Four-sandwich type piezoelectric actuator equidirectional central symmetry arrangement type multi-dimensional vibration platform and excitation method

By using a four-sandwich piezoelectric actuator arranged in a symmetrical manner to form a multidimensional vibration platform, the problem of parasitic modes and vibration coupling caused by the structural asymmetry of the multidimensional vibration platform was solved, and high-precision, low-interference six-degree-of-freedom vibration control was achieved.

CN121984375APending Publication Date: 2026-05-05HARBIN INST OF TECH
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
HARBIN INST OF TECH
Filing Date
2026-02-27
Publication Date
2026-05-05

AI Technical Summary

Technical Problem

Existing multidimensional vibration platforms suffer from severe parasitic modes due to structural asymmetry. Asymmetric layouts can easily induce additional vibration modes, making vibration coupling difficult to suppress and affecting control accuracy.

Method used

A multidimensional vibration platform with four sandwich piezoelectric actuators arranged in a co-directional, centrally symmetrical manner is used. The four piezoelectric actuators are arranged in a horizontal plane at 90-degree intervals orthogonal centrally symmetrical manner. Combined with a flexible hinge and end platform structure, it achieves the dual advantages of central symmetry and mirror symmetry, and excites specific modes through alternating voltage signals.

Benefits of technology

It achieves high-frequency vibration output with six degrees of freedom, significantly suppresses parasitic modes and cross-coupling, and improves stiffness and control accuracy, making it suitable for high-precision micro-operation and nanoscale precision scenarios.

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Abstract

The invention discloses a four-sandwich type piezoelectric actuator equidirectional central symmetry arrangement type multi-dimensional vibration platform and an excitation method, relates to the field of high-frequency vibration engineering and micro-nano control, and solves the problems that a parasitic mode is serious due to the fact that a plurality of existing piezoelectric actuators are asymmetric in structure in practical application, an additional vibration mode is easily caused by asymmetric layout, and the vibration performance is poor. The vibration platform comprises a tail end platform, four flexible hinges and four actuating units, the tail end platform is a motion output component with biaxial mirror symmetry, and the four actuating units are symmetrically arranged in a rectangular vertex mode and integrate longitudinal vibration, bending vibration ceramic sets around the Y axis and bending vibration ceramic sets around the Z axis. Through an in-phase or anti-phase excitation strategy, six-degree-of-freedom vibration output of three-axis translation and three-axis rotation can be realized. And each actuating unit realizes axial pre-tightening through a first bolt, so that the reliability of the piezoelectric ceramics is ensured. And the method is suitable for application scenes requiring high-stability and multi-axis cooperative motion, such as precision micromachining and ultrasonic-assisted manufacturing.
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Description

Technical Field

[0001] This invention relates to the fields of high-frequency vibration engineering and micro-nano manipulation technology, specifically to a four-sandwich piezoelectric actuator with a co-directional, centrally symmetrical arrangement of a multidimensional vibration platform and excitation method. Background Technology

[0002] In existing technologies, piezoelectric ceramic-based multidimensional vibration platforms are widely used in micromanipulation, precision positioning, and active vibration suppression systems. Traditional solutions often employ single or dual-actuator structures, achieving two-dimensional or three-dimensional motion output through longitudinal and bending mode coupling. Although some research has attempted to introduce multiple piezoelectric actuators to increase degrees of freedom, such as a triangularly distributed three-actuator structure, the following problems still exist in practical applications: structural asymmetry leads to severe parasitic modes; asymmetrical layout easily induces additional vibration modes, causing distortion of the motion trajectory; vibration coupling is difficult to suppress, and different degrees of freedom interfere with each other, affecting control accuracy. Although a "three-sandwich" structure has achieved good symmetry and six-degree-of-freedom output, it only possesses mirror symmetry characteristics and lacks central symmetry design, limiting the overall stiffness improvement and vibration decoupling capability. Therefore, there is an urgent need for a novel multidimensional vibration platform structure and its excitation method that combines the advantages of both central and mirror symmetry. Summary of the Invention

[0003] This invention addresses the shortcomings of existing multidimensional vibration platforms using piezoelectric ceramics, which employ multiple piezoelectric actuators. These platforms suffer from issues such as severe parasitic modes due to structural asymmetry, the potential for additional vibration modes and distortion of motion trajectories due to asymmetrical layouts, difficulty in suppressing vibration coupling, and mutual interference between different degrees of freedom, all of which affect control accuracy. Therefore, a novel multidimensional vibration platform structure and its excitation method, combining the advantages of both central symmetry and mirror symmetry, are urgently needed. This invention proposes a four-piezoelectric actuator co-directional, centrally symmetrically arranged multidimensional vibration platform and its excitation method. "Co-directional" means that the vibration axes of each actuator are aligned, and "central symmetry" means that their installation positions are 180 degrees rotationally symmetrical about the geometric center of the end platform. By symmetrically arranging the four piezoelectric actuators at rectangular vertices and combining them with a centrally symmetrical flexible hinge and end platform structure, higher structural stiffness, stronger vibration decoupling capability, and more stable six-degree-of-freedom motion output are achieved.

