Ultrahigh Electro-Bending Deformation in Lead-free Piezoelectric Ceramics via Defect Concentration Gradient Design.

Recent breakthroughs in defect-engineered lead-free piezoelectric ceramics have reported remarkable electro-strain values, surpassing the limit of lattice distortion. This has aroused wide concern on bending deformation and the associated underlying mechanism. Herein, via designing lead-free piezoelectric ceramics with varying volatilization characteristics, it is uncovered that the ultrahigh electro-bending deformation is primarily attributed to a large strain gradient induced by unevenly distributed defect dipoles. In 0.5mm-thick Sr/Sn co-doped potassium sodium niobate ceramics featuring volatile K/Na elements, the inherent bipolar electro-strain value can reach 0.3% at 20 kV cm-1 due to the existence of defect dipoles, while the gradient distribution of defect dipole generates significant bending displacement, amplifying apparent electro-strain value to 1.1%. Notably, non-volatile Ba0.99TiO2.99 ceramic with homogeneous defect dipole distribution does not present electro-bending. Of particular interest is that the electro-bending phenomenon can be observed through introducing a defect dipole gradient into barium titanate ceramic. A monolayer ceramic with defect dipole gradient can generate large tip displacement (±1.5 mm) in cantilever structure, demonstrating its promising potential in precise positioning. This study delves into the underlying mechanism driving electro-bending deformation and its impact on the apparent electro-strain measurement in defect-engineered piezoelectric ceramics, providing fresh perspectives for the development of piezoelectric bending actuators. This article is protected by copyright. All rights reserved.

A Single-Clamp Inchworm Actuator with Two Piezoelectric Stacks.

Inchworm piezoelectric actuators have attracted much attention in the field of precision positioning due to the advantages of a large stroke, high output force, and high resolution. However, traditional inchworm piezoelectric actuators use two sets of clamps and a set of drive structures to achieve stepping motion, which generally requires at least three piezoelectric stacks, resulting in a complex structure and the control system. Several methodologies have been advanced to minimize the utilization of piezoelectric stacks. However, there still exists the issue of excessive volume. Therefore, an inchworm piezoelectric actuator with a single-clamp and single drive structure is proposed in the study, which provides a compact size and smaller volume. The clamping mechanism comprises two sets of clamping feet with opposite displacement, which alternate contact with the guide frame and adjustable plate to ensure that the clamping mechanism always has frictional force and accomplishes the stepping motion. The testing of the actuator's step distance, output force, and other parameters was conducted utilizing a displacement sensor. Experimental results indicate that the actuator achieved a maximum speed of 174.3 µm/s and an output force of 8.6 N when the frequency and voltage were 19 Hz and 150 V.

Combined Control for a Piezoelectric Actuator Using a Feed-Forward Neural Network and Feedback Integral Fast Terminal Sliding Mode Control.

In recent years, there has been significant interest in incorporating micro-actuators into industrial environments; this interest is driven by advancements in fabrication methods. Piezoelectric actuators (PEAs) have emerged as vital components in various applications that require precise control and manipulation of mechanical systems. These actuators play a crucial role in the micro-positioning systems utilized in nanotechnology, microscopy, and semiconductor manufacturing; they enable extremely fine movements and adjustments and contribute to vibration control systems. More specifically, they are frequently used in precision positioning systems for optical components, mirrors, and lenses, and they enhance the accuracy of laser systems, telescopes, and image stabilization devices. Despite their numerous advantages, PEAs exhibit complex dynamics characterized by phenomena such as hysteresis, which can significantly impact accuracy and performance. The characterization of these non-linearities remains a challenge for PEA modeling. Recurrent artificial neural networks (ANNs) may simplify the modeling of the hysteresis dynamics for feed-forward compensation. To address these challenges, robust control strategies such as integral fast terminal sliding mode control (IFTSMC) have been proposed. Unlike traditional fast terminal sliding mode control methods, IFTSMC includes integral action to minimize steady-state errors, improving the tracking accuracy and disturbance rejection capabilities. However, accurate modeling of the non-linear dynamics of PEAs remains a challenge. In this study, we propose an ANN-based IFTSMC controller to address this issue and to enhance the precision and reliability of PEA positioning systems. We implement and validate the proposed controller in a real-time setup and compare its performance with that of a PID controller. The results obtained from real PEA experiments demonstrate the stability of the novel control structure, as corroborated by the theoretical analysis. Furthermore, experimental validation reveals a notable reduction in error compared to the PID controller.

