Showing papers on "Angular displacement published in 2022"
TL;DR: In this paper , a nano-displacement measurement system is proposed and demonstrated both theoretically and experimentally, which was based on a modified Mach-Zehnder (M-Z) interferometer using two conjugated orbital angular momentum (OAM) beams.
Abstract: In this study, a nano-displacement measurement system is proposed and demonstrated both theoretically and experimentally, which was based on a modified Mach-Zehnder (M-Z) interferometer using two conjugated orbital angular momentum (OAM) beams. In contrast to the previous M-Z-based OAM interferometer, a reflection module is inserted into the reference arm instead of a simple mirror. As a result, the effect of the transverse position-dependence phase-shift caused by the dove prism can be clearly eliminated and a stable and robust (off-axis insensitive) petal-like interference pattern can be obtained successfully. More importantly, a significant rotation angle of the petal-like pattern vs. the tiny displacement of the tested object can be clearly observed. In accordance with the modified measurement setup, a novel phase-demodulation method enabling to quickly and accurately characterize the rotation angle of the petal-like interference-patterns is proposed and demonstrated also. A tiny displacement ranging from 50 to 800 nm with resolution of $\sim 50$ pm has been measured successfully. The proposed approach may find applications in not only the ultra-high precision displacement sensor, but also the temperature, strain, and refractive index sensors.
8 citations
TL;DR: In this article , an absolute-type inductive angle sensor for detecting the position of the YRT turntable bearing was proposed, which consists of a multispeed incremental measuring unit and a single-speed absolute measuring unit sharing the same stator, rotor, and excitation circuit.
Abstract: This article proposes an absolute-type inductive angle sensor for detecting the position of the YRT turntable bearing. The sensor comprises a multispeed incremental measuring unit and a single-speed absolute measuring unit sharing the same stator, rotor, and excitation circuit. The stator is composed of a ferromagnetic gear groove, two groups of excitation coils, and one group of induction coils arranged according to certain rules. The end cover of the YRT turntable bearing is machined as rotor and it rotated eccentrically relative to the rotation of the stator. A bridge circuit is used to acquire and process the sensor signal from the single-speed measuring unit. Compared with the traditional dual-channel absolute measurement, the proposed measurement method avoids the effects of different magnetic circuit disturbances on signal quality and measurement accuracy, and has more advantages in the volume and weight of the sensor. The structure and working principles of the sensor are presented in detail, the feasibility of sensing scheme is verified via simulation, and a sensor prototype is designed for the final experiment. Experimental results show that the accuracy of the sensor prototype is –0.06758° to 0.1203° before compensation and –0.001139° to 0.0015° after compensation in the range of [0°, 360°], respectively.
7 citations
TL;DR: In this paper , the authors report neurons coding for angular and linear velocity, uniformly distributed across the medial entorhinal cortex (MEC), the presubiculum and the parasubicula, except for MEC layer II.
Abstract: An essential role of the hippocampal region is to integrate information to compute and update representations. How this transpires is highly debated. Many theories hinge on the integration of self-motion signals and the existence of continuous attractor networks (CAN). CAN models hypothesise that neurons coding for navigational correlates - such as position and direction - receive inputs from cells conjunctively coding for position, direction, and self-motion. As yet, very little data exist on such conjunctive coding in the hippocampal region. Here, we report neurons coding for angular and linear velocity, uniformly distributed across the medial entorhinal cortex (MEC), the presubiculum and the parasubiculum, except for MEC layer II. Self-motion neurons often conjunctively encoded position and/or direction, yet lacked a structured organisation. These results offer insights as to how linear/angular speed - derivative in time of position/direction - may allow the updating of spatial representations, possibly uncovering a generalised algorithm to update any representation.
6 citations
TL;DR: In this article , a multidimensional model of duplex angular contact ball bearings (DACBBs) is proposed to analyze the stiffness characteristics of DACBBs in three traditional configurations, and the implicit differential method is adopted to derive the analytical stiffness matrix formulation.
