The measurement of distance plays an important role in many aspects of modern societies. In this paper, an absolute distance measurement method for arbitrary distance is proposed and demonstrated using mode-resolved spectral interferometry with a gain-switched dual comb. An accuracy of 12 µm, when compared to a He-Ne fringe counting laser interferometer, for a displacement up to 2.5 m is demonstrated by tuning the repetition frequency of the dual comb from 1.1 GHz to 1.4 GHz. The compact measurement system based on a gain-switched dual comb breaks the constraint of periodic ambiguity. The simplification and improvements are significant for further industrial applications.

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.

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.

Distance measurement using frequency sweeping interferometry is an absolute distance measurement technique that allows for high accuracy over long distances. Notwithstanding, the measurement accuracy is affected by laser sweeping nonlinearity and limited sweeping range. In this work, an optimized post-processing linearization method is demonstrated to realize high-accuracy arbitrary distance measurement using a laser with small modulation range. The interference signal is sparsely resampled to eliminate the influence of the sweeping nonlinearity, and the absolute distance is obtained by analyzing the phase of the resampled signal. In the measurement system, a high-finesse Fabry–Pérot cavity placed in vacuum is used as the measurement reference, so the effect of dispersion mismatch is negligible. Moreover, the distance measurement result is determined by the linear fit of the phase of each resampled point. Therefore, the influence of target vibration and other external random noise can be partially eliminated, and the reliability of the result is high. In the experiment, the sweeping range of the laser source is only 88 GHz. Comparing with a fringe-counting interferometer, the standard deviation of the residual errors is 34 µm within a distance of 6.7 m.

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.