[0004] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution: Option 1: This invention proposes a four-sandwich piezoelectric actuator with a co-directional, centrally symmetrical arrangement of a multidimensional vibration platform, which includes an end platform, a flexible hinge, and an actuation unit. The actuation unit integrates multiple sub-components, each of which includes at least an amplitude rod, a piezoelectric actuator, an end cap, and a first bolt. The end-effector platform is centrally symmetrically arranged, and includes two mutually orthogonal mirror symmetry planes, which are planes passing through their geometric center points and parallel to the XZ plane and the XY plane, respectively; the central symmetry of the end-effector platform matches the orthogonal symmetrical arrangement of the four actuation units; The four actuation units are arranged orthogonally at equal intervals of 90 degrees in the horizontal plane with the geometric center of the end platform as the symmetry reference. The sub-components inside each actuation unit are collinear along the vibration transmission direction axis and are axially pre-tightened by the first bolt. The amplitude transformer is a variable cross-section rod with parallel end faces at both ends. One end has a larger contact area, while the other end has a smaller contact area. The end with the larger contact area has an internal threaded hole. The piezoelectric actuator has parallel end faces and an axial through hole. The end cap has parallel end faces and an axial through hole. One end face of the piezoelectric actuator is fitted with the upper end face of the end cap, and the other end face is fitted with the end face with the larger contact area of ​​the amplitude transformer. The first bolt passes through the axial through hole of the end cap and the through hole of the piezoelectric actuator in sequence, and is screwed into the internal threaded hole at the end with the larger contact area of ​​the amplitude transformer, thus achieving axial fastening of the three components. The axes of the first bolt, the end cap, and the piezoelectric actuator are collinear, and the head end face of the first bolt is fitted with the lower end face of the end cap. The thin end of the amplitude rod is connected to the lower end face of the flexible hinge, while the upper end face of the flexible hinge is fixedly connected to the lower end face of the end platform. Both the amplitude rod and the piezoelectric actuator are provided with brackets for installation and fixation in the circumferential direction to achieve efficient coupling of the overall platform constraint and vibration energy.

[0005] Furthermore, a preferred embodiment is provided in which the end platform is implemented using a planar structure with dual-axis symmetry, namely a circle, a square, or a cross, to ensure that the XZ plane and the XY plane are mirror symmetric.

[0006] Furthermore, a preferred embodiment is provided, wherein the piezoelectric actuator is any one of a longitudinal vibration ceramic group, a bending vibration ceramic group around the Y-axis, and a bending vibration ceramic group around the Z-axis, and each ceramic group is provided with a driving electrode and a ground electrode; by applying an alternating voltage signal between the corresponding driving electrode and the ground electrode, specific modes of longitudinal vibration, bending vibration around the Y-axis, or bending vibration around the Z-axis are excited.

[0007] Furthermore, a preferred embodiment is provided, wherein the piezoelectric actuator is one of a stacked type, a surface mount type, a piezoelectric tube type, or any combination thereof.

[0008] Furthermore, a preferred embodiment is provided in which the flexible hinge is fixed to the end platform and the amplitude rod by means of threaded connection, adhesive bonding, welding or integral molding.

[0009] Furthermore, a preferred embodiment is provided in which the flexible hinge adopts a biaxial symmetric or omnidirectional structure to transmit the axial linear motion and multi-directional bending deformation output by the actuation unit, and adapts to the six-degree-of-freedom motion requirements of the end platform.

[0010] Furthermore, a preferred embodiment is provided in which the vibration platform is installed and fixed by any one of the following methods: an amplitude transformer bracket, a piezoelectric actuator bracket, or a combination of the two, in order to achieve efficient coupling of vibration energy and stable support of the system.

[0011] Furthermore, a preferred embodiment is provided in which the axes of the four actuation units are arranged parallel to each other; the included angle between any two axes is less than 90 degrees.

[0012] Furthermore, a preferred embodiment is provided in which the geometric center point, XZ symmetry plane, and XY symmetry plane of the end platform in the vibration platform simultaneously satisfy both central symmetry and mirror symmetry.

