###### Abstract  
Measuring instruments are intended to be intelligent, precise, multi-functional and developing multidirectionally, scientific, and reasonable; the reliable evaluation of measurement uncertainty of precision instruments is also becoming more and more difficult, and the evaluation of the Coordinate Measuring Machines (CMM) measurement uncertainty is among the typical problems. Based on Geometric Product Specification (GPS), this paper has systematically studied the CMM uncertainty for evaluating the size and geometrical errors oriented toward measurement tasks, and thus has realized the rapid and reliable evaluation of the CMM uncertainty for task-oriented measurement. For overestimation of the CMM uncertainty for task-oriented measurements in the initial evaluation, a systematic optimization solution has been proposed. Finally, the feasibility and validity of the evaluation model and the optimization method have been verified by three different types of measurement examples of diameter, flatness and perpendicularity. It is typical and representative to systematically solve the problem of the CMM uncertainty for evaluating the measurement tasks targeted at dimensions and geometric errors, and the research contents can be effectively applied to solve the uncertainty evaluation problems of other precision instruments, which are of great practical significance not only for promoting the combination of modern uncertainty theory and practical applications but also for improving the application values of precision measurement instruments. measurement uncertainty; coordinate measuring machines; evaluation and optimization; geometrical product specifications +
Footnote †: journal: Applied Soft  
cannot be expressed and transmitted digitally, which has been for a long time a difficult technical bottleneck overcome in the field of mechanical manufacturing. In essence, the presence of CMM has solved the problem that geometric measurement cannot be digitalized [3,4]. Coordinate measurement technology is the most common and fundamental measurement technology in the field of modern machinery manufacturing, especially in aerospace, automobile manufacturing, mold processing, and other industries. At present, the whole life cycle of the product development, design, processing, measurement, acceptance, use, maintenance, scrapping and so on must follow the GPS standard system in the field of manufacturing. This standard system covers many aspects such as product size, geometric form and surface appearance. The GPS can effectively eliminate some technical barriers in international trade, boasting an important role in promoting the integration of the global economy as an important technical base for modern manufacturing informatization and quality management. The new generation of the GPS system has overcome the problem of digital representation and transmission of geometric quantities. The traditional measurement mainly relies on optical vernier technology, in which the role of the computer is limited. The development of the CAD technology and the presence of CMM has essentially solved the problem that geometric quantities cannot be expressed and transmitted digitally, which makes it possible to initialize a new generation of the GPS system based on measuring mathematical theory. As a measuring instrument for geometric characteristics of products, CMM plays its role under the guidance of the GPS, boasting important measuring equipment essential to quality control in modern enterprises [5,6]. As an important parameter to characterize the quality of the measurement results, measurement uncertainty reflects the credibility of measurement results. To give scientific and proper evaluation of measurement uncertainty is an important factor to guarantee the development of modern measuring science [7,8]. CMM can complete the measurement of spatial geometric elements (including size, geometrical error parameters) more conveniently, featuring a large measurement range, high measurement efficiency and strong measurement versatility.