4 citations
TL;DR: In this paper , the effect of two major design parameters, including stator and rotor number of turns combinations, as well as the transformation ratio, on angular position accuracy is investigated.
Abstract: In this study, the comprehensive design and analysis of a limited-angle wound rotor resolver (LAWRR) with high precision are presented. The effect of two major design parameters, including stator and rotor number of turns combinations, as well as the transformation ratio, on angular position accuracy is investigated. To determine the optimal number of turn combinations of LAWRRs with concentric windings (CWs), a simple analytical method consisting of calculating the total harmonic distortion (THD) percentage of the winding distribution waveform is employed. The fundamental operating principle and parametric analyses are carried out using finite element analysis (FEA), which is then followed by verification of the analytical calculations and determination of the optimal number of turn combinations. Moreover, the cross-correlation effect of the signal (stator) and excitation (rotor) winding configurations has been considered. Time-averaged, peak to peak, and maximum position errors were calculated for accuracy analyses. Finally, a prototype is built and tested to validate the analytical and numerical analyses, as well as the main parameters and angular position error.
4 citations
TL;DR: In this paper , a composite signal extraction method was proposed to extract high-precision angular position from the signals detected by Hall sensors in the gimbal servo system of single-gimbal magnetically suspended control moment gyro (SGMSCMG).
Abstract: This article explores a novel composite signal extraction method to extract high-precision angular position from the signals detected by Hall sensors in the gimbal servo system of single-gimbal magnetically suspended control moment gyro (SGMSCMG). Due to magnetic field distortion and other factors, the detected signals involve lots of harmonics and unequal amplitude, which decrease the position resolution accuracy significantly. In the proposed method, normalization is first performed to obtain signals with equal amplitude. Then, on the basis of offline analysis, the signal reconstructed model is established to suppress the most harmonics. Finally, the errors of the models and unmodeled noise are restrained by applying the discrete extended state observer (ESO). Simulated results show that the influence of harmonics and unequal amplitude on the angular position can be almost attenuated by the proposed method. Besides, plentiful experiments on an SGMSCMG demonstrate the validity of the proposed method, and the desired angular position of the ultralow speed servo system can be extracted effectively.
3 citations
01 Dec 2022
TL;DR: In this paper , the authors proposed a kinematic model for a serial-linked industrial robot that contains the bidirectional angular positioning deviations of each rotary axis, represented in a lookup table, in addition to its D-H parameters.
Abstract: To improve a robot’s absolute positioning accuracy, researchers have extensively studied the robot kinematic model containing position and orientation errors of rotary axis average lines, widely known as Denavit–Hartenberg (D-H) parameters. To further improve the absolute positioning accuracy of industrial robots, this article proposes a novel kinematic model and its identification scheme. The proposed kinematic model for a serial-linked industrial robot contains the bidirectional angular positioning deviations of each rotary axis, represented in a lookup table, in addition to its D-H parameters. The angular positioning deviations of the rotary axes are modeled as a function of angular command positions, along with the direction of rotation to model the influence of backlash. This article also proposes a novel approach to identify the proposed kinematic model with the bidirectional angular positioning deviations using a laser tracker with indexing each rotary axis at specified angular positions (“circle point method”). Moreover, the model-based compensation technique is being experimentally investigated to validate the prediction accuracy of the proposed model. The findings of the experiment show that the proposed model enhances the robot’s absolute positioning accuracy significantly over the entire workspace.
3 citations
TL;DR: In this paper , the displacement coordinate of magnetically suspended air-blower on multi degrees of freedom is firstly developed, and then the detection principle of eddy current displacement sensor is researched.
