This paper systematically summarized the technical state of art and research results on the motion error of a linear guideway, corrected some misconceptions, and further clarified the relationship between the straightness error of the guide rail itself and the motion error of the linear stage. Moreover, a new method based on parallel mechanism is provided to study the motion errors of the linear guide pair. The basic idea is to abstract the structural relationship between the stage and the guide rail into a 4-bar parallel mechanism. Thus, the stage can be considered as a moving platform in the parallel mechanism. Its motion error analysis is also transferred to moving platform position analysis in the parallel mechanism. The straightness motion error and angular motion error of the stage can be analyzed simultaneously by using the theory of parallel mechanism. Some experiments were conducted on the linear guideway of a self-developed parallel coordinate measuring machine. The experimental data and analysis verify the feasibility and correctness of this method.

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″.