[0013] Scheme 2: An excitation method for a multidimensional vibration platform with a co-directional, centrally symmetrical arrangement of four sandwich piezoelectric actuators, wherein the excitation method is based on the multidimensional vibration platform with a co-directional, centrally symmetrical arrangement of four sandwich piezoelectric actuators described in Scheme 1, and the method includes the following steps: The translational vibration of the end platform along the X-axis is excited by the longitudinal vibrating ceramic group in the four piezoelectric actuators when an in-phase alternating voltage signal is applied and the frequency matches the longitudinal resonant mode. The translational vibration of the end platform along the Y-axis is excited by the Z-axis bending ceramic group of four piezoelectric actuators when an in-phase alternating voltage signal is applied and the frequency matches the Z-axis bending resonant mode. The translational vibration of the end platform along the Z-axis is excited by the bending ceramic group around the Y-axis in four piezoelectric actuators when an in-phase alternating voltage signal is applied and the frequency matches the bending resonant mode around the Y-axis.

[0014] The advantages of this invention are: The present invention discloses a four-piezoelectric actuator co-directional centrally symmetrical multidimensional vibration platform and excitation method to achieve six-degree-of-freedom fully decoupled high-frequency vibration output: by arranging four piezoelectric actuators at 90-degree intervals orthogonally centrally symmetrically in the horizontal plane, and in conjunction with an end platform structure with biaxial mirror symmetry, the present invention simultaneously satisfies the conditions of central symmetry and XY / XZ biplane mirror symmetry under a single platform configuration, significantly suppressing parasitic modes and cross-coupling effects, thereby achieving high-precision, low-interference, and independently controllable vibration output with six degrees of freedom, including translation along the X / Y / Z axes and rotation around the X / Y / Z axes.

[0015] The present invention discloses a four-cage piezoelectric actuator co-directional centrally symmetrical arrangement multidimensional vibration platform and excitation method, which improves structural symmetry and enhances stiffness and stability: Compared with the traditional three-actuator configuration which only has mirror symmetry, the present invention adopts a four-actuator rectangular vertex centrally symmetrical layout to form a completely balanced force / torque excitation system with no eccentric excitation component in any direction, effectively improving the overall structural stiffness, reducing undesirable deformation, and enhancing the dynamic stability of the platform under high frequency and high load conditions.

[0016] The four-sandwich piezoelectric actuator multidimensional vibration platform and excitation method described in this invention exhibit excellent vibration decoupling performance and high control precision. Thanks to strict geometric and excitation symmetry, the motion coupling between degrees of freedom is significantly reduced. By rationally configuring the excitation phase and frequency of the longitudinal vibration, bending vibration around the Y-axis, and bending vibration around the Z-axis of each piezoelectric ceramic group, the target mode can be accurately excited without changing the hardware structure, avoiding motion trajectory distortion, and making it suitable for nanometer-level precision operation scenarios.

[0017] The four-sandwich piezoelectric actuator of the present invention, with a co-directional, centrally symmetrical arrangement, multidimensional vibration platform and excitation method, features flexible and diverse excitation modes and high system integration: each actuation unit integrates a multi-mode piezoelectric ceramic assembly, supporting various excitation strategies such as in-phase, out-of-phase, and differential; combined with the centrally symmetrical layout, only the phase relationship of the voltage signal needs to be adjusted to switch between translational or rotational motion modes, without the need for additional drive channels or complex mechanical structures, simplifying the control system design and improving response speed and energy efficiency.

[0018] The four-sandwich piezoelectric actuators of this invention, arranged in a co-directional, centrally symmetrical multidimensional vibration platform and excitation method, are highly modular and scalable, adaptable to various application scenarios. The platform adopts standardized actuation units and flexible hinge interfaces, supporting various symmetrical end platform configurations such as circular, square, and cross shapes. Meanwhile, the piezoelectric actuators can be stacked, patch-type, or piezoelectric tube-type structures, facilitating customized design based on displacement stroke, frequency bandwidth, and load requirements. It is widely applicable to cutting-edge fields such as micro-nano fabrication, biological cell manipulation, ultrasound-assisted manufacturing, micro-robotics, and active vibration isolation.

[0019] The four-sandwich piezoelectric actuator co-directional centrally symmetrical arrangement multidimensional vibration platform and excitation method described in this invention have reliable pre-tightening, long service life, and are suitable for long-term high-frequency operation: the piezoelectric actuator, end cover and amplitude transformer are axially pre-tightened by the first bolt to ensure that the piezoelectric ceramic is always under compressive stress, effectively preventing tensile failure; at the same time, the axes of each component are collinear and the assembly is compact, reducing energy loss and ensuring the reliability and durability of the platform under long-term high-frequency vibration.

[0020] In summary, the four-sandwich piezoelectric actuators of the present invention, arranged in a co-directional, centrally symmetrical manner, form a multidimensional vibration platform that overcomes the bottlenecks of traditional multi-degree-of-freedom piezoelectric platforms in terms of symmetry, decoupling, and stiffness. It also has the advantages of compact structure, flexible control, and stable performance, providing a new technical path for high-precision microscale multidimensional motion control.