Abstract: The displacement measurement is critical to the stable suspension and position control of magnetically suspended air-blower, and the eddy current sensor is a typical sensor to measure the dynamic displacements between the rotor shaft and the stator part. The displacement coordinate of magnetically suspended air-blower on multi degrees of freedom is firstly developed, and then the detection principle of eddy current displacement sensor is researched. Furthermore, the design processes of displacement sensor including dimensional parameters and quality factor are presented, and then the simulation had been conducted. Finally, the measurement experiments of magnetically suspended air-blower using the displacement sensor system are conducted, the results indicate that the linear range of displacement measurement approaches to 7.5 mm, the relative error is smaller than 2%, and the temperature stability is 0.022%/°C. Therefore, the displacement measurement and vibration analysis of magnetically suspended air-blower could be realized by the designed displacement sensor system.
3 citations
3 citations
TL;DR: In this paper , an orbital angular momentum (OAM) sensor is proposed to simultaneously measure the dynamic micro-displacement and the direction of a moving object in real time, which can achieve high precision and a longer measuring range.
Abstract: In this Letter, we propose an orbital angular momentum (OAM) sensor to simultaneously measure the dynamic micro-displacement and the direction of a moving object in real time. The micro-displacement of the moving object can be detected by the calculation of the petals' rotation angle caused by the coaxial interference between the measured OAM beam and its reference OAM beam, and the direction (forward or backward) of the moving object can be achieved by the clockwise or anticlockwise of the petals' rotation. We also develop an algorithm to monitor the petals' rotation angle and the rotation direction. The experimental results demonstrate that the proposed sensor can achieve high precision ([Formula: see text]) and a longer measuring range ([Formula: see text]). Additionally, the OAM sensor is sensitive to the topological charge in the OAM mode, the initial distance, and the velocity of the moving object. The sensor can perform the non-contact measurement, so it will be a promising method in micro-vibration sensing, surface unevenness sensing, and microbial movement sensing.
3 citations
TL;DR: In this article , a time-varying moment of inertia (MOI) measurement model based on the torsion pendulum method is studied, where the instantaneous frequency is calculated by the instantaneous angular frequency and envelope signal of angular displacement using Hilbert transform.
Abstract: A time-varying moment of inertia (MOI) measurement model based on the torsion pendulum method is studied. According to the principle of dynamics, the motion equation of torsion pendulum with single degree of freedom is established by using the second Lagrange equation modeling, which indicates the time-varying MOI can be obtained by the instantaneous undamped natural frequency of torsional pendulum motion and the torsion bar coefficient. Among them, the instantaneous frequency is calculated by the instantaneous angular frequency and envelope signal of angular displacement using Hilbert transform. The torsion bar coefficient is calibrated by the standard weight with known MOI, and has been compensated by temperature. Based on air floating turntable, the torsion pendulum system is built to measure the MOI of fine sand in the funnel, which can minimize the effects of mechanical friction. The relative error of MOI between calculating the result and measuring the value is less than 0.65%, which verifies the effectiveness of the proposed time varying temperature compensation method.
TL;DR: In this article , an active adaptive fault-tolerant control scheme for position tracking and vibration suppression of a constrained moving rigid-flexible manipulator system (RFMS) in three-dimensional (3D) space is proposed.
Abstract: This paper proposes an active adaptive fault-tolerant control scheme for position tracking and vibration suppression of a constrained moving rigid-flexible manipulator system (RFMS) in three-dimensional (3D) space. The investigated RFMS comprises four parts: a vehicle, a rotatable base, a rigid link, and a flexible link, which is first modeled using nonlinear partial differential equations (PDEs) in terms of Hamilton’s principle. The system may suffer from unknown actuator faults, and the proposed control strategy can compensate for the faults without knowing the fault type and information. The displacement constraint of the vehicle can be ensured by using the barrier Lyapunov function. In the presence of unknown actuator faults and the displacement constraint, the angular position tracking of rigid link, flexible link and rotatable base, and vehicle position tracking can be realized. At the same time, the vibration of the flexible link can be effectively suppressed. The closed-loop system is proven to be asymptotically stable via employing the extended LaSalle’s invariance. Numerical simulations are carried out to verify the effectiveness of the proposed control protocol.
TL;DR: In this paper , an angular displacement sensor based on the tunneling magnetoresistance (TMR) effect is proposed for the precise measurement of angular displacement, which mainly consists of a TMR element, a signal conditioning circuit, a permanent magnet and some necessary assembly components.
