Elliptical Trajectory Research Articles

Piezoelectric Hysteresis Modeling of Hybrid Driven Three-Dimensional Elliptical Vibration Aided Cutting System Based on an Improved Flower Pollination Algorithm.

Three-dimensional elliptical vibration assisted cutting technology has been widely used in the past few years. The piezoelectric stack drive structure is an important part of the three-dimensional elliptical vibration aided cutting system. Its piezoelectric hysteresis characteristics affects the final output of the elliptical trajectory. Aiming at this problem, a piezoelectric hysteresis modeling method based on a generalized Bouc–Wen model is presented in this paper. An improved flower pollination algorithm (IFPASO) was used to identify Bouc–Wen model parameters. Standard test result shows that IFPASO has better algorithm performance. The model identification effect experiment proved that the Bouc–Wen model obtained by IFPASO identification, the highest modeling accuracy of the three axial subsystems, can reach 98.86%. Therefore, the model can describe the piezoelectric hysteresis characteristics of the three axial subsystems of the 3D-EVC system effectively and has higher modeling accuracy and fitting accuracy.

Performance Estimation of a Wireless Sensor Network with a Mobile Sink Moving in Different Trajectories at Different Velocities

Background: Throughout the past few years, numerous Medium Access Control (MAC) protocols, routing protocols, node deployment mechanisms and duty cycle variation schemes have been designed for achieving high throughput, low delay and jitter, and long network lifetime in Wireless Sensor Networks (WSNs). In a WSN with static sink, voluminous sensors transmit their sensed data to the sink node. The coordinators mutually present in the range of sensors and sink have to forward a number of packets, which cause rapid depletion of their battery. These coordinators become dead too early resulting in the breakage of the communication channel and formation of energy holes. However, to save energy with a static sink, the duty cycle should be short. A mobile sink is a better option than a static sink if the duty cycle is long, as it balances energy consumption among the sensors. It is well observed that the mobile sink is capable of acquiring homogeneous energy depletion leading to stretched lifetime enhancing network performance. Methods: The vital benefaction of this paper is to present a simulation-based analysis of the network performance with a mobile sink having different trajectories of path traversed at different velocities. The intent is to find out the most appropriate and efficient trajectory and a particular velocity for a specific WSN with 100 nodes. The terrain area of the network is 210×210 m2 with the communication range of 20 m. The routing, network and MAC protocols implemented are Ad hoc On-Demand Distance Vector (AODV), Internet Protocol version 4 (IPv4) and Institute of Electrical and Electronics Engineers (IEEE) 802.15.4 respectively. This paper has evaluated and analyzed the influence of lawn mower, elliptical and circular trajectories of a mobile sink moving at different velocities of 0.5, 1 and 2 m/s. The optimum performance is achieved at the velocity of 2 m/s for a circular trajectory of the mobile sink. It is observed that performance has significantly varied with the variation of trajectories and velocities. The notion of precise utilization of sink mobility improves the performance than a static sink. It is equally important to determine the most effective mechanism to implement mobile sinks and to find out the most appropriate scheme out of them. Results: The attainment parameters just as total messages received, average end to end delay (seconds), jitter (seconds), throughput (bits per second), number of packets dropped, number of packets dropped due to channel access failure, residual battery (mAh) and network lifetime (hours) for different trajectories such as lawn mower, elliptical and circular at different speeds of 0.5, 1 and 2 m/s of the sink node are evaluated and compared. The simulation results present that the circular trajectory and the velocity of 2 m/s have provided optimum performance. Conclusion: The objective was to precisely analyze and evaluate the influence of different trajectories of a mobile sink moving at different velocities in a WSN of 100 nodes to determine the most effective and appropriate trajectory and velocity to optimize the attainments. The intent is to uniform the power exhaustion amidst the sensors. The purpose was to gain the attention of researchers of this field to significantly contribute to novel research.

Dynamics of elliptical vortices in a trapped quantum fluid

The nonequilibrium dynamics of vortices in 2D quantum fluids can be predicted by accounting for the way in which vortex ellipticity is coupled to the gradient in background fluid density. In the absence of nonlinear interactions, a harmonically trapped fluid can be analyzed analytically to show that single vortices will move in an elliptic trajectory that has the same orientation and aspect ratio as the vortex projection itself. This allows the vortex ellipticity to be estimated through observation of its trajectory. A combination of analysis and numerical simulation is then used to show that nonlinear interactions cause the vortex orientation to precess, and that the rate of vortex precession is once again mimicked by a precession of the elliptical trajectory. Both vortex ellipticity and rate of precession can therefore be inferred by observing its motion in a trap. An ability to anticipate and control local vortex structure and vortex trajectory is expected to prove useful in designing few-vortex systems in which ellipticity is a ubiquitous, as-yet-unharnessed feature.

