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Spherical joints have attracted increasing interest in the engineering applications of machine tools, industrial robots, medical equipment, and so on. As one of the promising methods of detecting the micro-clearance in spherical joints, the measurement accuracy of a spherical capacitive sensor could be affected by imperfectness during the manufacturing and installation of the sensor. This work presents error analysis of a spherical capacitive sensor with a differential structure and explores the dependence of the differential capacitance on manufacturing and the installation imperfectness. Five error sources are examined: the shape of the ball and the capacitive plate, the axial and radial offset of the plate, and the inclined installation of the plate. The mathematical models for calculating the capacitance errors of the spherical capacitive sensor are deduced and validated through a simulation using Ansoft Maxwell. The results show that the measurement accuracy of the spherical capacitive sensor is significantly affected by the shape of plates and ball, the axial offset, and the inclined angle of the plate. In contrast, the effect of the radial offset of the plate is quite small. [ABSTRACT FROM AUTHOR]

Due to the flexible and compact structures, spherical joints are widely used in parallel manipulators and industrial robots. Real-time detection of the clearance between the ball and the socket in spherical joints is beneficial to compensate motion errors of mechanical systems and improve their transmission accuracy. This work proposes an improved capacitive sensor for detecting the micro-clearance of spherical joints. First, the structure of the capacitive sensor is proposed. Then, the mathematical model for the differential capacitance of the sensor and the eccentric micro-displacement of the ball is deduced. Finally, the capacitance values of the capacitive sensor are simulated with Ansoft Maxwell. The simulated values of the differential capacitances at different eccentric displacements agree well with the theoretical ones, indicating the feasibility of the proposed detection method. In addition, the simulated results show that the proposed capacitive sensor could effectively reduce the capacitive fringe effect, improving the measurement accuracy. [ABSTRACT FROM AUTHOR]

Precision spherical joints are commonly employed as multiple degree-of-freedom (DOF) mechanical hinges in many engineering applications, e.g., robots and parallel manipulators. Real-time and precise measurement of the rotational angles of spherical joints is not only beneficial to the real-time and closed-loop control of mechanical transmission systems, but also is of great significance in the prediction and compensation of their motion errors. This work presents a novel approach for rotational angle measurement of spherical joints with a capacitive sensor. First, the 3-DOF angular motions of a spherical joint were analyzed. Then, the structure of the proposed capacitive sensor was presented, and the mathematical model for the rotational angles of a spherical joint and the capacitance of the capacitors was deduced. Finally, the capacitance values of the capacitors at different rotations were simulated using Ansoft Maxwell software. The simulation results show that the variation in the simulated capacitance values of the capacitors is similar to that of the theoretical values, suggesting the feasibility and effectiveness of the proposed capacitive detection method for rotational angles of spherical joints. [ABSTRACT FROM AUTHOR]

A spherical joint is a commonly used mechanical hinge with the advantages of compact structure and good flexibility, and it becomes a key component in many types of equipment, such as parallel mechanisms, industrial robots, and automobiles. Real-time detection of a precision spherical joint clearance is of great significance in analyzing the motion errors of mechanical systems and improving the transmission accuracy. This paper presents a novel method for the micro-clearance measurement with a spherical differential capacitive sensor (SDCS). First, the structure and layout of the spherical capacitive plates were designed according to the measuring principle of capacitive sensors with spacing variation. Then, the mathematical model for the spatial eccentric displacements of the ball and the differential capacitance was established. In addition, equipotential guard rings were used to attenuate the fringe effect on the measurement accuracy. Finally, a simulation with Ansoft Maxwell software was carried out to calculate the capacitance values of the spherical capacitors at different eccentric displacements. Simulation results indicated that the proposed method based on SDCS was feasible and effective for the micro-clearance measurement of the precision spherical joints with small eccentricity. [ABSTRACT FROM AUTHOR]