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Abstract:With the development of the modern manufacturing industry, the free-form surface is widely used in various fields, and the automatic detection of a free-form surface is an important function of future intelligent three-coordinate measuring machines (CMMs). To improve the intelligence of CMMs, a new visual system is designed based on the characteristics of CMMs. A unified model of the free-form surface is proposed based on T-splines. A discretization method of the T-spline surface formula model is proposed. Under this discretization, the position and orientation of the workpiece would be recognized by point cloud registration. A high accuracy evaluation method is proposed between the measured point cloud and the T-spline surface formula. The experimental results demonstrate that the proposed method has the potential to realize the automatic detection of different free-form surfaces and improve the intelligence of CMMs.

This paper aims at decreasing the assembly difficulty and reducing the cost of optical systems using multiple components. A strategy is proposed to substitute one freeform surface for multi-separated surfaces. A freeform-objective Chernin multipass cell is implemented as a typical instance for assembly simplification. The application of a freeform surface helps in decreasing the degree of objective assembly tolerances from 24 to 4, by representing the original four objectives with a linear combination of a 2D Gaussian radial basis function, which is analytical, global C smooth, and locally influencing. The simulation result verifies the feasibility and performance of the designed freeform-objective Chernin multipass cell, whose base length is 0.2 m, volume is less than 0.8 L, and adjustable optical length is 0.4-34 m. Results prove that by using a proper approach to approximate the original surfaces as an integrated freeform, one can simultaneously reduce the assembly cost and the assembly difficulty.

Stylus profilometry is one of the most significant technologies to measure freeform surfaces. However, the lateral force on a stylus usually leads to invalid measurements, especially for surfaces with a large curvature, due to the structure of the cantilever. Thus, we propose a novel radial scanform measurement for such surfaces, with an aim to reduce measurement errors. The precise 3D form of the workpiece was obtained using a series of profiles measured individually along the radial direction via a rotary mechanism. The lateral slope and force on the stylus for every profile are therefore much lower than those measured by traditional raster scan form measurements. We also propose a stable and accurate two-step registration procedure to evaluate the freeform surface form error; this eliminates the need to calibrate the spindle of both the workpiece and the rotary mechanism. A freeform surface with a 30 mm diameter aperture and 24 mm curvature radius was measured on a Form Taylorsurf PGI 1250A profilometer. Compared to traditional raster scan 3D form measurements, the peak-to-valley and root mean squared values of the form error decrease from 409.415 µm and 67.490 µm to 4.967 µm and 0.658 µm, respectively, via the proposed method. Results show that our method solves the problems of measuring surfaces with a large curvature.

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