Search

The sinusoidal encoder is used as an absolute position (velocity) transducer to implement the position (velocity) of actuators in many industrial applications. However, the performance of the position (velocity) can be degraded due to nonideal factors such as differential amplitudes of the encoder signals, offset, and phase shift. To analyze this problem, we formulate the relationship between the coefficients of ideal signals and the nonideal signals characteristic, which is an ellipse formed by plotting the encoder signals versus each other. In this article, we propose a nonideal signal calibration for the imperfect components of existing sinusoidal signals to improve position (velocity) regulation performance. The fictitious cosine function is used to detect the phase shift between the sine and cosine signals, and it can be designed by using the frequency of sinusoidal signals. The proposed method is validated by simulation and experimental implementation, showing noticeable improvement in estimating nonideal signal components, Lissajous error curve, phase distribution, and the position (velocity) error signal. Experimental results show that the proposed method is able to obtain the components of the nonideal signals and the accurate position (velocity) with a small error in real time, while other calibration methods are difficult to apply to fast motion.

A low-distortion 3×3 interrogation algorithm requires the accurate parameters calibration of the 3×3 coupler-based Michelson interferometer. The ellipse fitting method with a frequency modulation conducted on the laser is one way that contributes to the implementation of the calibration. However, the unused dangling tail fiber of the 3×3 coupler-based Michelson interferometer generates a harmful echo and leads to an unexpected triple-beam interference. Consequently, it gives rise to a drastic fluctuation on the desired elliptical Lissajous figure, which damages the accuracy and stability of the calibration greatly. In this paper, the echo influence on the calibration is studied theoretically and experimentally. A theoretical model is built based on the coupled mode theory and the interference theory, which is verified by the experiment. According to the model, the echo coefficient, the input state of polarization and the length of the unused dangling tail fiber are three factors that affect the intensity of the fluctuation. Two practical methods of angle cleaving and pulse delay are adopted to suppress the echo influence and restore the accuracy of the calibration in the paper, which are both demonstrated to be feasible and stable. In the end, the suitable applications of the two methods are discussed, which are different for them due to their characteristics. This research has laid the foundation for the practical application of the frequency-modulation-based calibration to the 3×3 coupler-based Michelson interferometric probe.

A new concept, called synchronized Lissajous curve , is proposed to study synchro-waveform measurements that are obtained from waveform measurement units (WMUs) in power distribution systems. Two types of synchronized Lissajous curves are discussed. The first one is created by plotting the difference of two synchronized voltage waveforms versus the difference of two synchronized current waveforms. The second one is created by plotting the difference of two synchronized voltage waveforms versus the difference of the derivatives of two synchronized current waveforms. These two curves carry valuable and complementary information about the state of the power system and the root cause of events and disturbances. We characterize the area , rotational angle , and shape of the introduced synchronized Lissajous curves to study events and disturbances in power distribution feeders.

In the framework of circular restricted three-body problem the libration point orbits form the families of periodic and quasi-periodic solutions. In the paper, the mapping of initial conditions is utilized to describe and study the structure and properties of these families. A new numerical method for orbit generation, which is applicable both for the periodic and quasi-periodic orbits, is provided and explored. The applicability area of the proposed method is constructed and analyzed for the vicinity of Sun-Earth L1. Based on the comprehensive numerical investigation of this area, the xz -maps aligning the initial conditions of the orbits crossing this plane perpendicularly with their properties were constructed and analyzed. The quasiperiodic Lissajous and quasi-halo orbit families appears on these maps as the domains surrounding the curves corresponding to periodic halo and vertical families. Accurate analysis of these domains made in possible to study the structure of resonant k -periodic families, which bifurcate from halo and vertical orbits. The initial conditions of these families are presented by the curves, which thread the quasi-halo and Lissajous domains. These k-periodic families are computed up to k = 10 for the resonant orbits bifurcating from the halo family, and up to k = 25 for the resonant orbits bifurcating from the vertical family. Some examples of such orbits different provided. The maps of initial conditions illustrate several important properties of the libration point orbit families, and can be useful for mission design as a tool to select the orbit fitting the mission requirements.

