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• A novel configuration with an inner stator is proposed to create a great compressed structure. • The magnetic field acts directly on the free end of the flexspline, so that a large deformation can be obtained. • The nonlinear dynamic equations of the flexspline are established, and analysis results for the chaos are obtained. • The influence of parameters on the chaos of the flexspline is revealed to provide a theoretical reference. To develop the miniaturization of the electromagnetic harmonic movable tooth drive system, a novel configuration with an inner stator is proposed to create a great compressed structure. To avoid undesirable design parameters that lead to bifurcation and chaotic behavior of the flexspline, the nonlinear dynamic equations of the flexspline are established, and the Duffing equation and analysis results for the chaotic vibration of the flexspline are obtained by using the Donnell-Karman theory of thin-walled cylindrical shells with employing large deflection, the Bubnov-Galerkin principle, and the Melnikov function, separately. According to initial system parameters, based on the bifurcation diagrams, phase diagrams, displacement time course diagrams, and Poincare maps of the flexspline vibration, the dynamic behaviors are investigated, and the stability and chaos intervals are obtained. This study aims to reveal the influence of parameters on the chaotic phenomenon of the flexspline and to provide a theoretical reference for the design of the electromagnetic movable teeth drive. [ABSTRACT FROM AUTHOR]

• Inspired by the skin and hair, a multiple-directional PEH device was proposed. • The dynamics model of the PEH device was established and solved the solution. • It can collect multi-directional energy with spatial internal resonance. • With the increase of the excitation level, its bandwidth further improves. To improve the ability of piezoelectric energy collection (PEH) devices to convert multi-directional energy sources, a body hair-inspired multi-directional broadband piezoelectric energy harvester with spatial internal resonance effect is proposed. It is constructed from a zigzag beam and a rigid pendulum. The motion of the pendulum in three orthogonal directions causes bending deformation of the fixed-end of the zigzag beam. Furthermore, the system can also achieve internal resonances in all three directions, broadening the system bandwidth. This paper presents the configuration and working principle inspired by this concept along with the dynamic equations of its electromechanical system. The resulting analytical and numerical solutions are given. The forced responses of the system at spatial internal resonance under different excitation levels were analyzed in the frequency domain. The prototype was fabricated and the experimental setup was built up to measure the output characteristics. Experimental results show that the proposed PEH device can achieve spatial multi-degree-of-freedom collection of vibration energy and provide stable and considerable voltage output levels under excitation in three orthogonal directions. Moreover, the working bandwidth of the system increases with the increase of external excitation level. The proposed PEH device exhibits high energy harvesting capability and potential application in complex excitation environments. [ABSTRACT FROM AUTHOR]

Planar movable tooth drives are compact in structure and simple in processing technology. However, the speed ratio of the single-stage drive is small, whereas the size of the double-stage drive is large. To obtain a planar movable tooth drive with small size and large speed ratio, a two-stage planar movable tooth drive with integrated structure is proposed. For it, the quasi-static force analysis is completed, and the equations of the force distribution and output torque for the drive are derived. According to Hertz's theory of point contact, the equation for the contact stress in the drive is given. Using these equations, the distribution of forces and output torque in the drive is studied. Changes of forces and torque distribution with main parameters are revealed. The contact stress of the drive is calculated under a given load. The finite element analysis software is used to simulate the contact stress of the drive, and the theoretical calculation is verified. [ABSTRACT FROM AUTHOR]

To explore a noncontact drive solution for linear piezoelectric actuators, a novel type of noncontact linear piezoelectric actuator modulated by the electromagnetic field is proposed. The proposed actuator employs electromagnetic force to modulate and transfer the locomotion between the stator and the runner. The drive scheme reduces the wear and friction between the stator and the runner and can control the coupling force by the electric system. Here, the design pattern and working principles are described. The amplification ratio equation of the flexible amplification mechanism is established, and the calculation method of the dynamic electromagnetic force is illustrated. For assessing the validity and measure the output characteristics of the proposed actuator, a prototype is fabricated to measure the output speeds, the stepping distances, and the output forces. The experimental results show the actuator with the driving frequency of 1 Hz, the electromagnetic modulation voltage of 4 V, and the piezoelectric driving voltage of 100 V can continuously output a stall load force of about 0.15 N and speed of 0.33 mm/s. [ABSTRACT FROM AUTHOR]

