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To measure a short arc is a notoriously difficult problem. In this study, the bidirectional prediction method based on the Radial Basis Function Neural Network (RBFNN) to the observed data distributed along a short arc is proposed to increase the corresponding arc length, and thus improve its fitting accuracy. Firstly, the rationality of regarding observed data as a time series is discussed in accordance with the definition of a time series. Secondly, the RBFNN is constructed to predict the observed data where the interpolation method is used for enlarging the size of training examples in order to improve the learning accuracy of the RBFNN's parameters. Finally, in the numerical simulation section, we focus on simulating how the size of the training sample and noise level influence the learning error and prediction error of the built RBFNN. Typically, the observed data coming from a °5 short arc are used to evaluate the performance of the Hyper method known as the 'unbiased fitting method of circle' with a different noise level before and after prediction. A number of simulation experiments reveal that the fitting stability and accuracy of the Hyper method after prediction are far superior to the ones before prediction.

A novel non-contact, five-axis measuring machine with high measurement accuracy of workpiece dimensions is introduced in this paper. The kinematic model, as well as the kinematic error model, is developed. A self-calibration method using a steel ball is proposed to improve the measurement accuracy in the workspace. The calibration process is low-budget and easy-to-operate due to the fact there is no need to rely on other instruments or devices except for the laser probe carried by the measuring machine itself. The objective function is defined in terms of center-to-center distance deviation, namely the theoretical ball center and tested ball center, and to improve the speed of the convergence rate and to increase the optimization accuracy of the genetic algorithm. The simulation and practical experiments both illustrate the feasibility and validity of the proposed kinematic model and self-calibration method. Finally, the actual measurement results of a Φ12 sphere illustrate that the measurement accuracy of this machine has improved greatly by using calibrated parameters against nominal parameters.

Aiming at the disadvantages of present methods for detecting machine geometrical precision, the multistation and time-sharing measurement method is used to detect the machine precision in the research. Laser tracker measures the same trajectory of the machine at different base stations successively. Then the coordinates of different measuring points in the machine motion process can be calibrated by a large amount of measured data. Only displacement is involved in the measurement process, and the method does not measure angle, therefore it has very high measurement accuracy. In the end, the 21 terms machine errors can be separated by a large number of measuring point coordinates. The method has high measurement accuracy and low cost, so it is particularly suitable for high grade NC machine in the geometric precision detection. Keywords-multistation and time-sharing measurement laser trackergeometric precision redundant equations error separation.

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