A dielectric barrier discharge (DBD) in atmospheric pressure air was excited by a high-voltage pulse power supply. Capacitors with different capacitance were connected in the discharge circuit and their effects on discharge power calculation were evaluated. The average power deposited into the discharge were calculated by three different methods: 1) Lissajous figure; 2) product of voltage and current; and 3) watt-hour meter. Further studies showed that the capacitor with 10 nF was suitable for power calculation. At applied voltage of 9 kV, discharge power calculated by three methods were similar (around 25–27 W). However, with the increase of applied voltage, the discharge power obtained by product of voltage and current was far beyond the real value. Lissajous method has proven more appreciable for discharge power calculation in a pulsed plasma at high voltage. This study provides a practical guide for power calculation in a pulsed-driven DBD system.

At the undergraduate level, the composite motion of simple harmonic vibrations has always been the main content of physics as well as several other scientific disciplines. Many textbooks tell us clearly that when the frequency ratio ω1/ω2 of two perpendicular vibrations is simple integer ratio n1/n2 (n1 and n2 are integers), their combined motion has stable and closed trajectories. This trajectory graph is the famous Lissajous figure. The Lissajous figure has been widely studied since it was discovered more than 100 years ago. Especially in the last 30 years, the shape, evolution trend, periodicity, and symmetry of the Lissajous figure have been studied and a series of meaningful characteristics and laws have been summarized. However there has been no analysis of the Lissajous figure from the perspective of three-dimensional space curve so far.

The study addresses the problem of detecting a short circuit fault in the three-phase induction motor winding by monitoring the stator current Park vector (Lissajous curves). Park's vector model is implemented using the Matlab software package. The experimental part of the study was carried out on an 11 kW three-phase induction motor. The Lissajous curves obtained for a healthy motor and a motor with short-circuited turns under various load conditions were compared with each other. The obtained results have demonstrated the effectiveness of the proposed method for detecting interturn short circuit faults in the three-phase stator windings of induction motors.

To overcome the inherent limitation of existing nanopositioning stages running in hundreds of micrometres, a novel normal-stressed electromagnetic actuator is developed to construct a direct drive XY nanopositioning stage, which features a contactless dual-axial actuation with a relatively high force density, a loosely-constrained stroke, and a monolithic magnetic circuit. Assisted by the established model, the mechanical-electromagnetic parameters for the stage are determined with a further verification through both finite element analyses and experimental tests. By combining a PID-based and a parallel resonant controller, the control system for the stage is constructed, which is then demonstrated by ultra-precisely tracking a Lissajous trajectory.

This paper examines the oscillations of a spherical pendulum with horizontal Lissajous excitation. The pendulum has two degrees of freedom: a rotational angle defined in the horizontal plane and an inclination angle defined by the pendulum with respect to the vertical z axis. The results of numerical simulations are illustrated with the mathematical model in the form of multi-colored maps of the largest Lyapunov exponent. The graphical images of geometrical structures of the attractors placed on Poincaré cross sections are shown against the maps of the resolution density of the trajectory points passing through a control plane. Drawn for a steady-state, the graphical images of the trajectory of a tip mass are shown in a three-dimensional space. The obtained trajectories of the moving tip mass are referred to a constructed bifurcation diagram.

As the light-emitting diode (LED) size gradually decreases, it is difficult to conventionally transfer an LED onto a donor substrate. In this paper, we propose a print transfer method that selectively transfers an LED onto a UV release tape, i.e., the donor substrate, via focused laser scanning with Lissajous patterns. We implemented an optical system based on focused laser scanning to perform selective transfer; this can adjust the scanning area immediately without changing the donor substrate size according to the LED size. Because the commercialized UV release tape is utilized as a donor substrate, the adhesion between the LED and donor substrate can be constantly maintained even after repeated experiments. In this study, several LEDs were transferred to a flexible printed circuit board—arranged in a circular and square shape to demonstrate a high degree of freedom of the system—and turned on.