Development and Improvement of a Piezoelectrically Driven Miniature Robot.

In this paper, we proposed a miniature quadrupedal piezoelectric robot with a mass of 1.8 g and a body length of 4.6 cm. The robot adopts a novel spatial parallel mechanism as its transmission. Each leg of the robot has two degrees of freedom (DOFs): swing and lift. The trajectory necessary for walking is achieved by the appropriate phasing of these two DOFs. A new manufacturing method for piezoelectric actuators was developed. During the stacking process, discrete patterned PZT pieces are used to avoid dielectric failure caused by laser cutting. Copper-clad FR-4 is used as the solder pad instead of copper foil, making the connection between the pad and the actuator more reliable. The lift powertrain of the robot was modeled and the link length of the powertrain was optimized based on the model. The maximum output force of each leg can reach 26 mN under optimized design parameters, which is 1.38 times the required force for successful walking. The frequency response of the powertrain was measured and fitted to the second-order system, which enabled increased leg amplitudes near the powertrain resonance of approximately 70 Hz with adjusted drive signals. The maximum speed of the robot without load reached 48.66 cm/s (10.58 body lengths per second) and the payload capacity can reach 5.5 g (3.05 times its mass) near the powertrain resonance.

Feasibility of Parylene C for encapsulating piezoelectric actuators in active medical implants.

Parylene C is well-known as an encapsulation material for medical implants. Within the approach of miniaturization and automatization of a bone distractor, piezoelectric actuators were encapsulated with Parylene C. The stretchability of the polymer was investigated with respect to the encapsulation functionality of piezoelectric chips. We determined a linear yield strain of 1% of approximately 12-µm-thick Parylene C foil. Parylene C encapsulation withstands the mechanical stress of a minimum of 5×105 duty cycles by continuous actuation. The experiments demonstrate that elongation of the encapsulation on piezoelectric actuators and thus the elongation of Parylene C up to 0.8 mm are feasible.

Modeling and Analysis of a Conical Bridge-Type Displacement Amplification Mechanism Using the Non-Uniform Rational B-Spline Curve.

This paper presents a new analytical model of a conical bridge-type displacement amplification mechanism (DAM) considering the effect of external loads and a piezostack actuator (PSA). With the merits of simple implementation and better fitting, the non-uniform rational B-spline (NURBS) is employed to parameterize conical connecting beams of the DAM, and an analytical model of the displacement amplification ratio and input stiffness is established based on Castigliano's second theorem. After that, considering the interactions with elastic loads and PSA, the actual displacement amplification ratio of the conical DAM is obtained, and the effect of the shape of connecting beams in the performance of the DAM is further analyzed. The proposed analytical model is verified by finite element analysis (FEA), and the results show a maximum error of 6.31% between the calculated value and FEA results, demonstrating the accuracy of the proposed model. A prototype of the conical DAM with optimized shape is fabricated and experimentally tested, which further validates the effectiveness and accuracy of the proposed analytical model. The proposed model offers a new method for analysis and shape optimization of the bridge-type DAM under specific elastic loads.

Design and Control of a Trapezoidal Piezoelectric Bimorph Actuator for Optical Fiber Alignment.

To align a pair of optical fibers, it is required that the micro actuators used be small and have the characteristics of high accuracy and fast response time. A trapezoidal piezoelectric bimorph actuator was proposed for pushing and pulling an optical fiber. Based on a mathematical model and finite element model established in this paper, we analyzed the output displacement and output force of the proposed trapezoidal piezoelectric actuator under the influence of structural parameters. Since the piezoelectric bimorph actuator had a hysteresis effect, we applied particle swarm optimization to establish a Prandtl-Ishlinskii (PI) model for actuator and parameter identification. Then, two control methods, namely feedforward control considering hysteresis effects and fuzzy proportional-integral-derivative (PID) control employing feedback, were proposed. Finally, a composite control model combining the two control methods with fewer tracking errors was designed. The results show that the output displacement of this actuator is larger than that of a rectangular one. Additionally, the fuzzy PID control has a lower response time (15 ms) and an overshoot (5%).

Haptic Feedback Device Using 3D-Printed Flexible, Multilayered Piezoelectric Coating for In-Car Touchscreen Interface.

