Recent product components have been designed as a combination of complex forms for advanced functionality. Such high degree-of-freedom forms are shaped by various manufacturing processes. In the industrial supply chain, the deviation of a manufactured form from its designed form must be verified to ensure product quality. Three-dimensional (3D) measuring systems are typically used for verification. To validate the product manufacturing performance accurately, a measurement procedure that can derive the measurands of forms with small measurement uncertainty is necessitated. For simple geometries such as flats, spheres, and cylinders, precise measurement and uncertainty evaluation methods have been established; however, those for complex forms are still being developed. In this study, measurement uncertainty is assessed by measuring a calibrated gauge and comparing the measured with calibrated values. Several gauges configured with basic geometric elements have been proposed as a reference for complex form measurements, and some issues remain. Some of the gauges do not sufficiently simulate the forms of actual product components, whereas other gauges are difficult to calibrate with small uncertainties. Herein, we discuss a possible approach for solving these problems in the metrology of complex forms using 3D measuring systems. First, a new gauge concept is proposed. The gauge is designed by extracting the complex features of the actual product form and segmenting the gauge’s form into various circular arc curvatures. The geometric parameters are well calibrated, and the measurable angular range of the curvature is not limited. A representative gauge based on this concept is described. Next, a robust and small-uncertainty calibration method for complex-form objects is described. The area encompassing the target cross-section is measured, and an envelope is generated on the probe tip mechanical surface from the probe tip centers to determine the measured surface. Finally, the calibration and measurement uncertainty evaluation for the geometric parameters of the new gauge are quantitatively presented. It is verified that the proposed calibration procedure is applicable to freeform measurements, and that both simple and complex forms can be measured within a 1.5 μm uncertainty.

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