Conventional rheological techniques in the linear viscoelastic region provide insights about the spatial configuration of the microstructural components of personal care formulations in their 'at-rest' state. However, they fail to describe the textural experience associated with large and fast deformations during daily consumer application. In this study we present a non-conventional rheological technique-large amplitude oscillatory shear (LAOS)-for probing the transformation of a material during its application. This technique is proposed a practical tool for formulators in their efforts to design products with desired textural attributes.A non-linear rheological technique termed LAOS was utilized to capture the textural expression perceived by consumers. Lissajous plots (stress vs. strain or strain rate) provide a fingerprint of the formula and are utilized to both analyse the thickening mechanism and monitor the influence of various parameters, such as the chemistry, molecular properties, colloidal parameters and processing conditions.In this study, we showcased several approaches for modifying the texture of personal care formulations and show the influence of various parameters on the characteristics of the Lissajous curves and their relation to sensorial perception. This fingerprinting technique shows that increasing the molecular weight or hydrophobic modification boosts the elasticity and thickening efficiency of a given polymer. Differences in the chemistry of rheological ingredients also influence the characteristic Lissajous fingerprint. In high concentration surfactant systems, which tend to form worm-like micelles, their unique Lissajous fingerprints indicate structure rebuild because of fast kinetics at large but slow deformations. Analysis of lamellar gel-based hair conditioner formulations demonstrates the unique high yield stress of these types of materials, accompanied by the fast breakdown transition from a solid to viscous structure because of their crystalline lamellar gel structure.The LAOS technique presented in this article is intended to better capture the textural expression perceived by consumers. Lissajous plots-generated from the LAOS experimental data-provide a fingerprint of the tested formula and are utilized to both analyse the thickening mechanism and monitor the influence of various parameters, such as the chemistry and molecular weight of the thickener, pH of the formula medium and influence of other ingredients in the formula (surfactants, emulsifiers, etc.).Les techniques rhéologiques conventionnelles dans la région viscoélastique linéaire fournissent des informations sur la configuration spatiale des composants microstructurels des formulations de produits cosmétiques dans leur état « au repos ». Mais elles ne décrivent pas l’expérience de texture associée à des déformations importantes et rapides lors de l’application quotidienne par les consommateurs. Dans cette étude, nous présentons une technique rhéologique non conventionnelle, le cisaillement oscillatoire à grande amplitude (Large Amplitude Oscillatory Shear, LAOS), pour examiner la transformation d’un matériau pendant son application. Cette technique est proposée comme outil pratique pour aider les formulateurs dans leurs efforts pour concevoir des produits qui ont les attributs texturaux désirés. MÉTHODES: Une technique rhéologique non linéaire appelée LAOS a été utilisée pour capturer le style textural perçu par les consommateurs. Les courbes de Lissajous (stress vs contrainte ou taux de déformation) fournissent une empreinte de la formule et sont utilisées pour analyser le comportement épaississant et surveiller l’influence de divers paramètres, tels que les propriétés moléculaires et chimiques, les paramètres colloïdaux et les conditions de traitement. RÉSULTATS: Dans cette étude, nous avons présenté plusieurs approches pour modifier la texture des formulations cosmétiques et montrer l’influence de divers paramètres sur les caractéristiques des courbes de Lissajous et leur relation avec la perception sensorielle. Cette technique d’empreintes montre que l’augmentation du poids moléculaire ou la modification hydrophobe stimule l’élasticité et l’épaississement d’un polymère donné. Les différences dans la chimie des ingrédients rhéologiques influencent également l’empreinte caractéristique de Lissajous. Dans les systèmes de tensioactifs à haute concentration, qui ont tendance à former des micelles semblables à des vers, leurs empreintes Lissajous uniques indiquent une reconstruction de la structure à cause de cinétiques rapides dans leur ensemble mais des déformations lentes. L’analyse des des formulations lamellaires d’après-shampooing à base de gel démontre le stress unique à haut rendement de ces types de matériaux, accompagnés par la transition de répartition rapide d’une structure solide à visqueuse à cause de leur structure lamellaire cristalline.La technique LAOS présentée dans cet article vise à mieux appréhender le style de texture perçu par les consommateurs. Les graphiques de Lissajous, générées à partir de données LAOS expérimentales, fournissent une empreinte de la formule testée et sont utilisés pour analyser le mécanisme épaississant et surveiller l’influence de divers paramètres, tels que la chimie et le poids moléculaire de l’épaississant, le Ph moyen et l’influence des autres ingrédients (tensioactifs, émulsifiants, etc.) dans la formule.