Features of picking cotton from the spindles of a vertical-spindle cotton picker with their variable kinematic modes

The paper considers the problem of increasing the efficiency of removing cotton from the spindles of vertical-spindle devices. The possibility of increasing the time of action of the stripper on the winding of cotton in the process of removing cotton from the spindles using an elliptical spindle drum based on a planetary-cam-lever mechanism is shown. Universal analytical expressions have been obtained to determine the limit and time of interaction of the stripper and the spindle with elliptical and circular trajectories of the spindle, the numerical experiment of which has carried out a comparative analysis of the work of the cotton picker in the area of picking cotton from the spindles. Some advantages in the operation of an elliptical drum in the removal zone are shown.

Analysis of a three-stator multi-degree-of-freedom piezoelectric actuator based on symmetrical distribution

In this paper, a piezoelectric actuator with three symmetrical distributions is designed. Piezoelectric ceramics are polarized in a set manner. The excitation voltage signals of the same amplitude and different phases are applied to the actuator, and an elliptical trajectory is generated on the driving foot to drive the slide rail to move. Its driving principle is different from that of previous drivers of this type. For example, when moving in a certain direction, the horizontal displacement is formed by a mixture of the longitudinal vibration of one sub-actuator and the bending vibration of two sub-actuators, while the vertical displacement is generated by the bending vibration of the actuator. Through the close cooperation of the three sub-actuators, the output efficiency is greatly improved. The actuator is suitable for small high-precision control. First, the overall structure and working principle of the piezoelectric actuator are briefly introduced. Then, through the finite element analysis, the working mode with output performance and the motion track on the driving foot are analyzed. Finally, the output performance of the actuator is analyzed. When the voltage frequency is 200 Hz and the amplitude is 200 V, the maximum output speed is 5.1 mm/s and the maximum load of about 1.2 kg can be applied, which verifies that the actuator has good driving ability.

Elliptic vibration assisted cutting of metal matrix composite reinforced by silicon carbide: an investigation of machining mechanisms and surface integrity

This paper aims to investigate the deformation mechanisms and surface integrity of SiCp/Al composites machined by elliptic vibration assisted cutting (EVAC). Self-designed EVAC device was applied to generate the elliptical trajectory on tool tip, which is driven by three piezoelectric actuators along different directions with phase difference. A two-dimensional (2D) microstructure-based finite element (FE) model of SiCp/Al composites was also established to research the deformation mechanisms and surface integrity in the process of EVAC, including material removal mechanisms, cutting force, surface roughness and microstructure. Systematic orthogonal cutting experiments shown that the relative position of tool-particles are changed by the time-varying cutting thickness in EVAC, leading to more obvious particle fracture during SiC particles removal process. Particle fracture appears in the area of particle clusters affected by chip lifting of tool. The intermittent cutting effect not only reduces the average cutting force, but also eliminates the scratch on machined surface caused by SiC particles entering the flank face–workpiece interface, improving the machined surface quality. Limited by the volume of material removal, 2D FE model has a high prediction accuracy for the micro-removal process of composite materials. The application of elliptical vibration is able to create the special functional surfaces. In order to increase the hydrophobicity of machined surface, larger feed rate and smaller cutting depth should be selected as far as possible.

Design and Analysis of a Stepping Piezoelectric Actuator Free of Backward Motion

Although the stick-slip principle has been widely employed for designing piezoelectric actuators, there still exits an intrinsic drawback, i.e., the backward motion, which significantly affects its output performances and applications. By analyzing the generation mechanism of backward motion in stick-slip piezoelectric actuators, the elliptical trajectory was employed to design a novel stepping piezoelectric actuator free of backward motion. Accordingly, a prototype of piezoelectric actuator was designed, which utilized a flexure hinge mechanism and two vertically arranged piezoelectric stacks to generate the required elliptical trajectory. The compliance matrix method was used to theoretically analyze the flexure hinge mechanism. The theoretical and measured elliptical trajectories under various phase differences were compared, and the phase difference of 45° was selected accordingly. Under a critical relative gap, output performances of the actuator working under the elliptical trajectory were characterized, and then compared with that obtained under the normal stick-slip driving principle. Experimental results indicated that forward and reverse stepping displacement with completely suppressed backward motion could be achieved when employing the elliptical trajectory, verifying its feasibility. This study provides a new strategy for designing a stepping piezoelectric actuator free of backward motion.

