from the error space of the error source, Vector to vector calculation pattern into vector collection to vector collection of calculation patterns, a good solution to the error space analysis of transmission problems. The method has the advantages of small calculation amount and visual image, which can deeply reflect the characteristics of error transmission in parallel mechanism, and provides a new tool for analyzing the influence of tolerance, random error and hinge clearance on terminal precision. The precision analysis of S tew art platform was used as an example to simulate the experiment, and the terminal error space and error extreme value were determined by the addition of vector set. The results show that compared with the traditional method, the method is more accurate and the computational efficiency is greatly improved.