For a non-contact piezoelectric motor modulated by an electromagnetic field, the design scheme of a piezoelectric micro-displacement amplifying mechanism is described. The relation formula between the output displacement of piezoelectric stacks and the output angle of the mechanism are given. Using the theory of electromagnetism, the static output torque equation of electromagnetic coupling mechanism based on the output angle of the piezoelectric amplifying mechanism is established, and the effect of system parameters on the static output moment is analyzed. Considering this piezoelectric motor driven by a square wave signal, the dynamic output torque equation of the non-contact piezoelectric motor is established, and the effect of system design parameters on the dynamic output torque is revealed. The analysis results show that the different output step precisions of the piezoelectric motor can be obtained by adjusting the length of the bar 1. A reasonably selected output angle is beneficial to increase electromagnetic torque. When the air gap is reduced to improve the torque, a larger output torque can be obtained by designing a reasonable output angle. At a certain amplitude of modulation voltage, the reasonable combination of external resistance and modulation signal frequency is beneficial to the design of an ideal dynamic torque response waveform and larger dynamic torque amplitude. The above analysis results can lay a theoretical foundation for the design of a high-performance non-contact piezoelectric motor modulated by electromagnetic and the optimization of the drive scheme. [ABSTRACT FROM AUTHOR]

For improving the service life of piezoelectric motors and the performance of noncontact piezoelectric motors, a novel noncontact piezoelectric motor modulated by the electromagnetic field is proposed. This type of piezoelectric motor uses an electromagnetic field to modulate the reciprocating vibrations of a piezoelectric drive mechanism to form the step motion of the rotor. The working principle and structural design of the piezoelectric motor are described in detail. A prototype motor is manufactured and the test system of output characteristics is established. An experiment of the output characteristics was carried out for exploring the driving scheme under different parameters of the drive signals. The results state that the proposed motor has a rotational speed of 0.038 rad/s, step angle of approximately 1°, output torque of 6 $\text{N}\cdot $ mm under the drive voltage of 150 V, frequency of 3 Hz, and modulation voltage of 7 V. [ABSTRACT FROM AUTHOR]

With the increased motion requirements of precision drive devices, multi-degree-of-freedom piezoelectric actuators have become key technologies for realizing multi-axis motion control. To expand upon the three-degree-of-freedom piezoelectric stick-slip driving method, a sandwich-type three-degree-of-freedom rotating inertial stick-slip piezoelectric actuator is proposed in this paper. Firstly, the structure and control strategy of the actuator were introduced. Statics analysis of the core component of the piezoelectric vibrator was carried out, and the relationship between the structural parameters and the deformation of the driving foot was obtained. Then the free and forced vibrations of the piezoelectric vibrator are analyzed to determine the dynamic response of the driving foot in the time domain. Finally, a prototype was fabricated and an experimental system was built to test its output characteristics. The test results show that when the driving voltage was 150 V and the frequency was 320 Hz, the proposed actuator achieves maximum speeds and load torques around the x- axis and y- axis of 306 mrad/s and 2 mN m, respectively. When the driving voltage was 150 V and the frequency was 450 Hz, the proposed actuator achieves a maximum speed and load torque around the z-axis of 140 mrad/s and 1.55 mN m, respectively. [Display omitted] • A piezoelectric actuator with three-degree-of-freedom motion is proposed. • The problem of structural redundancy caused by increasing the preload is solved. • The vibrator's dynamics model is established, solved, and analyzed. • Load capacity and speed are superior to the same type of actuator. [ABSTRACT FROM AUTHOR]

Several theoretical studies on modal superposition methods to achieve tactile differentiation have been reported. However, there is still a lack of in-depth analysis and understanding of the regularity of the superposition of vibration modes and the resulting differences in tactile sensation. The touch beam vibrations are no longer in the form of standing waves after the modal superposition. The vibration points on the touch beam will present a periodic motion over time, instead of simply moving harmonically. The vibration response of the touch beam at high frequency, gave subjects a dramatically different tactile perception from that of a single inherent mode. Therefore, this paper reshapes the modal superposition theory of the haptic feedback technique to classify the vibration modes generated by the modal superposition of touch beams showing differences in tactile sensations considering the time course. The analysis and tactile texture prediction theories are improved compared to previous studies. The tactile sensation generated by the vibration patterns of left-right sway were found in the touch beam. Finally, the correctness of the tactile differentiation achieved by the modal superposition method was demonstrated by psychophysical assessment for different finger conditions. [ABSTRACT FROM AUTHOR]

The coupled dynamic equations for an electromechanical integrated harmonic piezoelectric motor are proposed in this study. The vibration responses of the proposed motor are then determined using these equations. The mathematical models of dynamic optimization are established using the multi-objective optimization method. The optimal parameters are obtained through optimization. The vibration displacements are compared with the initial values. The effects of the parameters on the optimized amplitudes are also investigated. Results show that the vibration displacements of the piezoelectric motor decrease by over 89 % after dynamic optimization. These results can be used to improve the performance and decrease the vibration of the piezoelectric motor. [ABSTRACT FROM AUTHOR]