Design and experiment of a three-feet linear ultrasonic motor using third bending hybrid modes

A linear ultrasonic motor (USM) with two piezoelectric stators using the combination of two third bending vibration modes is proposed in this study, two orthogonal bending modes can simplify the effort of frequency degeneration. A square runner is driven by two stators through elliptical motions of their driving feet. Three driving feet in each stator are located at its middle and both ends, they vibrate with the same elliptical trajectory and push the runner together for improving the output performance. The finite element method (FEM) is adopted to optimize structural configuration of the stator, which ensures the amplitude uniformity of three driving feet. A prototype of the proposed USM is manufactured and its mechanical characteristics including velocity versus exciting voltage and velocity versus carrying load are tested in sequence. The tested results show that the maximum no-load velocity of the prototype is 117.22 mm/s at the exciting voltage of 65 Vp-p, and the maximum carrying load of the prototype is 350 g when the exciting voltage is 60 Vp-p. The tested results confirm that the developed USM has the advantages of simplified frequency degeneration in structure design and low exciting voltage.

The stability analysis for the motion of a nonlinear damped vibrating dynamical system with three-degrees-of-freedom

This article investigates the motion of double nonlinear damped spring pendulums with 3DOF in which its pivot point moves in an elliptic trajectory. The controlling system of motion is derived applying the Lagrange's equations and solved asymptotically up to the third approximation utilizing the multiple scales technique. The arising resonance cases are categorized in view of the solvability conditions in which the equations of modulation are obtained. The steady-state solutions in accordance with the stability and instability criteria are examined. The novelty of this work lies in obtaining high accuracy solutions compared with the previous works and in studying of the nonlinear stability analysis to identify the stability and instability areas. The time histories of the attained results, the response resonance curves, and the regions of stability are discussed and represented graphically to explore the good influence of the distinct parameters on the dynamical behaviour of the investigated system. The importance of this work is due to its great uses in various engineering applications.

Targeted muscle effort distribution with exercise robots: Trajectory and resistance effects

The objective of this work is to relate muscle effort distributions to the trajectory and resistance settings of a robotic exercise and rehabilitation machine. Muscular effort distribution, representing the participation of each muscle in the training activity, was measured with electromyography sensors (EMG) and defined as the individual activation divided by the total muscle group activation. A four degrees-of-freedom robot and its impedance control system are used to create advanced exercise protocols whereby the user is asked to follow a path against the machine’s neutral path and resistance. In this work, the robot establishes a zero-effort circular path, and the subject is asked to follow an elliptical trajectory. The control system produces a user-defined stiffness between the deviations from the neutral path and the torque applied by the subject. The trajectory and resistance settings used in the experiments were the orientation of the ellipse and a stiffness parameter. Multiple combinations of these parameters were used to measure their effects on the muscle effort distribution. An artificial neural network (ANN) used part of the data for training the model. Then, the accuracy of the model was evaluated using the rest of the data. The results show how the precision of the model is lost over time. These outcomes show the complexity of the muscle dynamics for long-term estimations suggesting the existence of time-varying dynamics possibly associated with fatigue.

The dynamical analysis for the motion of a harmonically two degrees of freedom damped spring pendulum in an elliptic trajectory

This article investigates the motion of two degrees of freedom non-linear dynamical system represented by a spring pendulum in which its suspension point moves in an elliptic trajectory. Lagrange's equations are utilized to derive the governing equations of motion in light of the generalized coordinates of this system. The asymptotic solutions for the governing equations of motion up to the third approximation are obtained using the multiple scales technique. The different resonance cases are classified according to the modulation equations. The steady-state solutions are verified in the presence of the solvability conditions. The time histories of the considered motion, the resonance curves, and steady-state solutions are presented graphically. In addition to the simulations of the non-linear equations of the system's evolution, the stability criteria are carried out. The stability and instability regions are investigated, in which it is found the behaviour of the system is stable for a large number of the system’s parameters. In various engineering applications, a better understanding of the vibrational motion near resonance is critical, in which it can be avoided continued exposure to events that can cause severe damage.

