Showing papers on "Angular displacement published in 2019"

Design of Microwave-Based Angular Displacement Sensor

Abstract: This letter presents a novel microwave-based rotation sensor having a wide dynamic range to detect and measure the angular displacement in terms of the change in resonant frequency. The proposed sensor is based on the microstrip technology, where a rotor comprised of a complementary split-ring resonator (CSRR) placed on the ground plane of the microstrip line is free to rotate around its axis. The mechanical rotation of CSRR determines a change in the cross coupling between the microstrip line and the CSRR, thus changing the overall inductance. The proposed planar unloaded microwave sensor, working around ISM band of 5.8 GHz, is quite sensitive to detect angular rotation in the wide dynamic range of 0°–90°. The linearity in dynamic range is achieved in the range of 30°–60°. Operating frequency and bandwidth can be adjusted by loading the rotor with dielectric. Depending on the type of dielectric loading of CSRR, it is possible to select the center frequency from a wide range of 4.67–5.94 GHz, with the bandwidth ranging from 116 to 250 MHz. Due to its features, the proposed sensor can be useful for various industrial applications.

Development of a Novel Two-DOF Pointing Mechanism Using a Bending–Bending Hybrid Piezoelectric Actuator

Abstract: A novel two-DOF pointing mechanism using a bending–bending hybrid piezoelectric actuator was proposed. The pointing mechanism realized rotary motions around two orthogonal axes by single actuator based on the inertial driving principle. The pointing mechanism was designed and its operating principles were described in detail. The theoretical analyses were performed to design the piezoelectric actuator. The piezoelectric actuator was fabricated and a prototype of the pointing mechanism was assembled. The measured results indicated that the maximum rotary velocities of the rotor were 0.153 rad/s around X -axis and 0.154 rad/s around Y -axis under the voltage of 400 V p - p and frequency of 460 Hz, respectively. Moreover, the angular displacement resolutions achieved 2.49 μrad around X -axis and 2.52 μrad around Y -axis under a voltage increment of 3 V. The two-DOF pointing mechanism could be applied to precision pointing and attitude adjustment systems as its merits of high speed, high resolution, and large motion space.

Optical Sensors for Multi-Axis Angle and Displacement Measurement Using Grating Reflectors.

Abstract: In dimensional metrology it is necessary to carry out multi-axis angle and displacement measurement for high-precision positioning. Although the state-of-the-art linear displacement sensors have sub-nanometric measurement resolution, it is not easy to suppress the increase of measurement uncertainty when being applied for multi-axis angle and displacement measurement due to the Abbe errors and the influences of sensor misalignment. In this review article, the state-of-the-art multi-axis optical sensors, such as the three-axis autocollimator, the three-axis planar encoder, and the six-degree-of-freedom planar encoder based on a planar scale grating are introduced. With the employment of grating reflectors, measurement of multi-axis translational and angular displacement can be carried out while employing a single laser beam. Fabrication methods of a large-area planar scale grating based on a single-point diamond cutting with the fast tool servo technique and the interference lithography are also presented, followed by the description of the evaluation method of the large-area planar scale grating based on the Fizeau interferometer.

Vibration analysis of rotating rods based on the nonlocal elasticity theory and coupled displacement field

Abstract: Free longitudinal vibration analysis of a rotating rod based on the Eringen’s nonlocal elasticity is studied in this paper. Rod is supposed to rotate around a fixed axis with a constant angular velocity. To capture the effect of the rotational motion into analysis of the continuous system, a linear proportional relation is introduced between axial and angular velocities. For the first time the mentioned relation is presented based on the internal motions of the infinitesimal element. This novelty makes the rotational displacement as a dependent function of axial displacement playing a significant role through the analysis. Variational approach is adopted to derive the equations of motion for clamped–clamped and clamped-free boundary conditions. For verification of the results obtained from the Galerkin approach, comparison with technical literature is reported. Finally current results illustrate the dependency of the dynamic-vibration analysis of the presented system on the nonlocality and the rotational velocity parameter. This dependency shows the decrement of the frequency with increment in both the angular velocity and the nonlocal parameter. As a result, the mentioned parameters are key factors in the design and analysis of such systems.