We perform an analytical study of the Lissajous and halo orbits around collinear points L1 and L2 in a spatial circular restricted three-body problem of an arbitrary value of the mass ratio. Using a canonical transformation procedure, we generate complete and resonant normal forms through reduction to center manifolds. The coefficients in the normal forms are explicitly expressed as functions of mass ratio for the first time so that one can evaluate the energy level at which bifurcation of halo orbit takes place. Another contribution of this paper is giving the analytical solutions of Lissajous and halo orbits in the initial synodic reference system through the inverse transformation of normalization. The analytical results are the series form of normalized action-angle variables, and their coefficients are also explicitly expressed as functions of mass ratio. Finally, comparison results demonstrate that the solutions for a Lissajous orbit derived through normalization method and Lindstedt–Poincare method are completely the same, while the solutions for a halo orbit derived through these two methods are different but have the roughly equal accuracy.

In scan-based 3-D systems, the achievable measurement time is strongly restrained by the moving mass. This limitation can be relaxed, by scanning the optical path instead of moving the entire sensor, such that a higher measurement speed can be achieved. This article deals with the design, the control, and the measurement results of a scanning triangulation sensor, in which the illumination and reflection paths of the sensor are scanned by a fast steering mirror (FSM). The system architecture is determined using ray-tracing simulations, such that the performance of the scanning system can be determined in advance. To scan the area of interest with the FSM, conventional raster trajectories and Lissajous trajectories are employed, which provide an early overview of the scan area. For tracking these trajectories, PID and dual-tone controllers are used, respectively. The experimental results demonstrate that for both scan trajectories, the sample can be captured correctly, with a frame rate of 1 frame/s, a maximum spatial resolution of 130 $\mu \text{m}$ , and a field of view of $11.5\,\,\times 18.5\,\,{\mathrm{ mm}}^{2}$ .

Research has supported two distinct forms of motor skill consolidation that can occur between practice sessions: (1) off-line learning, and (2) memory stabilization. Off-line learning describes performance improvement between practice sessions that is above the gain observed at the end of practice, while memory stabilization describes a gain in performance that is maintained between practice sessions. This study used a Lissajous plot to provide concurrent feedback to train participants to produce a 90° relative phase between the index fingers (flexion/extension motion). Significant improvements in performance emerged after ten trials (5 min) of practice. At the end of training, participants were divided into two delay interval groups before retesting, 2-h and 6-h. The retesting session started with participants performing an interference task (10 trials, 5 min) that required training on a 45° relative phase between the fingers with concurrent feedback from the Lissajous plot. When training with the interference task was completed participants were retested with the 90° relative phase without the Lissajous plot feedback. In the retest of the 90° pattern, a performance loss was found in the 2-h delay group, whereas the 6-h delay group maintained the end of practice performance level. Maintenance of the same level of performance without the Lissajous plot represents memory stabilization of the initially trained 90° pattern. The findings are discussed within the context of current positions regarding procedural consolidation and the coordination dynamics framework wherein action and perception are linked through the informational nature of relative phase.