This study focuses on the development of a piezoelectric device capable of generating feedback vibrations to the user who manipulates it. The objective here is to explore the possibility of developing a haptic system that can replace physical buttons on the tactile screen of in-car systems. The interaction between the user and the developed device allows completing the feedback loop, where the user's action generates an input signal that is translated and outputted by the device, and then detected and interpreted by the user's haptic sensors and brain. An FEM (finite element model) via ANSYS multiphysics software was implemented to optimize the haptic performance of the wafer structure consisting of a BaTiO3 multilayered piezocomposite coated on a PET transparent flexible substrate. Several parameters relating to the geometric and mechanical properties of the wafer, together with those of the electrodes, are demonstrated to have significant impact on the actuation ability of the haptic device. To achieve the desired vibration effect on the human skin, the haptic system must be able to drive displacement beyond the detection threshold (~2 µm) at a frequency range of 100-700 Hz. The most optimized actuation ability is obtained when the ratio of the dimension (radius and thickness) between the piezoelectric coating and the substrate layer is equal to ~0.6. Regarding the simulation results, it is revealed that the presence of the conductive electrodes provokes a decrease in the displacement by approximately 25-30%, as the wafer structure becomes stiffer. To ensure the minimum displacement generated by the haptic device above 2 µm, the piezoelectric coating is screen-printed by two stacked layers, electrically connected in parallel. This architecture is expected to boost the displacement amplitude under the same electric field (denoted E) subjected to the single-layered coating. Accordingly, multilayered design seems to be a good alternative to enhance the haptic performance while keeping moderate values of E so as to prevent any undesired electrical breakdown of the coating. Practical characterizations confirmed that E=20 V/µm is sufficient to generate feedback vibrations (under a maximum input load of 5 N) perceived by the fingertip. This result confirms the reliability of the proposed haptic device, despite discrepancies between the predicted theory and the real measurements. Lastly, a demonstrator comprising piezoelectric buttons together with electronic command and conditioning circuits are successfully developed, offering an efficient way to create multiple sensations for the user. On the basis of empirical data acquired from several trials conducted on 20 subjects, statistical analyses together with relevant numerical indicators were implemented to better assess the performance of the developed haptic device.

A Finite-Time Sliding-Mode Controller Based on the Disturbance Observer and Neural Network for Hysteretic Systems with Application in Piezoelectric Actuators.

Piezoelectric actuators (PEAs) have the benefits of a high-resolution and high-frequency response and are widely applied in the field of micro-/nano-high-precision positioning. However, PEAs undergo nonlinear hysteresis between input voltage and output displacement, owing to the properties of materials. In addition, the input frequency can also influence the hysteresis response of PEAs. Research on tracking the control of PEAs by using various adaptive controllers has been a hot topic. This paper presents a finite-time sliding-mode controller (SMC) based on the disturbance observer (DOB) and a radial basis function (RBF) neural network (NN) (RBF-NN). RBF-NN is used to replace the hysteresis model of the dynamic system, and a novel finite-time adaptive DOB is proposed to estimate the disturbances of the system. By using RBF-NN, it is no longer necessary to establish the hysteresis model. The proposed DOB does not rely on any priori knowledge of disturbances and has a simple structure. All the solutions of closed-loop systems are practical finite-time-stable, and tracking errors can converge to a small neighborhood of zero in a finite time. The proposed control method was compiled in C language in the VC++ environment. A series of comparative experiments were conducted on a platform of a commercial PEA to validate the method. According to the experimental results of the sinusoidal and triangular trajectories under the frequencies of 1, 50, 100, and 200 Hz, the proposed control method is feasible and effective in improving the tracking control accuracy of the PEA platform.

Precision Motion Control of a Piezoelectric Actuator via a Modified Preisach Hysteresis Model and Two-Degree-of-Freedom H-Infinity Robust Control.