A New Optical Angle Measurement Method Based on Second Harmonic Generation with a Mode-Locked Femtosecond Laser

Abstract: This paper proposes a new optical angle measurement method based on second harmonic generation with a mode-locked femtosecond laser source by taking use of the unique characteristic of high peak power and high-intensity electric field of the femtosecond laser pulses. The angle is measured from the second harmonic wave intensity, which is a function of the angle between the laser beam axis and the optic axis of a nonlinear crystal attached to the target of interest. It is found that the beta barium borate (BBO) crystal is suitable as the nonlinear crystal for this purpose through theoretical simulation. As the first step of research, an experimental demonstration is also carried out in such a way that a change of the second harmonic wave intensity due to the angular displacement of BBO crystal is measured to verify the feasibility of the proposed principle of the angle measurement method.

Improved Capacitive Sensor for Combined Angular and Linear Displacement Sensing

Abstract: This paper presents the design and development of a non-contact capacitive sensor suitable to measure both angular and linear displacements. The sensor is composed of two parts: a rotating shaft and three fixed pairs of electrodes. The shaft has a semi-cylindrical rectangular slot at its middle. Two pairs of electrodes are designed for the measurement of angular displacement and the remaining pair, for linear measurement. A suitable signal conditioning circuit is developed to obtain the change in capacitance between the electrodes and the shaft-slot combination. A function is defined to calculate the absolute angular and linear positions of the shaft. A prototype of the sensor, capable to measure 360° for angular measurement and ±45 mm for linear measurement, was built and tested in the laboratory. The measurement results show that the resolution of the prototype is 0.15° for angular displacement and $41~\mu \text{m}$ for the linear displacement. The linearity error in measurement was found to be less than 0.9% for both angular and linear displacements.

A High-Precision Absolute Angular Position Sensor With Vernier Capacitive Arrays Based on Time Grating

Abstract: This paper presents a high-precision absolute capacitive angular position sensor based on time grating. The sensor includes two single ring incremental type sensors arranged as outer and inner rings of capacitive arrays forming $N$ and $N-1$ measurement periods, respectively. The outer ring incremental sensor is employed as a fine measurement component to provide high-precision angular displacement values. The phase difference between the two incremental sensors is employed as a coarse measurement component to achieve absolute angular positioning according to a measurement principle similar to that of a vernier caliper. The proposed design is validated and optimized via tests conducted for a prototype sensor with $N\,\,=180$ and a diameter of 154 mm fabricated using standard printed circuit board manufacturing technology. Based on these results, a differential induction electrode structure is proposed to greatly reduce the magnitude of crosstalk interference signals captured by the induction electrodes of one array produced by the lead wires of the excitation electrodes of the other array. The optimized sensor achieves absolute angular position measurements with an original measurement accuracy of ±2” over a full 360° measurement range. The proposed sensor has advantages of low cost, high measurement precision, simple positioning method, and ease of manufacture.

Development of rotary-type noncontact-synchronous ultrasonic motor

Abstract: As an application of noncontact transportation utilizing the near-field acoustic levitation phenomenon, a rotary-type noncontact-synchronous ultrasonic motor (NCSyn-USM) using acoustic viscous force was examined. The NCSyn-USM consisted of six fan-shaped stators arranged in a circle and a flat fan-shaped rotor installed above stators via small an air gap. The possibility of the NCSyn-USM was investigated by both of numerical simulation and measurement. From the acoustic-structure and fluid-structure interaction analyzes by finite element method, the correlation between the sound pressure in the air gap and the rotational force was obtained, and it was found that the rotational force was increased by utilizing the acoustic resonance of the air gap. In the experiment, the change of rotational torque with respect to the rotor angular position approximately corresponded with analysis results. The rotation of the rotor by switching driving stators was actually obtained, so that a rotary-type NCSyn-USM would be realized.

The Method of Geometric Error Measurement of NC Machine Tool Based on the Principle of Space Vector’s Direction Measurement

Abstract: To achieve the quick and accurate calibration of the geometric errors of NC machine tool, a new method with laser tracker on the basis of space vector’s direction measurement principle is proposed in the paper. A series of measuring points are mounted on the moving part of the machine tool, and then adjacent measuring points are connected to form a space vector respectively. Due to the motion error of the machine tool, the direction of the vectors composed will be changed. Meanwhile, the deviation of vector’s direction only relates to angular displacement error rather than linear displacement error. Based on the characteristic, the change of vectors’ direction is measured by laser tracker based on the multi-station and time-sharing measurement during the motion of machine tool, and then the angular displacement errors and linear displacement errors of each axis can be accurately identified successively, which reduces the complexity of error identification. By establishing the mathematical model of geometric error measurement of machine tool based on the principle of space vector’s direction measurement, the base station calibration algorithm by measuring the motion of the designed precise turntable, the measuring point determination algorithm and geometric error separation algorithm are derived respectively, and the accuracy of these algorithms are verified by simulations. In addition, the results of the experiments show the feasibility of the proposed method.