Abstract: In the fields of robotics, machine tools and spacecraft, measurement of the gear angular position lays the foundation for closed-loop positional feedback. In this article, an angular displacement sensor based on the tunneling magnetoresistance (TMR) effect is proposed for the precise measurement of angular displacement. The developed sensor mainly consists of a TMR element, a signal conditioning circuit, a permanent magnet and some necessary assembly components. The TMR element is composed of eight magnetic tunnel junctions, which are arranged according to the dual-full bridge structure with a spatial electric angle difference of π/2. Signals containing time information and space information are obtained after the sinusoidal and cosine voltages signals are respectively connected in two bridges. The signals are processed by a signal conditioning circuit, and then the angular displacement is measured by counting the clock pulses. The structure, working principles and signal conditioning method of the sensor are presented in detail. Moreover, a sensor prototype and a conditioning circuit are designed for actual experiments, according to the measured gear with a modulus of 1 and tooth number of 240. The prototype sensor has a theoretical resolution of 0.00001°. The experimental results show that the prototype sensor has a working stability of ±0.00023° within 1 h, and its measurement accuracy is −0.0008611° to 0.001361° in the measurement range from 0° to 360°. Therefore, the proposed sensor can be applied to the highly precise measurement of angular displacement.
TL;DR: In this article , a probe-type inductive angular displacement sensor based on time-grating was proposed for large-diameter hollow rotary table position detection of the heavy-duty machine tools.
Abstract: This articledevelops a novel probe-type inductive angular displacement sensor based on time-grating, which is suitable for large-diameter hollow rotary table position detection of the heavy-duty machine tools. It abandons the traditional sensor precise marking lines in spatial domain, and integrates the tested mechanical component with the sensor, which realizes the angular displacement measurement directly. The sensor is divided into three parts: 1) a permalloy probe, which is adopted the simple structure to reduce the assembly errors; 2) a 45-steel rotor, which is a standard spur gear in a heavy-duty machine tool rotary table transmission system; 3) three groups of copper coils, which include sinusoidal coils, cosine coils and inductive coils. The theoretical model of angular displacement measurement is derived by means of mathematical equation in detail. Then the feasibility of the sensor structure is verified by finite element simulation. After that, a sensor prototype is built and tested in the laboratory, showing that the sensor has an original error of ±0.018° (approximately ± $64^{\prime \prime }$ ) over a full 360° range. The error analysis found that the systematic error is the main component. As a result, the mechanical structure and angular displacement algorithm of the sensor are optimized, which can significantly reduce the original errors of the sensor. After optimization, the final accuracy of the sensor is within ±0.0012° (approximately ± $4.4^{\prime \prime }$ ) in the range of 0°–360°.
29 May 2022
TL;DR: In this paper , the authors used a half wavelength dipole antenna as a probe on the hand and a metal strip (dipole resonator) placed on the object to detect the hand orientation with respect to the target.
Abstract: A preliminary study for a novel approach of detecting the orientation of a robotic hand with respect to non-metallic objects is illustrated. This goal is pursued by using a radiofrequency (RF) probe on the robotic hand and a printed resonator on the tagged item. In order to detect the hand orientation with respect to the target, the real part of the probe input impedance is examined for different angular orientations of the resonator placed on the object. The relation relating the oriented angle between the reader and the sensor to the impedance is addressed to define a proper calibration curve. A half wavelength dipole antenna as a probe on the hand and a metal strip (dipole resonator) placed on the object is employed. The sensing is performed within a near range distance from the object. As the result, it is observed that he proposed probe-resonator configuration allows the identification of the relative angular position of the hand with respect to the object with an encouraging level of accuracy.
TL;DR: In this article , the relative angular shift of the fringes with angular cross power spectral density was evaluated to isolate the uncertainty of depth position from depth displacement, and their relationship was quantitatively formulated.