The nonlinear hysteresis phenomenon can occur in piezoelectric-driven nanopositioning systems and can lead to reduced positioning accuracy or result in a serious deterioration of motion control. The Preisach method is widely used for hysteresis modeling; however, for the modeling of rate-dependent hysteresis, where the output displacement of the piezoelectric actuator depends on the amplitude and frequency of the input reference signal, the desired accuracy cannot be achieved with the classical Preisach method. In this paper, the Preisach model is improved using least-squares support vector machines (LSSVMs) to deal with the rate-dependent properties. The control part is then designed and consists of an inverse Preisach model to compensate for the hysteresis nonlinearity and a two-degree-of-freedom (2-DOF) H-infinity feedback controller to enhance the overall tracking performance with robustness. The main idea of the proposed 2-DOF H-infinity feedback controller is to find two optimal controllers that properly shape the closed-loop sensitivity functions by imposing some templates in terms of weighting functions in order to achieve the desired tracking performance with robustness. The achieved results with the suggested control strategy show that both hysteresis modeling accuracy and tracking performance are significantly improved with average root-mean-square error (RMSE) values of 0.0107 µm and 0.0212 µm, respectively. In addition, the suggested methodology can achieve better performance than comparative methods in terms of generalization and precision.

Macro Fiber Composite-Actuated Soft Robotic Fish: A Gray Box Model-Predictive Motion Planning Strategy Under Limited Actuation.

This work experimentally investigates a model-predictive motion planning strategy to impose oscillatory and undulation movements in a macro fiber composite (MFC)-actuated robotic fish. Most of the results in this field exploit sinusoidal input signals at the resonance frequency, which reduces the device's maneuverability. Differently, this work uses body/caudal fin locomotion patterns as references in a motion planning strategy formulated as a model-based predictive control (MPC) scheme. This open-loop scheme requires the modeling of the device, which is accomplished by deriving a gray box state-space model using experimental modal data. This state-space model considers the electromechanical coupling of the actuators. Based on the references and the model, the MPC scheme derives the input signals for the MFC actuators. An experimental campaign is carried out to verify two references for mimicking the locomotion patterns of a fish under limited actuation. The experimental results confirm the motion planning scheme's capability to impose oscillatory and undulation movements.

Modeling of Rapid Response Characteristics of Piezoelectric Actuators for Ultra-Precision Machining.

Piezoelectric actuators are characterized by high positioning accuracy, high stiffness and a fast response and are widely used in ultra-precision machining technologies such as fast tool servo technology and ultrasonic machining. The rapid response characteristics of piezoelectric actuators often determine the overall quality of machining. However, there has been little research on the fast response characteristics of piezoelectric actuators, and this knowledge gap will lead to low precision and poor quality of the final machining. The fast response characteristics of a piezoelectric actuator were studied in this work. Firstly, the piezoelectric actuator was divided into a no-load state and a load state according to the working state. A fast response analysis and output characteristic analysis were carried out, the corresponding dynamic model was established, and then the model was simulated. Finally, an experimental system was established to verify the dynamic model of the piezoelectric actuator's fast response by conducting an experiment in which the piezoelectric actuator bounces a steel ball. The experimental results verify the correctness of the model and show that the greater the cross-sectional area and height of the piezoelectric actuator, the higher the bouncing height of the ball, and the better the dynamic performance of the piezoelectric actuator. It is believed that this study has guiding significance for the application of the dynamic characteristics of piezoelectric actuators in the machining field.

Design and Experiment of a Clamping-Drive Alternating Operation Piezoelectric Actuator.

In recent years, piezoelectric actuators, represented by inertial and inchworm actuators, have been widely applied because of their high accuracy and excellent responsiveness. Despite the development of various piezoelectric actuators, there remain some flaws in this technology. The sticking point is that the piezoelectric actuators based on the friction driving principle are prone to unwanted backward motion when outputting stepping motion. It is thus urgent to explore solutions from the perspectives of principle and structure. In this paper, a clamping-drive alternating operation piezoelectric actuator is proposed, the two feet of which are driven by two piezoelectric stacks, respectively. Due to double-foot alternate drive guide movement, backward movement is prevented in theory. By adopting the double-layer stator structure, integrated processing and assembly are facilitated. Meanwhile, a double flexible hinge mechanism is installed in the stator to prevent the drive foot from being overturned due to ineffectiveness and premature wear. In addition, the stator is equipped with the corresponding preload mechanism and clamping device. After the cycle action mechanism of one cycle and four steps is expounded, a model is established in this study to further demonstrate the principle. With the prototype produced, a series of experiments are performed. In addition, the amplitude of actuation of the stator is tested through amplitude experiment. The performance of the stator is evaluated by conducting experiments in the alternating step and single step actuation modes. Finally, the test results are analyzed to conclude that the actuator operating in either of these two modes can meet the practical needs of macro and micro actuation.