Two Degree-of-Freedom Fiber-Coupled Heterodyne Grating Interferometer with Milli-Radian Operating Range of Rotation.

Abstract: In the displacement measurement of the wafer stage in lithography machines, signal quality is affected by the relative angular position between the encoder head and the grating. In this study, a two-degree-of-freedom fiber-coupled heterodyne grating interferometer with large operating range of rotation is presented. Fibers without fiber couplers are utilized to receive the interference beams for high-contrast signals under the circumstances of large angular displacement and ZEMAX ray tracing software simulation and experimental validation have been carried out. Meanwhile, a reference beam generated inside the encoder head is adopted to suppress the thermal drift of the interferometer. Experimental results prove that the proposed grating interferometer could realize sub-nanometer displacement measurement stability in both in-plane and out-of-plane directions, which is 0.246 nm and 0.465 nm of 3σ value respectively within 30 s.

A Linear Direct-Digital Converter for Sinusoidal Encoders

Abstract: This paper proposes a novel linear direct-digital converter for sinusoidal encoders (LDCS) to measure the angular position of a rotating shaft The outputs of a sinusoidal encoder vary as sine and cosine functions of the shaft angle The proposed LDCS, which has a low component count, processes these outputs and renders a linear accurate direct-digital output for full-circle range The LDCS is suitable for both static and dynamic measurements of the shaft angular position The working principle of the LDCS is mathematically derived and explained in this paper An elaborate evaluation of non-ideal parameters affecting the LDCS operation is carried out and reported Furthermore, the static and dynamic performances of the LDCS are verified using simulation and emulation studies The output nonlinearity obtained during emulation studies, for static measurement, is 0027 % A close agreement between simulation and emulation results is observed during these studies Later, a tunneling magnetoresistance (TMR) angle sensing unit which acts as a representative sinusoidal encoder is fabricated The LDCS is interfaced with the sensing unit, and several experimental tests are carried out The worst-case nonlinearity in the static measurement of shaft angle is 029 % Additional tests which study the dynamic performance and effect of mechanical misalignments of the combined TMR-LDCS system is also revealed in this paper

Lightweight Torque Sensor Based on a Gradient Grating Period Guided-Mode Resonance Filter

Abstract: This paper describes the design, fabrication, and testing of a lightweight and compact torque sensor system based on a gradient grating period guided-mode resonance (GGP-GMR) filter and a flexure–elastic-force-sensing element. The GMR filter exhibits a characteristic resonant reflection, when illuminated with a broadband light source at normal incidence. Instead of a fixed grating period, the GGP-GMR filter consists of grating periods varying from 250 to 550 nm with an increment of 2 nm. Given the flexibility of the plastic-based GGP-GMR filter, it can be bent conform to the cylindrical surface of the flexure. The applied torque induced deformation of the flexure and angular displacement of the attached GGP-GMR. For a stationary light source, the angular displacement of the GGP-GMR filter results in illumination at different locations (grating periods), leading to a shift of the resonant reflection wavelength. The magnitude of shift in the reflection wavelength can be correlated to the magnitude of deformation and the applied torque. In addition, commercial software based on the finite element method was used to simulate the proposed design, which indicates that the flexure made of medium-carbon steel can withstand the torque of 35 Nm without yielding. Furthermore, the simulation results (torque-induced deformation) were consistent with those obtained using the proposed torque sensor system. Torque measurements from 0 to 25 Nm showed good linearity. The limit of detection achieved was 0.77 Nm.

Impact and mitigation of angular uncertainties in Bragg coherent x-ray diffraction imaging.

Abstract: Bragg coherent diffraction imaging (BCDI) is a powerful technique to explore the local strain state and morphology of microscale crystals. The method can potentially reach nanometer-scale spatial resolution thanks to the advances in synchrotron design that dramatically increase coherent flux. However, there are experimental bottlenecks that may limit the image reconstruction quality from future high signal-to-noise ratio measurements. In this work we show that angular uncertainty of the sample orientation with respect to a fixed incoming beam is one example of such a factor, and we present a method to mitigate the resulting artifacts. On the basis of an alternative formulation of the forward problem, we design a phase retrieval algorithm which enables the simultaneous reconstruction of the object and determination of the exact angular position corresponding to each diffraction pattern in the data set. We have tested the algorithm performance on simulated data for different degrees of angular uncertainty and signal-to-noise ratio.

