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The position error of two parallel surfaces is generally constrained by parallelism. However, as a range of change, it cannot represent the positional relation between two parallel surfaces. Large-scale equipment such as machine tools are complex and difficult to move. It is also an engineering problem to perform field measurements on it. To this end, a method of describing the positional relation between two horizontal parallel surfaces and two vertical parallel surfaces on-site is proposed in this paper, which is a novel kind of position error, enriching the form of parallel surface position error, and solves the inconvenience problem of large equipment position error measurement. The measurement mechanisms are designed, and the measurement principle is given. Firstly, the combined projection waveform of the measured surface can be obtained by the geometric relationship between the measurement mechanism and the measured surface. Secondly, an algorithm is studied to process the obtained waveform, and the combined projection curve of the measured surface is acquired. Then, under the condition of considering the shape contours of the two surfaces, an algorithm is developed to acquire the calculated shape contour of the measured surface. According to the difference between the calculated surface shape contour and the known shape contour of the measured surface, the positional relation of the two surfaces can be determined. Meanwhile, the mathematical models of algorithms are established, and the measurement experiments are carried out, and the algorithms are verified by the mutual measurement method of the two surfaces. The results show that this method can accurately obtain the positional relation of two horizontal parallel surfaces and two vertical parallel surfaces.

A Method of On-Site Describing the Positional Relation between Two Horizontal Parallel Surfaces and Two Vertical Parallel Surfaces