平面轨迹机构运动误差的统计矩分析

Analyzing Statistical Moments of Motion Errors for Planar Path Linkage

轨迹型机构的运动综合误差具有强非线性,采用泰勒级数线性化处理难以高精度求解其均值与方差。为此,提出采用变量降维算法对轨迹机构的运动综合误差进行概率建模。以平面四杆轨迹机构为例,考虑机构构件尺寸的随机性,基于运动学分析提出机构的运动综合误差模型,采用双变量降维方法将机构运动误差函数近似为系列双变量函数与单变量函数之和,并应用GaussHermite积分公式对误差函数进行矩估计,由此导出机构运动综合误差的均值和方差。该方法处理实现了计算效率与精度的综合平衡。最后给出数值算例对所提方法的有效性进行验证。

Since the composite error of the motion of path generating mechanisms is multi-dimensional and strongly nonlinear, it is difficult to obtain the highly accurate mean and variance of the composite error with the Taylor series expansion. Therefore, this paper uses the dimensional reduction method to build the probabilistic model of the motion error. As an example, it presents a four-bar planar path linkage with random number of dimensions and establishes a model of the composite motion error based on kinematic analysis. With the bivariate dimension reduction method, the motion error is approximated by the sum of univariate and bivariate functions of dimensional variables. The Gauss- Hermite Quadrature rule is applied to evaluate the statistical moments of the motion error, and then its mean and standard deviation functions are derived. This application achieves an optimal balance between accuracy and efficiency. Finally, a numerical example is given to demonstrate the effectiveness of the bivariate dimensional reduction method.