A new method of two-dimensional (2D) plane displacement measurement based on an eddy current sensor is proposed in this paper. A series of grooves with different widths and depths are graved on the linear displacement table to form 2D absolute coding using the idea of pseudorandom coding. The eddy current sensor array is arranged above the groove to identify the coding. An artificial neural network is used to establish a measurement model which is the mapping relationship between the output of the eddy current sensor array and the 2D displacement of the workbench. A feasibility experiment showed that in the range of 20 × 20 mm, the root mean square error of measurement in the X- and Y-directions are 83 and 73 μm, respectively. The new method integrates eddy current sensor and artificial neural network modeling to realize 2D displacement measurement, which provides a new solution for displacement and angle measurement.

A precision spherical joint is a type of spherical motion pair that can realize three degrees of rotation freedom. In this paper, a specific method is used to assess the uncertainty of our measurement system. The measurement system uses the codes and eddy current sensor to measure the angle. Different codes are engraved on the surface of the spherical joint. Eddy current sensors are embedded in the spherical socket to detect and recognize the spherical code. The uncertainty of the measurement system hardware and an artificial neural network are studied. Based on the Monte Carlo method, the uncertainty components are evaluated and combined, and the comprehensive uncertainty of the measurement system is obtained. The evaluation results of system measurement uncertainty are verified from specific angles. In the three-axis measurement uncertainty, the minimum is about 2′, and the maximum uncertainty is about 1°. The proposed method can be used to evaluate the uncertainty of other multiple-input multiple-output measurement systems.

To improve the measurement accuracy of three-dimensional rotation angle of the spherical joint, a novel approach is proposed in this study, which combines the magnetic detection by Hall sensor and surface feature identification by eddy current sensor. Firstly, a permanent magnet is embedded in the ball head of spherical joint, and Hall sensors are set and distributed in the ball socket to measure the variation of magnetic flux density when spherical joint rotating, which are related to 3D rotation angle. In order to further improve measurement accuracy and robustness, we also set grooves on the ball head and use eddy current sensors to synchronously identify the rotation angle of the ball head. After the combination of two signals is adopted, a measurement model is established using the RBF neural network by training, and realized real-time measurement of the 3D rotation angle of spherical joint. The feasibility and superiority of this method are validated through experiments. The experimental results indicated that the measurement accuracy is promoted substantially compared to the preliminary measurement scheme based on spherical coding, the average measurement error of single axis is reduced by 9'9". The root mean square errors for the measurement of 3D rotation angles in this proposed method are as follows: the pitch angle α has an error of 1'8", the yaw angle β has an error of 2'15", and the roll angle γ has an error of 29'6".

To improve the measurement accuracy of the three-dimensional rotation angle of a spherical joint, a novel approach is proposed in this study, which combines magnetic detection by a Hall sensor and surface feature identification by an eddy current sensor. Firstly, a permanent magnet is embedded in the ball head of a spherical joint, and Hall sensors are set and distributed in the ball socket to measure the variation in the magnetic flux density when the spherical joint rotates, which are related to the 3D rotation angle. In order to further improve the measurement accuracy and robustness, we also set grooves on the ball head and use eddy current sensors to synchronously identify the rotation angle of the ball head. After the combination of two signals is performed, a measurement model is established using the RBF neural network by training, and the real-time measurement of the 3D rotation angle of the spherical joint is realized. The feasibility and superiority of this method are validated through experiments. The experimental results indicate that the measurement accuracy is substantially promoted compared to the preliminary measurement scheme based on spherical coding; the average measurement error of the single axis is reduced by 9′9″. The root mean square errors for the measurements of the 3D rotation angles in this proposed method are as follows: pitch angle α has an error of 1′8″, yaw angle β has an error of 2′15″, and roll angle γ has an error of 29′6″.