Study of the behavior of polymer solution flows in the region of nonlinear viscoelasticity allows one to more accurately evaluate the adequacy of rheological models and to describe the rheological properties of a material in more detail. The nonlinear viscoelastic properties manifesting themselves in the process of studying the behavior of a polymer material on significant deformations were investigated with the aid of time dependences of shear stresses calculated at different amplitudes. The present work considers the applicability of the modified Vinogradov–Pokrovskii rheological model to describing the oscillating shearing of polymer fluids with a large amplitude. It has been established that on increase of the deformation amplitude, the shear stresses cease to be a true harmonic, and one observes the appearance of a "step" on their left front, which speaks of the substantial nonlinearity in the behavior of the sample. The obtained theoretical dependences are compared with experimental data for a 5% solution of polyethylene oxide in dimethyl sulfoxide. The comparison was made as by plotting the time dependences of normalized stresses, so by analyzing Lissajous figures. Despite the simplicity, the modifi ed Vinogradov–Pokrovskii rheological model adequately describes the behavior of polymer materials on significant periodic deformations.

We present software-based methods for automatic phase control and for mosaicing high-speed, Lissajous-scanned images. To achieve imaging speeds fast enough for mosaicing, we first increase the image update rate tenfold from 3 to 30 Hz, then vertically interpolate each sparse image in real-time to eliminate fixed pattern noise. We validate our methods by imaging fluorescent beads and automatically maintaining phase control over the course of one hour. We then image fixed mouse brain tissues at varying update rates and compare the resulting mosaics. Using reconstructed image data as feedback for phase control eliminates the need for phase sensors and feedback controllers, enabling long-term imaging experiments without additional hardware. Mosaicing subsampled images results in video-rate imaging speeds, nearly fully recovered spatial resolution, and millimeter-scale fields of view.

Hypothesis Escin, a monodesmosidic triterpenoid saponin, was shown previously to form viscoelastic interfaces with a very high dilatational and surface shear storage modulus. This is expected to be due to the arrangement of Escin into 2D disordered soft viscoelastic solid interfacial structures, which results in turn in a distribution of relaxation times. Experiments The responses to dilatational and surface shear deformations of Escin-stabilized air-water interfaces were studied, both in the linear viscoelastic (LVE) and non-linear (NLVE) regime. Step relaxation and amplitude sweeps were performed in dilatation experiments. For surface shear, amplitude sweeps and creep recovery experiments were performed. Findings Escin stabilized-interfaces displayed a highly non-linear behavior in dilatation as seen in the Lissajous plots. In large oscillatory shear the Lissajous curves had a rhomboidal shape, indicating intracycle yielding and recovery, typical of glassy systems. The relaxation of the interface showed stretched exponential behavior, with stretched exponents typical of disordered solids with dynamic heterogeneity. The use of surface rheological measurements beyond the commonly measured LVE regime clearly has provided new insights into the behavior of these interfaces and their microstructure. These results highlight the need to reconsider other complex interfaces as disordered solids and not as 2D homogenous viscoelastic fluids.

This paper proposes a new signal transformed internal model control (STIMC) scheme for non-raster scanning patterns of piezo-actuated nanopositioning stages. To smooth the scanning signals superimposed with a ramp or time-varying amplitudes, a signal transformation operator is calculated to convert the references into standard harmonic waveforms. An inverse transformation operator is then added in the control loop to generate the driving signals. For the contained internal model control (IMC) design, an H∞ mixed-sensitivity method is utilized for the first order internal mode synthesis. A second and a third internal modes are included in the IMC for alleviating residual high-frequency errors resulted from the nonlinearity of hysteresis. To verify the proposed STIMC scheme, comparative experiments with conventional IMC are conducted based on a nanopositioning platform. Results prove that the STIMC is effective on non-raster signals’ tracking. A same tracking precision for Lissajous scanning can be obtained by STIMC compared with IMC. An improvement of larger than 50% and 80% of root-mean-square errors can be obtained for cycloid and spiral scanning patterns, respectively.

An attractive demonstration, observation of chaotic Lissajous curves originating from sound waves, was presented for the general public. A simple experimental setup used in this demonstration consists of an optical lever, a rotating mirror, and a laser beam source. This system can detect a variety of Lissajous patterns without an oscilloscope. Thus, this system can be regarded as a budget oscilloscope. The application to program-based learning in physics education is briefly discussed.

