The accuracy of traditional measuring machines is affected by the measuring range and sensitive geometric errors, and it is not possible to combine large caliber and high-precision measurements. This study proposes a differential geometric error-weighting method for designing a high-precision, large-diameter measuring machine. The machine utilized a zero-Abbe arm structure and applied the rigid body theory and small-angle hypothesis to model geometric errors. Weights were calculated for 23 geometric errors, identifying eight sensitive ones. A picometer-precision laser interferometer (quDIS) with a theoretical positioning accuracy of 0.2 nm/mm and standard flat rulers are used to ensure highly accurate positioning of the Y-axis/Z-axis of the measuring platform and reduce the straightness of both axes by approximately 75%, with radial and axial runout of the rotary table under 100 nm. The development and design method of the high-precision measuring machine proposed in this study is applicable to large-diameter high-precision flexible measurement, and the accurate control of measuring machine movement accuracy is realized by calculating the geometric error weights.

Magnetorheological finishing is widely used in the high-precision processing of optical components, but due to the influence of multi-source system errors, the convergence of single-pass magnetorheological finishing (MRF) is limited. Although iterative processing can improve the surface accuracy, repeated tool paths tend to deteriorate mid-spatial frequency textures, and for complex surfaces such as aspheres, traditional manual alignment is time-consuming and lacks repeatability, significantly restricting the processing efficiency. To address these issues, firstly, this study systematically analyzes the effect of six-degree-of-freedom positioning errors on convergence behavior, establishes a positioning error-normal contour error transmission model, and obtains a workpiece positioning error tolerance threshold that ensures that the relative convergence ratio is not less than 80%. Further, based on these thresholds, a hybrid self-positioning method combining machine vision and a probing module is proposed. A composite data acquisition method using both a camera and probe is designed, and a stepwise global optimization model is constructed by integrating a synchronous iterative localization algorithm with the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The experimental results show that, compared with the traditional alignment, the proposed method improves the convergence ratio of flat workpieces by 41.9% and reduces the alignment time by 66.7%. For the curved workpiece, the convergence ratio is improved by 25.7%, with an 80% reduction in the alignment time. The proposed method offers both theoretical and practical support for high-precision, high-efficiency MRF and intelligent optical manufacturing.