[0021] This invention is also applicable to high-rigidity, low-coupling, and high-symmetry multidimensional vibration platforms for six-degree-of-freedom high-frequency microscale motion control, and is particularly suitable for applications requiring high stability and multi-axis coordinated motion, such as precision micromachining, biological cell manipulation, ultrasound-assisted manufacturing, and microrobots. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the structure of the four-sandwich piezoelectric actuator co-directional centrally symmetrical multidimensional vibration platform described in Embodiment 1.

[0023] Figure 2 This is an exploded view of the four-sandwich piezoelectric actuators arranged in the same direction with central symmetry, as described in Embodiment 1.

[0024] Figure 3 This is a full cross-sectional schematic diagram of the four-sandwich piezoelectric actuators arranged in the same direction with central symmetry, as described in Embodiment 1.

[0025] Figure 4 This is a schematic diagram of the vibration of the end platform of the multidimensional vibration platform of the four-sandwich piezoelectric actuators arranged in the same direction and symmetrically arranged according to Embodiment 2, as it translates along the Y-axis.

[0026] Figure 5 This is a vibration diagram of the end platform of the four-sandwich piezoelectric actuator co-directional centrally symmetrical multidimensional vibration platform described in Embodiment 2, showing its rotation around the Z-axis.

[0027] Figure 6 This is a vibration diagram of the end platform of the four-sandwich piezoelectric actuator co-directional centrally symmetrical multidimensional vibration platform described in Embodiment 2, showing its rotation around the X-axis.

[0028] Figure 7 This is a schematic diagram of the vibration of the end platform of the multidimensional vibration platform with a co-directional, centrally symmetrical arrangement of four sandwich piezoelectric actuators as described in Embodiment 2, as it translates along the Z-axis.

[0029] Figure 8 This is a vibration diagram of the end platform of the multidimensional vibration platform of the four-sandwich piezoelectric actuators arranged in the same direction with central symmetry, as described in Embodiment 2, rotating around the Y-axis.

[0030] Figure 9This is a schematic diagram of the vibration of the end platform of the multidimensional vibration platform of the four-sandwich piezoelectric actuators arranged in the same direction and symmetrically along the X-axis as described in Embodiment 2.

[0031] The components include: end platform 1, flexible hinge 2, actuation unit 3, amplitude rod 3-1, piezoelectric actuator 3-2, end cap 3-3, and first bolt 3-4. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them.

[0033] Implementation Method 1, see [link] Figures 1 to 3 This embodiment describes a four-sandwich piezoelectric actuator with a co-directional, centrally symmetrical arrangement, multidimensional vibration platform. The vibration platform includes: End platform 1, flexible hinge 2, and actuation unit 3; Among them, the actuation unit 3 is a composite functional module. Each actuation unit 3 integrates multiple sub-components, including at least the amplitude rod 3-1, the piezoelectric actuator 3-2, the end cover 3-3, and the first bolt 3-4. The end platform 1 is a motion output component with a geometric configuration that is centrally symmetrical and includes two mutually orthogonal mirror symmetry planes, which are planes passing through its geometric center point and parallel to the XZ plane and the XY plane, respectively. This symmetrical structure matches the orthogonal symmetrical arrangement of the four actuation units 3, effectively suppressing eccentricity and parasitic modes. The four actuation units 3 are arranged in an orthogonal central symmetry at 90-degree intervals in the horizontal plane with the geometric center of the end platform 1 as the symmetry reference. The vibration platform satisfies both central symmetry and mirror symmetry conditions in its layout with respect to the geometric center point, XZ symmetry plane, and XY symmetry plane of the end platform 1. Each sub-component inside the actuation unit 3 is collinear along the axis of vibration transmission and is axially pre-tightened by the first bolt 3-4; The amplitude rod 3-1 is a variable cross-section rod with parallel end faces at both ends. One end has a larger cross-section and the other end has a smaller cross-section. The end with the larger cross-section is provided with an internal threaded hole. The piezoelectric actuator 3-2 has parallel end faces and a through hole along the axial direction; The two ends of the end cap 3-3 are parallel and have an axial through hole; One end face of the piezoelectric actuator 3-2 is in contact with the upper end face of the end cover 3-3, and the other end face is in contact with the end face of the larger cross section of the amplitude rod 3-1. The first bolt 3-4 passes through the axial through hole of the end cover 3-3 and the through hole of the piezoelectric actuator 3-2 in sequence, and is screwed into the internal thread hole at the larger cross-section end of the amplitude rod 3-1 to achieve axial fastening of the three; the axes of the first bolt 3-4, the end cover 3-3 and the piezoelectric actuator 3-2 are collinear, and the head end face of the first bolt 3-4 is in contact with the lower end face of the end cover 3-3 to provide a stable preload force and prevent the piezoelectric actuator 3-2 from being subjected to tensile stress during operation; The thin end of the amplitude rod 3-1 is connected to the lower end face of the flexible hinge 2, while the upper end face of the flexible hinge 2 is fixedly connected to the lower end face of the end platform 1. Both the amplitude rod 3-1 and the piezoelectric actuator 3-2 are provided with brackets for installation and fixation in the circumferential direction, so as to achieve efficient coupling of the overall platform constraint and vibration energy.

