基于集合理论的并联机构精度分析方法

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。

Accuracy analysis of parallel mechanisms based on set theory

A set theory based method was developed to analyze parallel mechanism motion accuracies with a known error space represented by a vector set.The end error space results from the addition of the vector sets of error source error spaces.The method changes the traditional vector-to-vector mode to a set-to-set mode for accuracy analyses to efficiently solve error space transfer problems.The method saves time and easily identifies the characteristics of the error transfer in parallel mechanisms.The method also provides a tool for analyzing the effects of tolerances,random errors,and joint clearances on the end precision.Simulations with a Stewart platform show that the method is more accurate and efficient than conventional methods with the end error space and the error extremes determined using additive operations of vector sets.