Tracking Control of a Miniature 2-DOF Manipulator With Hydrogel Actuators

Due to the nature of the complex spatiotemporal dynamics of stimuli-responsive soft materials, closed-loop control of hydrogel-actuated mechanisms has remained a challenge. This letter demonstrates, for the first time, closed-loop trajectory tracking control in real-time of a millimeter-scale, two degree-of-freedom manipulator via independently-controllable, temperature-responsive hydrogel actuators. A linear state-space model of the manipulator is developed from input-output measurement data, enabling the straightforward application of control techniques to the system. The Normalized Mean Absolute Error (NMAE) between the modeled and measured displacement of the manipulator's tip is below 10%. We propose an Observer-based controller and a robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller and evaluate their performance in a trajectory tracking output-feedback framework, compared with and without sinusoidal disturbances and noise. We demonstrate in simulation that the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller, which is computed using Linear Matrix Inequality (LMI) methods, tracks an elliptical trajectory more accurately than the Observer controller and is more robust to disturbances and noise. We also show experimentally that the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller can be used to track different trajectories with an NMAE below 15%, even when the manipulator is subject to a 3 g load, 12.5 times an actuator's weight. Finally, a payload transport scenario is presented as an exemplar application; we demonstrate that an array of four manipulators is capable of moving a payload horizontally by applying the proposed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal trajectory-tracking controller to each manipulator in a decoupled manner.

Flexible power control strategy for elliptical trajectory based dynamic voltage restorer during voltage sags

Dynamic voltage restorer (DVR) plays an essential role in achieving high-quality voltage restoration in the distribution system. This paper presents an elliptical-trajectory-based approach to guarantee continuous power delivery by considering the active and reactive power limits during voltage sags. Besides, two parameters are proposed in the accurate mathematical analysis of current references. Thus, the control objective can be fulfilled by the flexible current injection strategy that combines a precise balance between the positive and negative sequences. The proposed control method can determine the required power injections by selecting the two proper values to support that the converter output current is smaller than the maximum rated value. Under the presented control, the maximum power limit and flexible power dispatch are combined together to develop four operation schemes. The main advantage is the smooth transition process during changes in the operation schemes and the disappearance of active and reactive power oscillations. Also, these four control states are applied to reveal the flexibility of the proposed designs. Finally, the hardware tests in a laboratory prototype are implemented to validate the feasibility of the proposed method.

Brainless Walking: Animal Gaits Emerge From an Actuator Characteristic.

In this study, we discovered a phenomenon in which a quadruped robot without any sensors or microprocessor can autonomously generate the various gait patterns of animals using actuator characteristics and select the gaits according to the speed. The robot has one DC motor on each limb and a slider-crank mechanism connected to the motor shaft. Since each motor is directly connected to a power supply, the robot only moves its foot on an elliptical trajectory under a constant voltage. Although this robot does not have any computational equipment such as sensors or microprocessors, when we applied a voltage to the motor, each limb begins to adjust its gait autonomously and finally converged to a steady gait pattern. Furthermore, by raising the input voltage from the power supply, the gait changed from a pace to a half-bound, according to the speed, and also we observed various gait patterns, such as a bound or a rotary gallop. We investigated the convergence property of the gaits for several initial states and input voltages and have described detailed experimental results of each gait observed.

Dynamics analysis of ellipsoid in a dual-beam fiber-optic trap with transverse offset

For an ellipsoid suspended in a dual-fiber optic trap with transverse offset, the optical force, torque and posture are theoretically analyzed. When importing a transverse offset between two fibers, in the water environment, the azimuthal angle between the long axis and the optical axis increases with the offset distance. In the vacuum environment, the ellipsoid will spin in the trap center. When the offset is great than the threshold, the ellipsoid will move around the trap center along an elliptic trajectory, accompanied with the spin motion. The results will contribute to better understanding of the spin motion in the transversely misaligned dual-beam fiber-optic trap.

Significance of Slippage and Electric Field in Mucociliary Transport of Biomagnetic Fluid

Shear stress at the cilia wall is considered as an imperative factor that affects the efficiency of cilia beatings as it describes the momentum transfer between the fluid and the cilia. We consider a visco-inelastic Prandtl fluid in a ciliated channel under electro-osmotic pumping and the slippage effect at cilia surface. Cilia beating is responsible for the stimulation of the flow in the channel. Evenly distributed cilia tend to move in a coordinated rhythm to mobilize propulsive metachronal waves along the channel surface by achieving elliptic trajectory movements in the flow direction. After using lubrication approximations, the governing equations are solved by the perturbation method. The pressure rise per metachronal wavelength is obtained by numerically integrating the expression. The effects of the physical parameters of interest on various flow quantities, such as velocity, pressure gradient, pressure rise, stream function, and shear stress at the ciliated wall, are discussed through graphs. The analysis reveals that the axial velocity is enhanced by escalating the Helmholtz–Smoluchowski velocity and the electro-osmosis effects near the elastic wall. The shear stress at the ciliated boundary elevates with an increase in the cilia length and the eccentricity of the cilia structure.