[0034] In this embodiment, the first bolt 3-4 passes through the end cap 3-3 and the piezoelectric actuator 3-2 in sequence, and is screwed into the internal threaded hole at the larger cross-section end of the amplitude rod 3-1, thereby axially fastening the three together as one, thus applying a stable initial preload to the piezoelectric ceramic. This preload can effectively prevent the piezoelectric actuator 3-2 from bearing tensile stress during high-frequency vibration, prevent performance degradation or structural damage caused by tensile failure, and significantly improve the service life and output stability of the device.

[0035] The four actuation units 3 are arranged in a 90-degree orthogonal central symmetry in the horizontal plane with the geometric center of the end platform 1 as the reference. This not only satisfies the biaxial mirror symmetry about the XZ plane and the XY plane, but also has strict central symmetry. This layout enables the system to achieve global balance of inertial force and torque in any direction, completely eliminates the force eccentricity caused by unilateral or asymmetrical excitation, effectively suppresses parasitic modes and cross-coupled vibrations, and significantly improves the purity of the target master mode and the consistency of the dynamic response of each degree of freedom.

[0036] With its six-degree-of-freedom omnidirectional controllable high-frequency micro-vibration capability, this vibration platform is not only suitable for precision manufacturing scenarios with stringent requirements for multi-dimensional high-frequency motion accuracy, such as laser micromachining, ultrasonic-assisted cutting, and micro-nano assembly, but can also be used as an active vibration damping unit to counteract external multi-directional high-frequency interference. It shows significant advantages, especially in applications such as complex spatial trajectory tracking, multi-axis collaborative control, and multi-directional vibration isolation.

[0037] The overall design integrates a slender actuation unit with a low-profile platform, which extends the effective vibration transmission path while reducing the lateral dimension. This is beneficial for frequency separation and directional coupling control of multiple modes such as longitudinal vibration, bending vibration around the Y-axis, and bending vibration around the Z-axis. At the same time, it significantly reduces the overall height and space occupation of the platform, making it easy to embed in space-constrained application environments such as minimally invasive surgical instruments, microfluidic chips, microrobots, or compact optomechanical systems.

[0038] By selectively exciting the longitudinal vibration ceramic group, the bending vibration ceramic group around the Y-axis, or the bending vibration ceramic group around the Z-axis in each actuation unit 3, and flexibly adjusting the phase relationship and operating frequency of the excitation signal, any combination of vibration output from single translation / rotation to complete six degrees of freedom can be achieved on the same hardware platform. In addition, the vibration amplitude and resonant frequency of the end platform 1 can be customized by adjusting the structural stiffness of the flexible hinge 2 without changing the platform shape, height, or actuation unit layout, supporting rapid optimization and adaptation for specific working conditions such as different loads, frequency bands, or stroke requirements.

[0039] The end platform 1 adopts a planar structure with dual-axis symmetry, such as a circle, square, or cross, to ensure that it is mirror symmetric about the XZ plane and the XY plane, and has a clear geometric center as a symmetric layout reference.

[0040] The geometric center serves as the arrangement reference for the four actuation units 3, ensuring that the overall structure meets the strict conditions of central symmetry and biaxial mirror symmetry, effectively suppressing eccentric excitation and parasitic modes, and improving the decoupling and dynamic stability of the six-degree-of-freedom vibration output.

[0041] The piezoelectric actuator 3-2 includes any combination of longitudinal vibration ceramic group, Y-axis bending vibration ceramic group and Z-axis bending vibration ceramic group. Each ceramic group is provided with a driving electrode and a ground electrode. By applying an alternating voltage signal between the corresponding driving electrode and the ground electrode, specific modes such as longitudinal vibration, Y-axis bending vibration or Z-axis bending vibration can be selectively excited.