This article presents a novel piezo-actuated fast steering mirror (FSM) and focuses on the integration of control design and system operation in order to improve its tracking performance for high-speed scanning. The FSM is centered around a membrane-like flexure design and two pairs of stack actuators operated in a push–pull configuration, employing an optical sensor for position measurement. With the flexure membrane, the first fundamental resonance mode is placed as high as 6.7 kHz, while still enabling an angular range of $\pm$ 2.4 mrad mechanical. This results in the highest performance metric given by the product of mechanical range times main resonance mode frequency reported for piezo FSMs so far. To improve the tracking performance under high-speed scanning compared to a conventional raster scan operation, an integrated control and trajectory design yields a Lissajous trajectory together with tailored single tone and dual tone feedback controllers. It is demonstrated that in the Lissajous scan case, the rms tracking error can be reduced by one order of magnitude, as compared to the conventional raster scan case with a PI+ controller providing a closed-loop bandwidth of 2.7 kHz.

The use of engineered nanoscale magnetic materials in healthcare and biomedical technologies is rapidly growing. Two examples which have recently attracted significant attention are magnetic particle imaging (MPI) for biological monitoring, and magnetic field hyperthermia (MFH) for cancer therapy. Here for the first time, the capability of a Lissajous scanning MPI device to act as a standalone platform to support the application of MFH cancer treatment is presented. The platform is shown to offer functionalities for nanoparticle localization, focused hyperthermia therapy application, and non-invasive tissue thermometry in one device. Combined, these capabilities have the potential to significantly enhance the accuracy, effectiveness and safety of MFH therapy. Measurements of nanoparticle hyperthermia during protracted exposure to the MPI scanner's 3D imaging field sequence revealed spatially focused heating, with a maximum that is significantly enhanced compared with a simple 1-dimensional sinusoidal excitation. The observed spatial heating behavior is qualitatively described based on a phenomenological model considering torques exerted in the Brownian regime. In vitro cell studies using a human acute monocytic leukemia cell line (THP-1) demonstrated strong suppression of both structural integrity and metabolic activity within 24 h following a 40 min MFH treatment actuated within the Lissajous MPI scanner. Furthermore, reconstructed MPI images of the nanoparticles distributed among the cells, and the temperature-sensitivity of the MPI imaging signal obtained during treatment are demonstrated. In summary, combined Lissajous MPI and MFH technologies are presented; demonstrating for the first time their potential for cancer treatment with maximum effectiveness, and minimal collateral damage to surrounding tissues.

An electrical model of Dielectric Barrier Discharge (DBD) is proposed to model the homogeneous and filamentary discharge. In the first part, for the homogeneous discharge, an equivalent circuit based on the electrical behaviour of DBD is studied. The discharge current and the gap voltage signals are given as a result of model simulation. The analysis of charge transfer has been carried out by means of Lissajous figures, and the dynamic of the discharge is depicted by the discharge characteristic. In the second part, for the filamentary discharge, the randomness of streamers breakdowns and the high frequency of the current pulses have been modelled based on a statistical study of breakdowns distribution. The results of the simulation for the two modes of discharge will be compared to the experimental outcomes.

In this work, the Restricted Four-Body Problem is formulated in Hamiltonian form. The canonical form for the system is obtained which represents the equations of motion. The collinear libration points are obtained, we have five collinear libration points. The non-collinear libration points are found which are three non collinear libration points, they are obtained for different angles between the sight of Sun and the plane of Earth-Moon. The periodic orbits around each of these libration points are studied using two methods. The first method depends on the reduction of order of differential equations and the second method depends on the Eigen values of the characteristic equation. Two codes of MATHEMATICA are constructed to apply these two methods on the Sun- Earth-Moon-Spacecraft. The Poincare sections are obtained using the first method, these sections are used to illustrate the intersect points of the trajectories with the plane perpendicular to the plane of motion about each of the collinear libration points. Mirror symmetry is explored about each of these points. The Lyapunov orbits, and the Lissajous orbits about each of the collinear libration points are the results obtained by the second method. The eccentricities and the periods of each orbit are obtained. This study illustrates that the motion about the libration point L2 is more stable than the motion about any other collinear libration points.

