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The rotation orientation and the angle of precision of an intelligent ball joint cannot be automatically obtained in passive motion. In this paper, a new method based on a Hall sensor with a permanent magnet (PM) is proposed to identify the spatial rotation orientation and angle. The basic idea is to embed a PM on a ball while the Hall sensors are arrayed into the ball socket. When the ball rotates, the Hall sensor array detects the variation of the magnetic induction intensity in space. By establishing a mathematical model between the variation of the magnetic induction intensity and the orientation and angle of rotation, the rotation angle in the space where the ball is located can be inversely solved. The establishment of the theoretical model is based on the theory of the equivalent magnetic charge method, which has a few native defects that cannot be overcome by itself. This paper presents the relationship between the magnetic induction intensity change and the rotation angle of the ball in space, which was constructed by an artificial neural network (ANN) and will simplify the mathematical model, shorten the operation time, and improve the efficiency of real-time detection. Based on the simulation analysis, the optimal matching scheme between the PM and the magnetic effect sensor was determined, and the structural parameters of the ball joint prototype were optimized. The data training and comparison test of the neural network model were completed on a self-developed calibration device. The experimental results show that for a ±20° measurement range, the average errors of the uniaxial measurements are 1′51″ and 1′55″ on the two axes, respectively. At present, the measurement accuracy of the prototype is still relatively low; however, this idea of modeling based on ANN removes the shackles of mathematical modeling, reminding us that we can consider the design of sensors or complete geometric measurement modeling from a new perspective.

Error averaging effect is one of the advantages of a parallel mechanism when individual errors are relatively large. However, further investigation is necessary to clarify the evidence with mathematical analysis and experiment. In the developed parallel coordinate measuring machine (PCMM), which is based on three pairs of prismatic-universal-universal joints (3-PUU), error averaging mechanism was investigated and is analyzed in this report. Firstly, the error transfer coefficients of various errors in the PCMM were studied based on the established error transfer model. It can be shown how the various original errors in the parallel mechanism are averaged and reduced. Secondly, experimental measurements were carried out, including angular errors and straightness errors of three moving sliders. Lastly, solving the inverse kinematics by numerical method of iteration, it can be seen that the final measuring errors of the moving platform of PCMM can be reduced by the error averaging effect in comparison with the attributed geometric errors of three moving slides. This study reveals the significance of the error averaging effect for a PCMM.