Measurement Method of Three-Dimensional Rotation Angle of Spherical Joint Based on Neural Network and Magnetic Effect

Conventional high precision spherical joints provide three degrees of freedom for rotation, but lack the capability to measure the rotation angle by themselves. This limitation restricts their use in some high-precision applications. However, by utilizing the non-linear magnetic field of permanent magnets in conjunction with magnetic sensors, measurement of rotation angle becomes achievable. Based on previous research, the measurement of three-dimensional rotation angle of spherical joint was investigated. Unlike the mathematical models and optimization algorithms, the artificial neural network model was adopted to achieve the measurement. The influences of different factors such as the type of neural network, sampling interval, data partition, and the quantity of sensor on the measurement accuracy were explored. Some empirical equations of measurement accuracy were summarized. The distributions of measurement accuracy of 3D rotation angles were quantitatively known. The combined ELM-RBF neural network model was proposed to realize real-time and high-precision 3D angle measurement. The optimal measurement accuracies of three-dimensional rotation angles α, β, and γ of the spherical joint with the sampling interval of 0.1°, eight sensors, data partition of γ rotation angle, and combined ELM-RBF neural network reach 0.01°. It can provide more guidance for further research.