Abstract: The astigmatic interferometric particle imaging (AIPI) model reveals that the fringe orientation shifts with droplet depth displacement, and their relationships are quantitatively formulated. The depth displacement is directly evaluated from the relative angular shift of the fringes with angular cross power spectral density, and this algorithm isolates the uncertainty of droplet depth position from depth displacement. Proof-of-concept experiments on micrometer-sized transparent droplets with a 5 kHz AIPI system demonstrates that droplet three-dimensional (3D) trajectories are accurately obtained with the accuracy of depth displacement up to tens of micrometers, improving an order of magnitude from hundreds of microns in a traditional Lagrangian framework by comparing droplet depth positions.
TL;DR: In this article , a spherical capacitive sensor was proposed to measure the 2-DOF angular displacement of the spherical pair by integrating the spherical electrode groups in the ball head and the ball socket of a spherical pair.
Abstract: The spherical pair has an important role in the inner frame of the stabilization mechanism of the aviation optoelectronic pod. However, its two-degrees-of-freedom (2-DOF) angular displacement signal is difficult to detect, seriously restricting its application in aviation optoelectronic pods. Therefore, this study proposes a new method to measure a spherical pair’s 2-DOF angular displacement using a spherical capacitive sensor. The capacitive sensor presented by this method realizes the measurement of the 2-DOF angular displacement of the spherical pair by integrating the spherical electrode groups in the ball head and the ball socket of the spherical pair. First, based on the geometric structure of the spherical pair, the structure of the capacitive sensor is designed, and the mathematical model for the capacitive sensor is deduced. Then, the sensor’s output capacitance, in different directions, is simulated by Ansoft Maxwell software. Finally, an experiment device is built for the measurement experiments. The simulation analysis and experimental results show that the spherical capacitive sensor has an approximately linear output in different directions, and the measured output capacitance is as high as 89.7% of the theoretical value. Compared with the existing sensors that measure the 2-DOF angular displacement signal of the ball pair, the sensor proposed in this study has an integrated structure, which can be integrated into the spherical pair. That makes it possible to apply the spherical pair to the inner frame of the aviation optoelectronic pod.
TL;DR: In this paper , a novel angle measurement method that combines a special visual encoder and an accurate angular position detection method is investigated; the method requires only a simple and flexible telecentric vision measurement system.
Abstract: Angular vibration calibration is required to determine the sensitivity of sensors such as dynamic inclinometers, gyroscopes, and angular accelerometers, which are used for angular motion measurement in engineering applications. Additionally, the calibration performance depends on the accuracy of the angle measurement by laser interferometry or a circular grating (CG) method that is commonly used in vibration calibration. However, these methods usually own a complex and high-cost system or limited frequency and amplitude ranges. In this study, a novel, to the best of our knowledge, angle measurement method that combines a special visual encoder and an accurate angular position detection method is investigated; the method requires only a simple and flexible telecentric vision measurement system. Comparison experiments with the CG method demonstrate that the investigated method has the maximum measurement deviation of 0.0014° and 0.0138° for static angle measurement in the small-angle range and continuous full circle, respectively. The relative deviation of the angular vibration measurement in the range of 0.1-8 Hz with amplitudes 0-100° is less than 0.173%. Additionally, the relative deviation of calibrated sensitivity of a gyroscope by the investigated and CG methods is less than 0.096%.
TL;DR: In this paper , an optoelectronic-based joint measurement sensor is proposed to measure a larger angular range of [0°-140°, with increased sensitivity (0-3.5 V) along with investigation of a light intensity model for estimation of sensor output.
Abstract: The miniaturization of robotic applications, such as flexible manipulators or robotic prosthetics, while maintaining high-precision closed-loop position control, faces the challenge of integrating all their mechanisms, sensors, and actuators within a limited space. For this reason, position sensors are usually installed outside the actuated joints, by for example using a wire (tendon)-driven system. In this case, high-precision position control may not be guaranteed due to wire slack or wire deformation caused by high tension. As such, this letter presents an optoelectronic-based joint measurement sensor capable of not only being integrated directly within joints of a versatile range of robotic applications, but also enhancing further miniaturization of these robot applications. Using a variable thickness reflecting surface for proximity-based intensity modulation, the proposed sensing system is shown to be able to measure a larger angular range of [0°–140°], with increased sensitivity (0–3.5 V) along with investigation of a light intensity model for estimation of sensor output.
