Some Linear Models for Estimating the Motion of Rigid Bodies with Applications to Geometric Quality Assurance
本文研究用坐标测量机采样点与计算机模型匹配来评估零件几何质量的方法，当零件表面由平面区域构成时，将估计旋转和平移向量转化为线性模型，并识别残差平方和的三个分量以检验几何缺陷。
Abstract Abstract A geometrical method to assess the quality of a part is to sample points on the surface of the part and to bring an ideal computer representation of the part as close as possible to the sampled locations. The points are sampled with a coordinate measuring machine (CMM) that gives the coordinates, with respect to the machine's own three-dimensional system of axis, of the sampled locations. Computer-assisted design (CAD) gives the ideal representation of the part. The matching involves estimating a rotation and a translation vector characterizing the rigid body transformation needed to go from the computer model to the sampled locations. The sum of the squared residual distances between the sampled locations and the fitted computer part is a measure of the quality of the part. This article investigates the statistical properties of this method when the surface of the part is made of planar regions. Estimating the translation vector and the rotation matrix is shown to be "locally" equivalent to fitting a linear model to the localization data. Three components of the residual sum of squared distances are identified. They measure within planar region variability, the orientation conformity of the planar regions, and the size discrepancies of the regions. Diagnostics for linear models are adapted to yield statistical tests for specific geometric failures of a part. The developments use first-order asymptotic expansions of the estimators and of the sum of squared residuals for the local linear model, as the errors associated with the sampled locations go to 0. Key Words: Computer-assisted designCoordinate measuring machineDirectional dataRegression diagnosticsRotationsSpherical regression.