Determination of food rheological and tribological behaviors is imperative for understanding both processing behaviors and texture attributes. The objective of this study was to determine wear behavior of Cheddar and Monterey Jack cheeses. Wear measurements were performed at 50 mm/s sliding speed, 1N normal load, and 25 °C. Cheese linear and nonlinear viscoelastic properties were also determined. Compared to Cheddar, Monterey Jack showed significantly greater small-strain storage and loss moduli values and lower extent of nonlinear viscoelastic behavior. Lissajous plots agreed with these results. Overall, Monterey Jack had lower penetration depth increase and lower mass loss during wear testing than Cheddar. The results of this study provided fundamental information on cheese rheology–wear relationships.

Both intrapersonal and interpersonal coordination dynamics have traditionally been investigated using relative phase patterns of in-phase (ϕ = 0°) and/or anti-phase (ϕ = 180°). Numerous investigations have demonstrated that coordination tasks that require other relative phase patterns (e.g., 90°) are difficult or near impossible to perform without extended practice. Recent findings, however, have demonstrated that an individual can produce a wide range of intrapersonal bimanual patterns within a few minutes of practice when provided integrated feedback. The present experiment was designed to directly compare intra- and interpersonal coordination performance and variability when provided Lissajous feedback or pacing metronome. Single participants (N = 12) and pairs of participants (N = 24, 12 pairs) were required to produce relative phase patterns between 0° and 180° in 30° increments using either pacing metronomes or Lissajous displays. The Lissajous displays involved a goal template and a cursor providing integrated feedback regarding the position of the two effectors. The results indicated both single and pairs of participants could effectively produce a large range of coordination patterns that typically act as repellers after only 6 min of practice when provided integrated feedback. However, single participants performed the in-phase coordination pattern more accurately and with less variability than paired participants, regardless of the feedback condition. These results suggest an advantage for intrapersonal coordination when performing in-phase coordination, possibly due to the stabilizing effect occurring via the neuro-muscular linkage between effectors.

This paper proposes a phase modulation method for Lissajous scanning systems, which provides adaptive scan pattern design without changing the frame rate or the field of view. Based on a rigorous analysis of Lissajous scanning, phase modulation constrains and a method for pixel calculation are derived. An accurate and simple metric for resolution calculation is proposed based on the area spanned by neighboring pixels and used for scan pattern optimization also considering the scanner dynamics. The methods are implemented using MEMS mirrors for verification of the adaptive pattern shaping, where a 5-fold resolution improvement in a defined region of interest is demonstrated.

We present a systematic overview on laser transverse modes with ray-wave duality. We start from the spectrum of eigenfrequencies in ideal spherical cavities to display the critical role of degeneracy for unifying the Hermite–Gaussian eigenmodes and planar geometric modes. We subsequently review the wave representation for the elliptical modes that generally carry the orbital angular momentum. Next, we manifest the fine structures of eigenfrequencies in a spherical cavity with astigmatism to derive the wave-packet representation for Lissajous geometric modes. Finally, the damping effect on the formation of transverse modes is generally reviewed. The present overview is believed to provide important insights into the ray-wave correspondence in mesoscopic optics and laser physics.

Aluminum nitride (AlN) started to draw attentions as a material for piezoelectric actuation owing to its CMOS process compatibility and safeness for biomedical applications. Due to its relatively low piezoelectric coefficients, AlN-based piezoelectric actuators have been mostly operated in resonance modes, especially in optical scanning. This paper presents a novel design of a 2-axis-tilt microscanner with AlN piezoelectric quad-actuators and meander-shaped hinges for reasonable quasi-static operation. Through finite-element-method simulation, it is shown that the proposed device can have about 9 degree of optical scan angle in two dimensions with the voltage amplitude of 50 V. Lissajous scanning operation of the device is demonstrated as well via simulation.