TL;DR: In this paper , the effects of angular and translational alignment changes with equal displacement between the foot and the socket were not directly compared; however, the authors did find that the displacement of the prosthetic feet was set to be equal between the angular and translation changes, and no significant changes in walking speed were found.
22 Nov 2022
TL;DR: In this paper , a PID-based controller for a 3D DoF manipulator is proposed, where the desired angular velocity and the desired angle are used as the input of the PID controller to control the angular velocity.
Abstract: This research proposes the PID-based controller for a 3 Degree-of-Freedom (DoF) manipulator. The manipulator has three servo motors which can measure the angular position and the angular velocity. The forward kinematics defines the desired angular velocity of each servo motor that will be used as a feed-forward value of the PID controller. The inverse kinematic provides the desired angle of each motor to reach the desired position. Correspondingly, the desired angular velocity and the desired angle are used as the input of the PID controller to control the angular velocity. Here, the PID controller is tuned using the Ziegler-Nichols Tuning 1st method. To show the effectiveness of the proposed method, we conduct three cases experiment: (1). 2D rectangular shape with four constant reference points, (2). 2D circular shape with time-varying reference points, (3). 3D rectangular shapes with time-varying reference points. It is shown that the proposed method gives less than 1% of angle error and less than 5% of velocity error.
TL;DR: In this article , a microwave angular displacement sensor with dynamic range up to 180° and ultra high sensitivity is designed and fabricated, where a stator is designed for reference and a rotatable rotor is attached to it to implement real-time measurement of the rotation angle.
Abstract: A microwave angular displacement sensor with dynamic range up to 180° and ultrahigh sensitivity is designed and fabricated. In the proposed sensor, a stator is designed for reference and a rotatable rotor is attached to it to implement real‐time measurement of the rotation angle. As the rotor is attached to the stator, a CSRR‐like resonant structure would be formed, with the resonant frequency linearly changing with the angular displacement. The measurement results show that the resonant frequency of the designed angular displacement sensor increases from 2.398 to 6.348 GHz linearly as the angle varies from 0° to 180°, with an excellent sensitivity of 21.94 MHz/° achieved.
TL;DR: In this article , the angular difference is used as the output variable of a two-DoF rotating system with a rigid body mode and the measured displacement is positively feedback to the input force.
Abstract: Integral resonant control (IRC) is a vibration control method that has attracted much attention recently. In IRC, the measured displacement is integrated and positively feedback to the input force. It has been shown that IRC is highly effective in vibration control of flexible structures, e.g., nano-positioners, despite its simple first-order controller. IRC cannot apply to the system including poles at the origin (i.e., including rigid body modes). This paper shows that IRC is applicable for a two DoF rotating system including a rigid body mode if we appropriately select the angular difference as the output variable of the system.
TL;DR: In this paper , the first single-phase then two-phase power-off method (FSPTTPPM) is proposed to realize zero sliding displacement between the friction material and the stator during the torsional oscillation of the shaft by controlling the driving circle frequency and the duration of the single phase power off period.