[0042] In this embodiment, the piezoelectric actuator 3-2 adopts a high-rigidity structural design, suitable for vibration applications in the high-frequency and even ultrasonic frequency ranges. Its integrated longitudinal, Y-axis, and Z-axis bending ceramic groups exhibit rapid response and high energy conversion efficiency under electrical excitation. Compared to traditional electromagnetic motors or mechanical transmission mechanisms, it can not only operate stably in the ultrasonic frequency range above tens of kilohertz, but also consumes less power and is free from electromagnetic interference. This high-rigidity characteristic helps to increase the system resonant frequency of the entire vibration platform, achieving efficient and stable ultrasonic excitation. It is particularly suitable for precision micromanipulation scenarios with stringent requirements for environmental noise suppression, vibration purity, and motion repeatability, such as cell manipulation, micro / nano assembly, or ultrasound-assisted processing.

[0043] Furthermore, the four actuation units 3 are arranged orthogonally and symmetrically at 90-degree intervals in the horizontal plane, with respect to the geometric center of the end platform 1, while simultaneously satisfying the biaxial mirror symmetry condition about the XY and XZ planes. Based on this highly symmetrical layout, by applying excitation signals with specific phase relationships to different ceramic groups in each piezoelectric actuator 3-2, the longitudinal vibration, bending vibration around the Y-axis, and bending vibration modes independently generated by each actuation unit can be accurately vector-synthesized in space.

[0044] The piezoelectric actuator 3-2 can adopt a stacked, patch, piezoelectric tube, or any combination thereof structure to flexibly adapt to the needs of different application scenarios for displacement output range, mechanical response characteristics and spatial constraints.

[0045] Specifically, the structural form of the piezoelectric actuator 3-2 can be optimized according to the actual working conditions: the stacked structure has a large output displacement and high axial stiffness, and is suitable for precision operation scenarios that require high frequency and high output drive, such as ultrasonic-assisted cutting or micro-force loading; the patch structure is compact, has low power consumption and fast response, and is particularly suitable for integration into space-constrained and energy-sensitive systems, such as microfluidic chips, implantable micro-devices or portable micro-manipulation platforms; the piezoelectric tube structure can simultaneously excite axial extension and radial bending deformation, and has multi-directional excitation potential, which is suitable for complex control tasks that require composite modal excitation within the same actuation unit.

[0046] The flexible hinge 2 is fixed to the end platform 1 and the amplitude rod 3-1 by means of threaded connection, adhesive bonding, welding or integral molding.

[0047] The connection method between the flexible hinge 2, the end platform 1, and the amplitude transformer 3-1 directly affects the structural integrity, interface stiffness, and dynamic reliability of the entire vibration platform. Under high-frequency or ultrasonic operating conditions, loosening, slippage, or stress concentration at the connection interface can easily lead to energy loss, modal distortion, and even fatigue failure. Therefore, selecting a suitable connection process is crucial for ensuring the long-term stable operation of the system.

[0048] The flexible hinge 2 adopts a biaxial symmetric or universal structure to efficiently transmit the axial linear motion and multi-directional bending deformation output by the actuation unit 3, and adapts to the six-degree-of-freedom motion requirements of the end platform 1.

[0049] Biaxially symmetric flexible hinges, with their regular geometry and symmetrical stiffness, are beneficial for maintaining modal consistency of the system in the XZ and XY planes, making them suitable for high-precision resonant control scenarios. Universal flexible hinges, on the other hand, possess multi-directional bending degrees of freedom, making them suitable for applications requiring large-angle deflection or combined directional deformation. By selecting the appropriate type, the excitation force transmission path can be optimized, energy loss reduced, and non-target modal excitation suppressed, thereby improving the platform's dynamic stability and motion accuracy while ensuring structural strength.

[0050] The vibration platform is installed and fixed by means of the amplitude rod 3-1 bracket, the piezoelectric actuator 3-2 bracket, or a combination of the two, so as to achieve efficient coupling of vibration energy and stable support of the system.

[0051] The support is arranged in the nodal areas of the main vibration modes of the platform, providing reliable mechanical constraints while minimizing interference with the working modes. This design ensures that the vibration energy generated by the piezoelectric actuator 3-2 is efficiently transmitted to the end platform 1, and prevents external installation from introducing additional stiffness or damping, which helps maintain the system's high electromechanical conversion efficiency, modal purity and dynamic response consistency.

[0052] The axes of the four actuation units 3 are optimally configured to be parallel to each other; as an alternative, the axes of each actuation unit 3 are allowed to be slightly tilted, but the included angle between any two axes is less than 90 degrees.

[0053] This constraint ensures that the system maintains high structural symmetry while avoiding significant torque imbalance or modal distortion caused by excessive tilt angles. The spatial arrangement of the four actuators 3 directly affects the vibration amplitude distribution, coupling characteristics between degrees of freedom, and overall compactness of the end platform 1: parallel axis configuration is beneficial for achieving minimum installation envelope and reducing cross-interference, making it suitable for high-precision decoupling control; while a moderately tilted arrangement can enhance modal coupling capability in specific directions while maintaining symmetry, expanding the flexibility of multidimensional motion output. During the design process, synergistic optimization can be performed between structural compactness, motion decoupling, and excitation efficiency according to specific applications.