Efficient sliding locomotion of three-link bodies.

We study the efficiency of sliding locomotion for three-link bodies with prescribed joint angle motions. The bodies move with no inertia, under dry (Coulomb) friction that is anisotropic (different in the directions normal and tangent to the links) and directional (different in the forward and backward tangent directions). Friction coefficient space can be partitioned into several regions, each with distinct types of efficient kinematics. These include kinematics resembling lateral undulation with very anisotropic friction, small-amplitude reciprocal kinematics, very large-amplitude kinematics near isotropic friction, and kinematics that are very asymmetric about the flat state. In the two-parameter shape space, zero net rotation for elliptical trajectories occurs mainly with bilateral or antipodal symmetry. These symmetric subspaces have about the same peak efficiency as the full space but with much smaller dimension. Adding the second or third harmonics greatly increases the numbers of local optimal for efficiency, but only modestly increases the peak efficiency. Random ensembles with higher harmonics have efficiency distributions that peak near a certain nonzero value and decay rapidly up to the maximum efficiency. A stochastic optimization algorithm is developed to compute optima with higher harmonics. These are simple closed curves, sharpened versions of the elliptical optima in most cases, and achieve much higher efficiencies mainly for small normal friction. With a linear (viscous) resistance law, the optimal trajectories are similar in much of the friction coefficient space, and relative efficiencies are much lower except with very large normal friction.

Spin angular momentum of gravitational wave interference

Spin angular momentum (SAM) is an important feature for wave systems, prominent in various properties like spin-momentum locking of wave propagations. Here, we study the SAM of gravitational waves in general relativity based on the Noether theorem in classical field theory. We demonstrate gravitational wave spin in various interference cases and evanescent waves, which is manifested as locally rotating metric perturbations, driving particles on geodesic spheroid locally deformed in elliptical trajectories. For non-polarized gravitational wave modes of zero SAM, their superpositions can induce nonzero density of SAM with interfered patterns. The evanescent gravitational wave shows clear SAM, which is also a consequence of wave interference between propagating and transverse evanescent components. The spin-momentum locking relations are clearly present for all different interference cases of wave modes and components based on general relativity.

Guiding center and gyrokinetic orbit theory for large electric field gradients and strong shear flows

The guiding center and gyrokinetic theory of magnetized particle motion is extended to the regime of large electric field gradients perpendicular to the magnetic field. A gradient in the electric field directly modifies the oscillation frequency and causes the Larmor orbits to deform from circular to elliptical trajectories. In order to retain a good adiabatic invariant, there can only be strong dependence on a single coordinate at lowest order, so that resonances do not generate chaotic motion that destroys the invariant. When the gradient across magnetic flux surfaces is dominant, the guiding center drift velocity becomes anisotropic in response to external forces and additional curvature drifts must be included. The electric polarization density remains gyrotropic, but both the polarization and magnetization are modified by the change in gyrofrequency. The theory can be applied to shear flows that are even stronger than those observed in the edge transport barrier of a high-performance tokamak (H-mode) pedestal, even if the toroidal field is as small as or even smaller than the poloidal field. Yet, the theory retains a mathematical form that is similar to the standard case and can readily be implemented within existing simulation tools.

Real-time optimization of an ellipsoidal trajectory orientation using muscle effort with Extremum Seeking Control

We present an approach for real-time model-free optimization of the orientation of the elliptical trajectory. The performance is evaluated in simulation and experimental stages. Our model-free approach is based on the use of Extremum Seeking Control (ESC) as the real-time optimizer. The experimental stage is performed using a 4 degrees-of-freedom robot and its impedance control system to create advanced exercise protocols whereby the user is asked to follow a path against the machine’s neutral path and resistance. Another model-free approach based on the use of the global optimizer Biogeography-based optimization (BBO) was previously reported for simulation results. This last framework has a good performance as a result of exhaustive searches but with a high computational cost limiting its use on real-time experiments. The performance of the ESC approach was validated by comparing the results with those of BBO using five different arm models representing real human arms. In the real-time experiments, muscle activations representing the participation of each muscle in the training activity were measured with electromyography sensors (EMG) and real-time processed from raw signals. The muscle objective can be professionally selected by a therapist to emphasize or de-emphasize certain muscle groups. The robot establishes a zero-effort circular path, and the subject is asked to follow an elliptical trajectory. The control system produces a user-defined stiffness between the deviations from the neutral path and the force/torque applied by the subject. The results show that the framework was able to successfully find the optimal ellipsoidal orientation converging to similar solutions in short period trials of 50 s.