For a non-contact piezoelectric driving system modulated by electromagnetic field, the dynamic equations of the driving system under coupling excitation are deduced. Using the Duhamel’s integral, forced response of displacement in the time-domain and frequency-domain were investigated, and the influence of some system parameters on the displacement response is analyzed. The results show that in the same excitation frequency, the displacement responses of the driving beams is the most significant, and the vibration response of the central shaft is relatively less obvious. The larger displacement responses of the driving beam end is beneficial to increasing the step angle of the driving system, and the smaller vibration of the central is beneficial to stable torque output of drive system. Therefore, the design of this structure is more reasonable. The results are useful for design of the operating performance of the driving system. [ABSTRACT FROM AUTHOR]

The mesh-type harmonic piezoelectric motor has advantages of low speed, large torque and long lifetime. However, the nonlinear axial forces of driving part affect the dynamic performance of the motor, which can result in a motor with a deteriorated load-capability. Hence, to deal with the above problem, the effects of nonlinear axial forces on chaotic vibration are investigated in this paper. Firstly, applying dynamic theory of continuous system, the nonlinear dynamic equations contains nonlinear axial forces of the driving system for a mesh-type piezoelectric motor are established. And then, using Runge-Kutta numerical method, the effects of nonlinear axial forces on chaotic vibrations of the system are investigated. The results show that the chaotic vibrations occur in driving system of the motor under some parameters. The vibration displacements of the driving system become larger when considering nonlinear axial forces of displacement amplification mechanism. Under the effect of nonlinear axial forces, the chaotic vibrations occur easily when the system parameter is much smaller. The results can be used to predict the dynamic load and optimize power density of the mesh-type harmonic piezoelectric motor. [ABSTRACT FROM AUTHOR]

The nonlinear dynamic equations of the drive system for movable tooth piezoelectric motor are established. Using these equations, the chaotic vibrations of the system are investigated. The results show that chaotic vibrations occur in the movable tooth drive system under some parameters. The average mesh stiffness, theoretical radius, and wave generator offset significantly influence the nonlinear chaotic vibrations of the drive system of the movable tooth piezoelectric motor. The ranges for the system parameters that lead to a motor with bad dynamics are shown. The results can be used to predict the dynamic load and optimize power density of the proposed piezoelectric motor. [ABSTRACT FROM AUTHOR]

For a novel inertial piezoelectric rotary motor, the equation of the voltage response on the piezo-ceramic bimorph under the excitation signals is deduced and the dynamic equation of the motor rotor is given. Using the equations, the voltage responses on the piezo-ceramic bimorph and the responses of the displacement, velocity and acceleration on the rotor to the sawtooth voltage excitation are investigated. The results show that when the frequency of the excitation signal is quite low, the waveform of the displacement response of the rotor is identical to one of the excitation signal; the outer diameter of the rotor, its length and thickness, etc., have obvious effects on the inertial moment applied to the rotor. The results are useful for design and control of the operating performance of the motor. [ABSTRACT FROM AUTHOR]

To delve deeper into the phylogenetic relationships within Cicadellidae and the taxonomic arrangement of Evacanthinae, our study focuses on the mitochondrial genome sequencing of five Nivanini species: Extensus latus, Concavepiana hamulusa, Sophonia nigrilineata, Sophonia microstaina, and Sophonia fuscomarginata. The results showed that the length of the five mitochondrial genomes ranged from 15,610 to 16,032 bp and included 37 typical genes. The A + T content of Nivanini ranged from 72.5% to 78.7%, which is consistent with that of other sequenced Evacanthinae species. All transfer RNAs (tRNAs) exhibit the typical cloverleaf secondary structure, except for trnS (AGY), which lacks the dihydrouracil (DHU) arm. With regard to protein‐coding genes, all started with ATN codons, except for atp8, and most of them use TAA or TAG as termination codons. Using the Bayesian inference and maximum likelihood methods, a phylogenetic tree based on all 37 genes was constructed, with a total of 57 Cicadellidae species and two outgroups included as research objects. The analyses confirmed the monophyletic nature of each subfamily, highlighting Deltocephalinae as the oldest, distinctively parallel to the others. [ABSTRACT FROM AUTHOR]

In this paper, the structural design and driving mechanism of a non-contact piezoelectric motor modulated by electromagnetic force are introduced. The equations of the electromagnetic force and torque of the electromagnetic modulation mechanism for the motor are deduced. Based on the piezoelectric constitutive equation and torque balance equations of the driving system, the equation of the piezoelectric driving torque is also obtained. Using these equations, the influences of the related parameters on the relationship between electromagnetic torque and angle difference between pole and rotor are studied. The influences of the main parameters and signal frequency on piezoelectric driving torques are analyzed. Based on them, the torque optimization of the motor is completed and the load-carrying ability of the motor is increased by about 50 times. A prototype of the motor is developed. Its output torque is tested and compared with calculated one which illustrates the theoretical model here. [ABSTRACT FROM AUTHOR]