Background: A major player in industry is the induction motor. The constant motion and mechanical nature of motors causes much wear and tear, creating a need for frequent maintenance such as changing contact brushes. Unmannered and infrequent monitoring of motors, as is common in the industry, can lead to overexertion and cause major faults. If a motor fault is detected earlier through the use of automated fault monitoring, it could prevent minor faults from developing into major faults, reducing the cost and down-time of production due the motor repairs. There are few available methods to detect three-phase motor faults. One method is to analyze average vibration signals values of V, I, pf, P, Q, S, THD and frequency. Others are to analyze instantaneous signal signatures of V and I frequencies, or V and I trajectory plotting a Lissajous curve. These methods need at least three sensors for current and three for voltage for a three-phase motor detection. Methods: Our proposed method of monitoring faults in three-phase industrial motors uses Hilbert Transform (HT) instantaneous current signature curve only, reducing the number of sensors required. Our system detects fault signatures accurately at any voltage or current levels, whether it is delta or star connected motors. This is due to our system design, which incorporates normalized curves of HT in the fault analysis database. We have conducted this experiment in our campus laboratory for two different three-phase motors with four different fault experiments. Results: The results shown in this paper are a comparison of two methods, the V and I Lissajous trajectory curve and our HT instantaneous current signature curve. Conclusion: We have chosen them as our benchmark as their fault results closely resemble our system results, but our system benefits such as universality and a cost reduction in sensors of 50%.

Parametrically-resonant micro-mirrors have proven highly effective in generating large amplitude, high-frequency motion for laser scanning in endoscopic microscopy, using Lissajous scan patterns to create a 2D image. However, Lissajous scanning produce low scanning density at the center of an image. In this work, a strategy for exciting additional harmonic behavior in a parametrically-resonant electrostatic micro-mirror is identified. The mirror’s nonlinear dynamics produce substantial changes in natural frequency with bias voltage. This allows a biased, duty-cycled square wave to produce higher harmonic oscillations that can be naturally synchronized with primary resonance in integer ratios. This in turn allows for alternate scanning distributions in 2D imaging that increase pixel sampling near the center of an image. In simulation, use of a biased square wave signal is found to be capable of producing steady-state oscillations at first and third harmonics of natural frequency for a micro-mirror operated via parametric resonance. Multiple harmonic motion is also realized without increasing input voltage amplitude beyond nominal amplitude, with a greater than 50% reduction fill time for the center of the imaging region. Parameterized relationships between input and output oscillations are identified, sensitivity of output trajectory to model variation, and impact on scanning density for a 2D MEMS micro-mirror are briefly described.

The modes delivered by proper orthogonal decomposition (POD) are uncorrelated as per definition; but interestingly, they are not necessarily independent in terms of spatio-temporal flow-pattern dynamics. For instance, periodic structures that travel as waves through a series of snapshots often consist of pairs of modes with harmonic functions shifted 90 degree in phase and/or a spatial offset by a quarter of the spatial wave length of the convective flow pattern. Identification of such pairs, however, largely builds upon experience, visual inspection and/or the analysis of the reconstructed coefficients in cyclograms (Lissajous figures). This effort becomes even more challenging if measurement noise or other spurious information contaminates the raw data under consideration. One possibility to automatically pair corresponding patterns with common POD algorithms is the immediate application of the POD method to complex data (see Pfeffer et al., 1990). As outlined by Horel (1984), the Hilbert transform is a well-known and straight forward means to obtain the required extension of the original signal with an appropriate 90 degrees phase shift, which is independent of the fundamental frequencies. The complex extension of the original (real) signal Xi and its (discrete) Hilbert transform HT{Xi} as the imaginary part Xi +iHT{Xi} with the imaginary unit i is commonly known as the so-called analytical signal.