Abstract: To address the problems of the large positioning error and long positioning time of the traditional positioning strategy, namely, the two-phase simultaneous power-off method (TPSPM), a new positioning strategy, called the first single-phase then two-phase power-off method (FSPTTPPM), based on the ultrasonic friction reduction theory, has been proposed in this work. This method realizes zero sliding displacement between the friction material and the stator during the torsional oscillation of the shaft by controlling the driving circle frequency and the duration of the single-phase power-off period, which reduces the deviation of the displacement reservation value. In order to verify the correctness of the driving mechanism, a test platform has been built, and two positioning strategies have been used for experimental verification. The following experimental results have been obtained: compared to TPSPM, FSPTTPPM has the advantages of higher positioning accuracy and short positioning time. In terms of the positioning accuracy, the relative errors of the displacement reservation values of FSPTTPPM and TPSPM vary with the initial angular velocity (0.24 to 1.18 rad/s) in the range of −0.4 to 0.1 and −0.8 to 0.8, respectively. In addition, the relative error of the displacement reservation value is closer to zero than that of TPSPM at the same initial angular velocity. In terms of the positioning time, when the initial angular velocity is greater than 0.7 rad/s, the positioning time of the FSPTTPPM is approximately 10 ms smaller than that of the TPSPM.
23 May 2022
TL;DR: In this paper , a prove of rotational encoder concept based on coherent optical vortex interferometry was proposed to determine small angular rotations, which employed a computer processing of resulting images of interferograms with a characteristic circular motion of the zero intensity.
Abstract: We present a prove of rotational encoder concept based on a coherent optical vortex interferometry to determine small angular rotations. Employing a computer processing of resulting images of interferograms with a characteristic circular motion of the zero intensity allows exact measurements of angular movement of rotational stage over a range of about ±21° with the smallest measurable displacement around 0.75 arcsec.
TL;DR: In this paper , a simple Bennett mechanism is described, which is obtained through the pyramid of its base and sides, where the angles of inclination and heights of the sides are determined to obtain standard equalities.
Abstract: This article provides reasoning and research of spatial mechanisms. The creation of the first simple Bennett mechanism obtained through the pyramid of its base and sides is described. In the pyramid, the angles of inclination and heights of the sides are determined to obtain standard equalities. Thanks to all the parameters, the theoretical link lengths that have practical values are determined. All parameters of length and angles are presented on the structural diagram for each received mechanism. On the basis of two identical, but mirrored mechanisms, a five-bar Bennett mechanism is synthesized. The five-link mechanism is obtained by mutual integration of two identical links, for which the calculation method is described. The article contains a calculation to determine the length and angle of the frame. The frame is obtained by the specified parameters of the ghost angle, the parameters of the two mirrored links derived into one expression. The specified inequality is used for a five-link mechanism in which it is obtained by a driving and a driven full-turn link. The text defines the main kinematic parameters of the links that make a complete turn around its axis without contact. All parameters of the mechanism are metered intuitively. Principle kinematic parameters of the mechanism: angular displacement, angular velocity and angular acceleration are determined. The kinematics is determined with respect to the driving and driven link, taking into account the angular displacement, speed and acceleration. For a more accurate calculation, the dependence of the additional ghost angle of the mechanism on the kinematic parameters is considered. The obtained data are visualized using diagrams of relationships of the rotation of the input link to the output using the Maple application. In trigonometric functions, there is a negative and a positive value determined by the quadrants on the sectors of the circle. Diagrams of angular displacement and angular velocity according to the calculations show negative numerical values. The angular acceleration of the driven link during the rotation of a full turn of the driving link of the mechanism changes its acceleration 4 times. The analysis of the data obtained allows us to conclude that the driven link will rotate jerkily, at these moments there is a possibility of destruction of the mechanism and an increase in the load on the driven link and imbalance of the mechanism.
TL;DR: Based on the Talbot effect of optical gratings, a novel out-of-plane optical displacement sensor with an ultracompact structure, to the best of our knowledge, was proposed in this paper .
Abstract: Based on the Talbot effect of optical gratings, we propose a novel out-of-plane optical displacement sensor with an ultracompact structure, to the best of our knowledge. Using two optical gratings with a slight angle between them, two angular-modulated signals with a phase difference of 90° are obtained associated with a two-quadrant photodetector, which are in sinusoidal relationship with the displacement in the direction perpendicular to the grating plane. Using an interpolation subdivision circuit with a subdivision factor of 1000, out-of-plane displacement measurement with a resolution of 11.23 nm within a range of 1 mm is obtained.