Aluminum Nitride Out-of-Plane Piezoelectric MEMS Actuators.

Integrating microelectromechanical systems (MEMS) actuators with low-loss suspended silicon nitride waveguides enables the precise alignment of these waveguides to other photonic integrated circuits (PICs). This requires both in-plane and out-of-plane actuators to ensure high-precision optical alignment. However, most current out-of-plane electrostatic actuators are bulky, while electrothermal actuators consume high power. Thus, piezoelectric actuators, thanks to their moderate actuation voltages and low power consumption, could be used as alternatives. Furthermore, piezoelectric actuators can provide displacements in two opposite directions. This study presents a novel aluminum nitride-based out-of-plane piezoelectric MEMS actuator equipped with a capacitive sensing mechanism to track its displacement. This actuator could be integrated within PICs to align different chips. Prototypes of the device were tested over the range of ±60 V, where they provided upward and downward displacements, and achieved a total average out-of-plane displacement of 1.30 ± 0.04 µm. Capacitance measurement showed a linear relation with the displacement, where at -60 V, the average change in capacitance was found to be -13.10 ± 0.89 fF, whereas at 60 V the change was 11.09 ± 0.73 fF. This study also investigates the effect of the residual stress caused by the top metal electrode, on the linearity of the displacement-voltage relation. The simulation predicts that the prototype could be modified to accommodate waveguide routing above it without affecting its performance, and it could also incorporate in-plane lateral actuators.

A Single Oscillator-Excited Piezoelectric Actuator with Internal Contact Teeth.

The tail rotor of a helicopter, a crucial component, traditionally relies on a complex drive mode involving reducers and transmission gears. This conventional setup, with its lengthy transmission chain and numerous components, hinders miniaturization efforts. In response to this challenge, our paper presents a novel piezoelectric drive approach. Our objective was to suggest an innovative design capable of minimizing the components involved in the tail rotor drive. This design can be adjusted in size according to specific requirements and is effective up to a specified speed. Moreover, it facilitates the process of miniaturization and integration. The piezoelectric actuator's stator comprises an ultrasonic amplitude transformer, a ring, and three drive teeth. Utilizing the rod-like structure of the tail brace, the actuator is simplified by adhering ceramic sheets to it. The rotary piezoelectric actuator combines the first longitudinal mode of a rod with torus bending modes. The drive teeth then amplify the ring's displacement, facilitating rotor rotation. The resonant frequency and modal shape of the actuator were determined using the finite element method. Furthermore, an investigation was conducted to analyze the influence of the drive teeth positioning on the motion trajectory at the contact point. Theoretically, we infer that the declination angle of the drive tooth is a crucial parameter for achieving high speeds. To test our idea, we built three prototype stators with different drive tooth declination angles. Our actuator stands out for its cost-effectiveness, structural simplicity, compatibility with harmonic signals, and ease of miniaturization. It can be considered for the drive of the tail rotor of a microhelicopter.

Experimental Analysis of the Influence of Carrier Layer Material on the Performance of the Control System of a Cantilever-Type Piezoelectric Actuator.

The subject of this article is an experimental analysis of the control system of a composite-based piezoelectric actuator and an aluminum-based piezoelectric actuator. Analysis was performed for both the unimorph and bimorph structures. To carry out laboratory research, two piezoelectric actuators with a cantilever sandwich beam structure were manufactured. In the first beam, the carrier layer was made of glass-reinforced epoxy composite (FR4), and in the second beam, it was made of 1050 aluminum. A linear mathematical model of both actuators was also developed. A modification of the method of selecting weights in the LQR control algorithm for a cantilever-type piezoelectric actuator was proposed. The weights in the R matrix for the actuator containing a carrier layer made of stiffer material should be smaller than those for the actuator containing a carrier layer made of less stiff material. Additionally, regardless of the carrier layer material, in the case of a bimorph, the weight in the R matrix that corresponds to the control voltage of the compressing MFC patch should be smaller than the weight corresponding to the control voltage of the stretching MFC patch.

Modeling and Design Optimization of a New Piezoelectric Inchworm Actuator with Screw Clamping Mechanisms.