• A novel non-resonant harmonic piezoelectric motor is proposed. • The electromechanical coupling dynamic models and equations of the proposed non-resonant piezoelectric motor are developed. • The influence of parameters on natural frequency and resonant response is analyzed. • The natural frequencies of the motor are tested by building an experimental platform. Most of the traditional piezoelectric motors are driven by the resonance of piezoelectric ceramics and can achieve a large output torque. However, these motors also have the defects of high speed and difficulty to adjusting the speed when working. To overcome these issues, a novel non-resonant harmonic rotary piezoelectric motor operating at low speed is presented. Electromechanically coupled vibration has a great influence on the dynamic performance of the piezoelectric motor, which may lead to instability of the output performance of the motor. Therefore, the electromechanical coupling dynamic characteristics of the proposed non-resonant piezoelectric motor are studied in this paper. The working principle of the motor is illustrated, and the electromechanical dynamic model and nonlinear dynamic equations are established. Utilizing the dynamic equations, the coupled natural frequencies, amplitude-frequency characteristics, and dynamic responses of the motor are developed. Meanwhile, the influence of parameters on natural frequency and nonlinear response is analyzed. What's more, the natural frequencies of the system are tested by building an experimental platform. Results show the minimum coupled natural frequency of the motor is 11231 rad/s. The length of the piezoelectric stack, the length, and mass block of the harmonic rod have an important influence on the natural frequency of the proposed non-resonant harmonic piezoelectric motor. The nonlinear piezoelectric effect has a larger effect on the forced response amplitude when the excitation frequency is far away from resonance, but a smaller effect on the forced response amplitude when the excitation frequency is near resonance. What's more, the maximum error between the theoretical natural frequencies and the test frequencies is 3%, which verifies the correctness of the theoretical model. [ABSTRACT FROM AUTHOR]

The phylogenetic relationships among the nymphalid subfamilies have largely been resolved using both morphological and molecular datasets, with the exception of a conflicting basal clade position for Libytheinae or Danainae that remains contentious between morphological and molecular studies. Several phylogenomic analyses have found that the danaine clade is sister to other nymphalid subfamilies; however, it largely depends on utilizing different molecular datasets, analysis methods, and taxon sampling. This study aimed to resolve the basal clade position and relationships among subfamilies and tribes of Nymphalinae by combining the most comprehensive available mitogenomic datasets with various analyses methods by incorporating a new Symbrenthia lilaea Hewitson sequence data. Phylogenetic relationships among 11 nymphalid subfamilies and the tribes of Nymphalinae were inferred by combining new and available mitogenomic sequence data from 80 ingroup and six outgroup species. The phylogenetic trees were reconstructed using maximum‐likelihood (ML) and Bayesian inference (BI) methods based on five concatenated datasets: amino acid sequences and nucleotides from different combinations of protein‐coding genes (PCGs), ribosomal RNA (rRNAs), and transfer RNA (tRNAs). Danainae is well‐supported as the basal clade and sister to the remaining nymphalid subfamilies, except for the paraphyletic Libytheinae. Libytheinae was either recovered as a sister to the danaine clade followed by the satyrine clade or sister to the nymphaline + heliconiine clades, and is consistent with recent phylogenetic studies on Nymphalidae. The monophyletic Nymphalinae has been recovered in all analyses and resolves tribal‐level relationships with high support values in both BI and ML analyses. We supported the monophyletic Nymphalini as a sister clade to Victorini, Melitaeini, and Kallimini + Junoniini with high supporting values in BI and ML analyses, which is consistent with previously published morphological and molecular studies. [ABSTRACT FROM AUTHOR]

To increase the output displacement of the linear piezoelectric actuator, a linear piezoelectric actuator with large displacement and three operation modes is proposed. The operating principle of the piezoelectric actuator is presented. The magnification factor of the displacement amplification mechanism is deduced and verified by finite element analysis. To improve the output precision of the actuator, a feedforward PID control model is established. Based on the experimental test platform, the output characteristics of the piezoelectric actuator are tested. Results show the maximum output displacement of the piezoelectric actuator is 558.3 μm under a driving voltage of 150 V with two piezoelectric stacks. When the driving frequencies are less than 3 Hz, the control accuracy of feedforward PID is higher than that of PID, and the error between the measured displacement and the ideal value is less than 10% after applying the control to the piezoelectric actuator. [ABSTRACT FROM AUTHOR]