High-Resolution Angular Displacement Technology Based on Varying Moiré Figure Phase Positions

Abstract: Angular displacement measurement is a popular research subject. The grating of traditional angular measurement devices uses multi-circle code and is difficult to miniaturize. This paper proposes a novel angular displacement technology based on varying moire figure phase positions which allows for reduced volume and high-resolution angle measurements in small-size gratings. First, a moire figure phase model is established and the calculation arithmetic is written. Second, the proposed arithmetic based on differences in moire figure phase positions is completed accordingly. At last, a test device was fabricated based on the proposed theory with a total diameter of 35 mm and grating diameter of 25 mm. These tests show that angular displacement method based on differences of moire figure phase positions can achieve a high resolution measurement when the diameter of calibration grating is small. We hope the results of this paper provide a workable theoretical foundation for future photographic encoders.

Free flight wind tunnel test similarity law derivation for light store separation from aircraft

Abstract: Based on the linear displacement motion similarity and angular displacement motion similarity, the similarity law for free flight test of light store separation from aircraft is deduced. The proble...

An inverse kinematic model of the human training centrifuge motion simulator

Abstract: The paper presents an inverse kinematic model for a centrifuge motion simulator used to verify newly defined absolute acceleration profiles. The modelling is concerned with a human training centrifuge with three degrees of freedom. The values of kinematic parameters have been obtained for this three-jointed manipulator. Validation of the developed model has been performed by comparing the results obtained from the centrifuge motion simulator with the results of numerical simulations. The simulation revealed that the inverse kinematic model enabled calculation of the angular displacement, velocity and acceleration of the links that are needed for the given linear acceleration of the simulator cabin.

Three-degrees-of-freedom laser interferometer based on differential wavefront sensing with wide angular measurement range

Abstract: We present a three-degrees-of-freedom laser interferometer based on differential wavefront sensing with a wide angular measurement range. To obtain measurement signals with a high AC/DC ratio and improve the linearity of differential wavefront sensing in a wide range angular displacement measurement, a fiber bundle instead of a quadrant photodiode is applied to receive the interference light. Meanwhile, a decoupled algorithm with quadratic correction derived by the ray tracing method and kinematic analysis is detailed in the case of the wide range angular displacement. The simulation and experimental results prove that the laser interferometer with the proposed structure could realize hundreds of microradian range of angular displacement measurement, which are expanded in the differential wavefront sensing.

Characterizing the Impact of Sampling Rate and Filter Design on the Morphology of Lower Limb Angular Velocities

Abstract: The angular velocity of lower limb segments during walking is useful for calculating temporal–spatial parameters and joint kinematics in the inertial measurement unit (IMU)-based gait analysis. While many IMU-based methods for gait analysis have been proposed, configurations of data acquisition and signal conditioning parameter have not been standardized across studies. This study examined the effect of sampling rate and filter design on the characteristic angular velocity waveform obtained from IMUs donned on the lower limbs. Specifically, the frequency analysis of this waveform was performed, and the difference in timing and magnitude of the signal at gait events was evaluated relative to the initial signal. A minimum sampling rate of 35 Hz and a lowpass filter (LPF) cutoff of greater than 10 Hz were found to be appropriate parameters for acquisition and conditioning of the lower limb angular velocity signals. The required low minimum sampling rate suggests that gyroscope data are appropriate for use in bandwidth and battery life limited mobile health applications. Our results also showed that while the commonly employed LPF cutoffs of 5 Hz or less may be appropriate for mid-stance detection, they were not optimal for calculation of heel-strike, toe-off, mid-swing, or angular displacement, obtained with heel-strike and toe-off as delimiters.

Self-Calibration of Nonlinear Signal Model for Angular Position Sensors by Model-Based Automatic Search Algorithm.

Abstract: This study proposes a novel model-based automatic search algorithm to realize the self-calibration of nonlinear signal model for angular position sensors. In some high-precision angular position sensors, nonlinearity of the signal model is the main source of errors and cannot be handled effectively. By constructing a signal flow network framework and by embedding a modeling search network, the parameters of the nonlinear signal model can be searched, and the calibration signal can be obtained. The convergence of the network search process was analyzed. The relationship between the optimization threshold and the convergence accuracy was also studied in simulations. Compared with the maximum angular error reduction to 47.42% after the calibration with simplified model that ignores signal nonlinearities, the proposed scheme was able to reduce this error to 0.0025% in simulations. By implementing the technique in a capacitive angular position sensor, the experimental results showed that the maximum angular error was reduced to 1.63% compared to a reduction of 86.02% achieved with the simplified model calibration. The effects of the search network order and layer number on the calibration accuracy were also analyzed, and the optimal parameters under experimental conditions were obtained. Correspondingly, the proposed scheme is able to handle calibration of nonlinear signal model and further improve sensor accuracy.