A new piezoelectric inchworm actuator with screw clamping mechanisms has been developed recently for the wing folding mechanism of a small unmanned aircraft where the actuator power density is a great concern. Considering that the prototype actuator was designed just with engineering intuition and the performance optimization through experimental developments would take a vast amount of cost and time, a mathematical model was developed to investigate the actuator's critical design parameters and optimize its presently undesirable performance. Based on the lumped parameter method reported previously, and taking full account of the detailed modeling of the complex actuator housing and the actual nonlinear behaviors from the high-force contact and friction occurring at the screw-nut interface, as well as the output performance of the main drive elements including the piezoelectric stack and hollow ultrasonic motors (HUSMs), this model was built and then was experimentally verified for its accuracy and availability. Finally, nine design parameters were studied for their individual effect on the actuator's output using the proposed model. The simulation results indicate that the performance can be considerably improved by performing a slight modification to the prototype, and the dynamic modeling and parameter optimization methods used in this study can also serve as a useful reference for the design of similar piezoelectric inchworm actuators with intermittent clamping behaviors.

Intelligent Predictive Solution Dynamics for Dahl Hysteresis Model of Piezoelectric Actuator.

Piezoelectric actuated models are promising high-performance precision positioning devices used for broad applications in the field of precision machines and nano/micro manufacturing. Piezoelectric actuators involve a nonlinear complex hysteresis that may cause degradation in performance. These hysteresis effects of piezoelectric actuators are mathematically represented as a second-order system using the Dahl hysteresis model. In this paper, artificial intelligence-based neurocomputing feedforward and backpropagation networks of the Levenberg-Marquardt method (LMM-NNs) and Bayesian Regularization method (BRM-NNs) are exploited to examine the numerical behavior of the Dahl hysteresis model representing a piezoelectric actuator, and the Adams numerical scheme is used to create datasets for various cases. The generated datasets were used as input target values to the neural network to obtain approximated solutions and optimize the values by using backpropagation neural networks of LMM-NNs and BRM-NNs. The performance analysis of LMM-NNs and BRM-NNs of the Dahl hysteresis model of the piezoelectric actuator is validated through convergence curves and accuracy measures via mean squared error and regression analysis.

Low-cost, open-source XYZ nanopositioner for high-precision analytical applications.

Nanoscale positioning has numerous applications in both academia and industry. A growing number of applications require devices with long working distances and nanoscale resolutions. Friction-inertia piezoelectric positioners, which are based on the stick-slip mechanism, achieve both nanometer resolution and centimeter-scale travel. However, the requirements of complex preload mechanism, precision machining, and precise assembly increase the cost of conventional friction-inertia nanopositioners. Herein we present the design of an open-source XYZ-axis nanopositioning system. Utilizing a magnet-based stick-slip driving mechanism, the proposed XYZ nanopositioner provides several advantages, including sub-nanometer resolution, a payload capacity of up to 12 kg (horizontal), compact size, low cost, and easy assembly; furthermore, the system is adjustment-free. The performance tests validate the precision of the system in both scanning and stepping operation modes. Moreover, the resonant spectra affirm the rigidity and dynamic response of the mechanism. In addition, we demonstrate the practical applications of this nanopositioner in various measurement techniques, including scanning electron microscopy, vibrometry, and atomic force microscopy. Furthermore, we present 11 variations of the nanopositioner designs that are either compatible with ultra-high-vacuum systems and other existing systems, 3D printable, or hacking commercial linear slides.

Highly Linear and Wide Non-Resonant Two-Degree-of-Freedom Piezoelectric Laser Scanner.

Laser scanners with mechanically driven mirrors have exhibited increasing potential for various applications, such as displays and laser radar. Resonant scanners are the predominantly used scanners; however, non-resonant scanners are required for applications where point-to-point driving is desirable. Because a non-resonant drive cannot amplify the drive angle owing to the resonance phenomenon, high values are difficult to achieve for the main performance metrics of the scanners: mirror area, drive angle, and operating frequency. In this paper, we present a two-axis scanner with a piezoelectric actuator made of a piezoelectric single-crystal Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 as the actuation force source. The scanner contains a circular mirror with a diameter of 7 mm and achieves an average static mechanical deflection angle amplitude of 20.8° in two axes with a resonant frequency of 559 Hz. It is equipped with a transmission mechanism that can decouple each axis to achieve high linearity; in our study, the nonlinearity error was less than 1°.