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The laser multi-coordinate measuring system has the advantages of high precision and wide measuring range and has wide application prospects in the fields of large-scale high-precision coordinate measurement. The positional relationship between the measuring equipment and the measured point is the key factor affecting the accuracy of the system. To quantify the influence of the positional relationship between the measuring equipment and the measured point on the uncertainty of coordinate measurement, the partial derivative operation of the coordinate solving formula is obtained. The coordinate of the measuring point and the mathematical model for measuring the distance from the base station to the measured point. Firstly, the mathematical model is simulated. The results of the simulation experiment show that the nonlinearity of the measurement uncertainty of the system increases significantly when the measured target point is close to the measurement plane composed of multiple stations. Finally, the simulation results are verified by experiments. When the distance between the retroreflector and the measuring plane is reduced from 1010.7 mm to 509.6 mm, the measurement deviation increases by 4 times. When the distance continues to decrease to 10.9 mm, the measurement deviation increases to 76 times before. The results show that the mentioned error model can accurately describe the relationship between the position of the measured point and the error of the measurement accuracy, and can provide theoretical support for the layout optimization method of the laser multi-coordinate measuring system.
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