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Metrology is the science of measurement and can be divided into three overlapping activities: (1) the definition of units of measurement, (2) the realization of units of measurement, and (3) the traceability of measurement units [...]

Currently, the widely used pendulum-type precision level cannot be miniaturized because reducing the size of the pendulum will reduce its displacement so as to decrease the measurement accuracy and resolution. Moreover, the commercial pendulum-type level can only sense one direction. In this paper, an innovative compact and high-accuracy dual-axis precision level is proposed. Based on the optical principle of light refraction and the reference of the invariant liquid level, the pendulum is no more needed. In addition, based on the light transmission design, there is no reflection signal to interfere with the true signal. Therefore, the level can achieve a high accuracy and small-sized design. The calibration result shows the error of the proposed precision level is better than ±0.6 arc-sec in the measurement range of ±100 arc-sec, and better than ±5 arc-sec in the full measurement range of ±800 arc-sec.

A low-cost miniature homodyne interferometer (MHI) with self-wavelength correction and self-wavelength stabilization is proposed for long-stroke micro/nano positioning stage metrology. In this interferometer, the displacement measurement is based on the analysis of homodyne interferometer fringe pattern. In order to miniaturize the interferometer size, a low-cost and small-sized laser diode is adopted as the laser source. The accuracy of the laser diode wavelength is real-time corrected by the proposed wavelength corrector using a modified wavelength calculation equation. The variation of the laser diode wavelength is suppressed by a real-time wavelength stabilizer, which is based on the principle of laser beam drift compensation and the principle of automatic temperature control. The optical configuration of the proposed MHI is proposed. The methods of displacement measurement, wavelength correction, and wavelength stabilization are depicted in detail. A laboratory-built prototype of the MHI is constructed, and experiments are carried out to demonstrate the feasibility of the proposed wavelength correction and stabilization methods.

The structural deformations caused by environmental changes in temperature, vibration, and other factors are harmful to the stability of high precision measurement equipment. The stability and optimal design method of a 2D optoelectronic angle sensor have been investigated in this study. The drift caused by structural deformations of the angle sensor has been studied and a drift error model has been achieved. Key components sensitive to thermal and vibrational effects were identified by error sensitivity analysis and simulation. The mounts of key components were analyzed using finite element analysis software and optimized based on the concept of symmetric structures. Stability experiments for the original and optimized angle sensors have been carried out for contrast. As a result, the stability of the optimized angle sensor has been improved by more than 63%. It is verified that the modeling and optimal design method is effective and low-cost, which can also be applied to improve the stability of other sensors with much more complex principles and structures.

A robust laser measurement system (LMS), consisting of a sensor head and a detecting part, for simultaneously measuring five-degree-of-freedom (five-DOF) error motions of linear stages, is proposed and characterized. For the purpose of long-travel measurement, all possible error sources that would affect the measurement accuracy are considered. This LMS not only integrates the merits of error compensations for the laser beam drift, beam spot variation, detector sensitivity variation, and non-parallelism of dual-beam that have been resolved by the author’s group before, but also eliminates the crosstalk errors among five-DOF error motions in this study. The feasibility and effectiveness of the designed LMS and modified measurement model are experimentally verified using a laboratory-built prototype. The experimental results show that the designed LSM has the capability of simultaneously measuring the five-DOF error motions of a linear stage up to one-meter travel with a linear error accuracy in sub-micrometer and an angular error accuracy in sub-arcsecond after compensation.

Precision dimensional measurements always play the critical role in workshop quality control [...]

The geometric error motions of rotary stages greatly affect the accuracy of constructed machines such as machine tools, measuring instruments, and robots. In this paper, an embedded sensor system for real-time measurement of two radial and three angular error motions of a rotary stage is proposed, which makes use of a rotary encoder with multiple scanning heads to measure the rotational angle and two radial error motions and a miniature autocollimator to measure two tilt angular errors of the axis of rotation. The assembly errors of the grid disc of the encoder and the mirror for autocollimator are also evaluated and compensated. The developed measuring device can be fixed inside the rotary stage. In the experiments, radial error motions of two points on the axis (h = 5 mm and 60 mm) were measured and calibrated with LVDTs, and the data showed that the radial error motions of the axis were less than 20 μm, and the calibration residual errors were less than 2 μm. When intermittent external forces were applied to the stage, the change of the stage’s error motion could also be monitored accurately.