[0054] Implementation Method 2: This implementation method proposes an excitation method for a multidimensional vibration platform with a four-sandwich piezoelectric actuator arranged in the same direction and with central symmetry. The excitation method is based on the multidimensional vibration platform with a four-sandwich piezoelectric actuator arranged in the same direction and with central symmetry described in Implementation Method 1. The method includes the following steps: The translational vibration along the Y-axis of the end platform 1 is excited by the Z-axis bending ceramic group of the four piezoelectric actuators 3-2 when an in-phase alternating voltage signal is applied and the frequency matches the bending resonant mode around the Z-axis. There are two ways to excite the rotational vibration of the end platform 1 around the Z-axis: one is to excite it by applying an in-phase alternating voltage signal to the four piezoelectric actuators 3-2 around the Z-axis bending ceramic group, and the frequency matches the bending resonant mode around the Z-axis; the other is to excite it by applying an in-phase alternating voltage signal to the two piezoelectric actuators 3-2 on one side of the XZ plane, and applying another alternating voltage signal with a phase difference of 180 degrees to the former to the two piezoelectric actuators 3-2 on the other side of the XZ plane, and the frequencies of both signals match the longitudinal vibration mode. The excitation methods for the rotational vibration of the end platform 1 around the X-axis include the following four: The first method involves applying an alternating voltage signal to the ceramic assemblies of the two piezoelectric actuators 3-2 that bend around the Z-axis on one side of the XY plane; and applying another alternating voltage signal to the ceramic assemblies of the other two piezoelectric actuators 3-2 that bend around the Z-axis on the other side of the XY plane. This signal is 180 degrees out of phase with the first signal, and the frequencies of both signals are matched with the bending vibration mode frequency around the Z-axis, thereby effectively exciting the rotational vibration of the end platform 1 around the X-axis. The second method is as follows: On one side of the XZ plane, an alternating voltage signal is applied to the bending vibration ceramic groups around the Y-axis in the two piezoelectric actuators 3-2; on the other side of the XZ plane, another alternating voltage signal is applied to the bending vibration ceramic groups around the Y-axis in the other two piezoelectric actuators 3-2. This signal is 180 degrees out of phase with the first signal, and the frequencies of both signals are matched with the bending vibration mode frequency around the Y-axis, thereby effectively exciting the rotational vibration of the end platform 1 around the X-axis. The third method: In a piezoelectric actuator 3-2 located on the positive half-axis of the Y-axis on one side of the XY plane, an alternating voltage signal is applied to the ceramic assembly that bends and vibrates around the Z-axis; In a piezoelectric actuator 3-2 located on the negative half-axis of the Y-axis on the other side of the XY plane, another alternating voltage signal is applied to the ceramic assembly that bends and vibrates around the Z-axis. This signal is 180 degrees out of phase with the first signal, and the frequencies of both signals are matched with the bending vibration mode frequency around the Z-axis. This excitation method can also excite the rotational vibration of the end platform 1 around the X-axis. The fourth method: In a piezoelectric actuator 3-2 located on one side of the XZ plane at the positive half-axis of the Y-axis, an alternating voltage signal is applied to the ceramic assembly that bends and vibrates around the Y-axis; In a piezoelectric actuator 3-2 located on the other side of the XZ plane at the negative half-axis of the Y-axis, another alternating voltage signal is applied to the ceramic assembly that bends and vibrates around the Y-axis. This signal is 180 degrees out of phase with the first signal, and the frequencies of both signals are matched with the bending vibration mode frequency around the Y-axis. This excitation method can also be used to excite the rotational vibration of the end platform 1 around the X-axis. The translational vibration along the Z-axis of the end platform 1 is excited by the bending ceramic group around the Y-axis in the four piezoelectric actuators 3-2 when an in-phase alternating voltage signal is applied and the frequency matches the bending resonant mode around the Y-axis. There are two ways to excite the rotational vibration of the end platform 1 around the Y-axis: one is to excite it by applying an in-phase alternating voltage signal to the four piezoelectric actuators 3-2 around the Y-axis bending ceramic group, and the frequency matches the bending resonant mode around the Y-axis; the other is to excite it by applying an in-phase alternating voltage signal to the two piezoelectric actuators 3-2 on one side of the XY plane, and applying another alternating voltage signal with a 180-degree phase difference to the former to the two piezoelectric actuators 3-2 on the other side of the XY plane, and the frequencies of both signals match the longitudinal vibration mode. The translational vibration along the X-axis of the end platform 1 is excited by the longitudinal vibration ceramic group in the four piezoelectric actuators 3-2 when an in-phase alternating voltage signal is applied and the frequency matches the longitudinal vibration resonant mode.