Small High-Resolution Angular Displacement Measurement Technology Based on Near-Field Image Acquisition

Abstract: Advances in fine photoelectric displacement measurement technology have made image angular displacement measurement technology via imaging method a popular research topic; it is now easier than ever to realize small-scale high-resolution angular displacement measurement. This paper proposes a small-sized high-resolution image angular displacement measurement technique based on near-field image acquisition. A measuring mechanism based on the lensless near-field image acquisition is first established. Next, based on the error code problem, a space-value-based code value correction algorithm is proposed. Finally, the proposed device is validated on an experimental system. The proposed technology can achieve 21-bit resolution and 20.14” angle measurement accuracy. The results presented here may provide a workable foundation for further research on image-type fine photoelectric displacement measurement technology.

Synthesis of the Optimal Control of the Spacecraft Orientation Using Combined Criteria of Quality

Abstract: The dynamic problem of a spacecraft’s (SC) rotation from an arbitrary initial angular position to a given final angular position is considered and solved. The case is investigated when the control is limited, and the minimized functional combines, in a given, proportion, the time of the maneuver and the integral of the energy of rotation. The construction of the optimal control is based on the quaternionic differential equation relating the vector of the angular momentum of the SC with the quaternion of the orientation of the body-related coordinate system. The control law is formulated in the form of an explicit dependence of the control variables on the phase coordinates. The analysis of the special control regime of the SC is carried out. Based on the conditions of transversality, as the necessary conditions for optimality, the optimal value of the kinetic energy of rotation when moving in a special control regime is determined. The created control algorithms allow turning of an SC with a kinetic rotation energy, which does exceed a predetermined level. For a dynamically symmetric SC, the problem of spatial reorientation is solved completely. The results of the mathematical modeling of the motion of an SC under the optimal control are presented, demonstrating the practical feasibility of the developed algorithm for controlling the spatial orientation of the SC.

A Self-Calibration Method for Angular Displacement Sensor Working in Harsh Environments

Abstract: This paper presents a new self-calibration method for angular displacement sensor, named coaxial sensors relative rotation (CSRR) method, which is suitable for sensors working in harsh environments. With a few slight modifications to the machine, CSRR method can also self-calibrate sensors on their application axes. This method works with two sensors. One sensor provides a benchmark and the other provides relative rotation against the benchmark, then each sensor can be self-calibrated by measuring the synchronized angular displacements of sensors and calculating the relative rotation angles. Experimental results indicate that this method is insensitive to relative rotation error of the two coaxial sensors, and it is also insensitive to sampling uniformity in particular situation. In that particular situation, the calibration accuracy can be better than ±2” when the system error of sensor is about ±650”. Compared with equal division averaged method, CSRR method mostly requires fewer sensors to get the same calibration accuracy; and compared with time-measurement dynamic reversal method, CSRR method performs better on the axis supported by rolling bearing. What is more, we propose an evaluation indicator $\vert Y_{\boldsymbol {\Omega }}\vert $ to evaluate the effective range of the CSRR method, and the $\vert Y_{\boldsymbol {\Omega }}\vert $ makes it easier for others to determine whether this method is suitable for their applications.

Uniaxial Attitude Stabilization of a Rigid Body under Conditions of Nonstationary Perturbations with Zero Mean Values

Abstract: This paper deals with the problem of uniaxial stabilization of the angular position of a rigid body exposed to a nonstationary perturbing torque. The perturbing torque is represented as a linear combination of homogeneous functions with variable coefficients. It is assumed that the order of homogeneity of perturbations does not exceed the order of homogeneity of the restoring torque, and the variable coefficients in the components of the disturbing torque have zero mean values. A theorem on sufficient conditions for the asymptotic stability of a programmed motion of the body is proven using the Lyapunov direct method. The determined conditions guaranteeing the solution to the problem of body uniaxial stabilization do not impose any restrictions on the amplitudes of oscillations of the disturbance torque coefficients. Results of numerical modeling are presented that confirm the conclusions obtained analytically.