To meet the requirement of high precision measurement of coordinate measurement machine system, a compact microprobe has been designed for 3D measurement in this paper. Aiming to reduce the influences of signal coupling during the probing process, the probe has been designed by adopting two elastic mechanisms, in which the horizontal and vertical motions of the probe tip can be separated by differential signals of quadrant photodetectors in each elastic mechanism. A connecting rod has been designed to transfer the displacement of the probe tip in vertical direction from lower to upper elastic mechanisms. The sensitivity models in horizontal and vertical directions have been established, and the sensor sensitivity has been verified through experiments. Furthermore, the signal coupling of three axes has been analyzed, and mathematical models have been proposed for decoupling. The probing performance has been verified experimentally.

This paper presents a miniature three-degree-of-freedom laser measurement (3DOFLM) system for displacement feedback and error compensation of a nanopositioning stage. The 3DOFLM system is composed of a miniature Michelson interferometer (MMI) kit, a wavelength corrector kit, and a miniature autocollimator kit. A low-cost laser diode is employed as the laser source. The motion of the stage can cause an optical path difference in the MMI kit so as to produce interference fringes. The interference signals with a phase interval of 90° due to the phase control are detected by four photodetectors. The wavelength corrector kit, based on the grating diffraction principle and the autocollimation principle, provides real-time correction of the laser diode wavelength, which is the length unit of the MMI kit. The miniature autocollimator kit based on the autocollimation principle is employed to measure angular errors and compensate induced Abbe error of the moving table. The developed 3DOFLM system was constructed with dimensions of 80 mm (x) × 90 mm (y) × 20 mm (z) so that it could be embedded into the nanopositioning stage. A series of calibration and comparison experiments were carried out to test the performance of this system.

Low-frequency vibration is a harmful factor that affects the accuracy of micro/nano-measuring machines. Low-frequency vibration cannot be completely eliminated by passive control methods, such as the use of air-floating platforms. Therefore, low-frequency vibrations must be measured before being actively suppressed. In this study, the design of a low-cost high-sensitivity optical accelerometer is proposed. This optical accelerometer mainly comprises three components: a seismic mass, a leaf spring, and a sensing component based on a four-quadrant photodetector (QPD). When a vibration is detected, the seismic mass moves up and down due to the effect of inertia, and the leaf spring exhibits a corresponding elastic deformation, which is amplified by using an optical lever and measured by the QPD. Then, the acceleration can be calculated. The resonant frequencies and elastic coefficients of various seismic structures are simulated to attain the optimal detection of low-frequency, low-amplitude vibration. The accelerometer is calibrated using a homemade vibration calibration system, and the calibration experimental results demonstrate that the sensitivity of the optical accelerometer is 1.74 V (m·s−2)−1, the measurement range of the accelerometer is 0.003–7.29 m·s−2, and the operating frequencies range of 0.4–12 Hz. The standard deviation from ten measurements is under 7.9 × 10−4 m·s−2. The efficacy of the optical accelerometer in measuring low-frequency, low-amplitude dynamic responses is verified.

Patterned leaf springs made of a beryllium bronze sheet are the key components of certain micro/nano contact probes. The accuracy of the probe is determined based on the precision of the formed pattern. However, a traditional manufacturing method using wire-electrode discharge machining (wire-EDM) is subject to poor tolerance at the sharp edges and corners. In addition, high energy consumption and costs are incurred for complex patterns. This paper presents a new chemical etching method for the manufacturing of a patterned leaf spring with high precision. Both the principle and process are introduced. Taguchi experiments were designed and conducted and the optimal process parameters were obtained based on the mean value and a variance analysis. Four V-shaped and some other complex patterned leaf springs were successfully fabricated. Comparison experiments concerning the characteristic parameters of the leaf spring were also conducted. The experimental results reveal that the patterned leaf springs manufactured through this method are much better than those achieved using wire-EDM. This manufacturing method can be used to fabricate different high-precision patterned leaf springs or membranes for coordinate measuring machines (CMM) probes and other measuring equipment.

This paper presents a novel method to fabricate temperature sensor arrays by dispensing a graphite-polydimethylsiloxane composite on flexible polyimide films. The fabricated temperature sensor array has 64 sensing cells in a 4 × 4 cm2 area. The sensor array can be used as humanoid artificial skin for sensation system of robots. Interdigitated copper electrodes were patterned on the flexible polyimide substrate for determining the resistivity change of the composites subjected to ambient temperature variations. Polydimethylsiloxane was used as the matrix. Composites of different graphite volume fractions for large dynamic range from 30 ºC to 110 ºC have been investigated. Our experiments showed that graphite powder provided the composite high temperature sensitivity. The fabricated temperature sensor array has been tested. The detected temperature contours are in good agreement with the shapes and magnitudes of different heat sources.

In gear measuring machines (GMMs), the tested gear is mounted on a mandrel, which is pivoted at both ends by two centers in a vertical arrangement. The upper center is fixed and the lower center is driven by the spindle of rotation. The coaxiality error between the central line of the mandrel and the spindle average line of a GMM always exists in terms of the offset and angle measured in one plane. Such a coaxiality error would cause an angular indexing error of tested gear resulting in measurement error. This phenomenon has rarely been investigated. In this paper, a GMM is taken as an example and its coaxiality error of the mandrel and spindle error of the rotary stage are measured. The difference of rotated angles between the mandrel and spindle is theoretically analyzed by derived formulae. Calibrated by a precision polygon and an autocollimator, the predicted angular index error of the mandrel was consistent with experimental results. Through the experimental verification, it was found that, when the coaxial deviation between the two centers was 10 μm and the lower center tip’s radial motion error was 1.6 μm, the angular indexing deviation of the mandrel was ±5″. If the errors were compensated according to the analyzed model, the residual error was reduced to ±2″. A significant improvement in the angular positioning accuracy of the GMM can be achieved.

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.

A micro Coordinate Measuring Machine (CMM) with the measurement volume of 50 mm × 50 mm × 50 mm and measuring accuracy of about 100 nm (2σ) has been developed. In this new micro CMM, an XYZ stage, which is driven by three piezo-motors in X, Y and Z directions, can achieve the drive resolution of about 1 nm and the stroke of more than 50 mm. In order to reduce the crosstalk among X-, Y- and Z-stages, a special mechanical structure, which is called co-planar stage, is introduced. The movement of the stage in each direction is detected by a laser interferometer. A contact type of probe is adopted for measurement. The center of the probe ball coincides with the intersection point of the measuring axes of the three laser interferometers. Therefore, the metrological system of the CMM obeys the Abbe principle in three directions and is free from Abbe error. The CMM is placed in an anti-vibration and thermostatic chamber for avoiding the influence of vibration and temperature fluctuation. A series of experimental results show that the measurement uncertainty within 40 mm among X, Y and Z directions is about 100 nm (2σ). The flatness of measuring face of the gauge block is also measured and verified the performance of the developed micro CMM.

To measure various components with nano-scale precision, a new high-precision touch-trigger probe using a single low-cost sensor for a micro-coordinate measuring machine (CMM) is presented in this paper. The sensor is composed of a laser diode, a plane mirror, a focusing lens, and a quadrant photo detector (QPD). The laser beam from the laser diode with an incident angle is reflected by the plane mirror and then projected onto the quadrant photo detector (QPD) via the focusing lens. The plane mirror is adhered to the upper surface of the floating plate supported by an elastic mechanism, which can transfer the displacement of the stylus’s ball tip in 3D to the plane mirror’s vertical and tilt movement. Both motions of the plane mirror can be detected by respective QPDs. The probe mechanism was analyzed, and its structural parameters that conform to the principle of uniform sensitivity and uniform stiffness were obtained. The simulation result showed that the stiffness was equal in 3D and less than 1 mN/µm. Some experiments were performed to investigate the probe’s characteristics. It was found that the probe could detect the trigger point with uniform sensitivity, a resolution of less than 5 nm, and a repeatability of less than 4 nm. It can be used as a touch-trigger probe on a micro/nano-CMM.