[0055] The excitation method described in this embodiment is based on the four-sandwich piezoelectric actuators arranged in a co-directional, centrally symmetrical multidimensional vibration platform as described in Embodiment 1. By coordinating the excitation of the longitudinal, Y-axis bending, and Z-axis bending ceramic groups within the four actuator units 3 in an orthogonal, centrally symmetrical manner, it successfully achieves high-frequency micro-vibration output with six degrees of freedom: three-axis translational motion along the X, Y, and Z axes and three-axis rotation around the X, Y, and Z axes. This multidimensional excitation strategy supports flexible switching between independent modal excitation and coupled motion modes by adjusting the excitation phase, amplitude, and frequency of different ceramic groups in each piezoelectric actuator 3-2, meeting the needs of advanced applications such as complex spatial trajectory generation, multi-directional micro-manipulation, and omnidirectional active vibration suppression.

[0056] The method uses a piezoelectric actuator 3-2 as the actuation core, fully utilizing the high rigidity of the sandwich structure and the rapid response capability of the inverse piezoelectric effect to achieve high-precision, high-bandwidth vibration control at the micron to nanometer scale. Compared with traditional mechanical or electromagnetic drive methods, this solution has no moving pairs, no contact friction, and no wear, and has significant advantages such as long life, high reliability, and maintenance-free operation. It is particularly suitable for cleanroom environments, biomedical micromanipulation, ultra-precision manufacturing, and high-stability engineering systems that require long-term continuous operation.

[0057] Example 1: A multidimensional vibration platform with a four-sandwich piezoelectric actuator arranged in a co-directional, centrally symmetrical configuration, mainly comprising: End platform 1, flexible hinge 2, and actuation unit 3; Among them, the actuation unit 3 is a composite functional module. Each actuation unit 3 integrates multiple sub-components, including at least the amplitude rod 3-1, the piezoelectric actuator 3-2, the end cover 3-3, and the first bolt 3-4. The end platform 1 is a motion output component with a geometric configuration that is centrally symmetrical and includes two mutually orthogonal mirror symmetry planes, which are planes passing through its geometric center point and parallel to the XZ plane and the XY plane, respectively. This symmetrical structure matches the orthogonal symmetrical arrangement of the four actuation units 3, effectively suppressing eccentricity and parasitic modes. The four actuation units 3 are arranged in an orthogonal central symmetry at 90-degree intervals in the horizontal plane with the geometric center of the end platform 1 as the symmetry reference. The vibration platform satisfies both central symmetry and mirror symmetry conditions in its layout with respect to the geometric center point, XZ symmetry plane, and XY symmetry plane of the end platform 1. Each sub-component inside the actuation unit 3 is collinear along the axis of vibration transmission and is axially pre-tightened by the first bolt 3-4; The amplitude rod 3-1 is a variable cross-section rod with parallel end faces at both ends. One end has a larger cross-section and the other end has a smaller cross-section. The end with the larger cross-section is provided with an internal threaded hole. The piezoelectric actuator 3-2 has parallel end faces and a through hole along the axial direction; The two ends of the end cap 3-3 are parallel and have an axial through hole; One end face of the piezoelectric actuator 3-2 is in contact with the upper end face of the end cover 3-3, and the other end face is in contact with the end face of the larger cross section of the amplitude rod 3-1. The first bolt 3-4 passes through the axial through hole of the end cover 3-3 and the through hole of the piezoelectric actuator 3-2 in sequence, and is screwed into the internal thread hole at the larger cross-section end of the amplitude rod 3-1 to achieve axial fastening of the three; the axes of the first bolt 3-4, the end cover 3-3 and the piezoelectric actuator 3-2 are collinear, and the head end face of the first bolt 3-4 is in contact with the lower end face of the end cover 3-3 to provide a stable preload force and prevent the piezoelectric actuator 3-2 from being subjected to tensile stress during operation; The thin end of the amplitude rod 3-1 is connected to the lower end face of the flexible hinge 2, while the upper end face of the flexible hinge 2 is fixedly connected to the lower end face of the end platform 1. Both the amplitude rod 3-1 and the piezoelectric actuator 3-2 are provided with brackets for installation and fixation in the circumferential direction, so as to achieve efficient coupling of the overall platform constraint and vibration energy.

[0058] The end platform 1 adopts a circular planar structure.

[0059] The piezoelectric actuator 3-2 includes a longitudinal vibration ceramic group, a bending vibration ceramic group around the Y-axis, and a bending vibration ceramic group around the Z-axis. Each ceramic group is provided with a driving electrode and a ground electrode. By applying an alternating voltage signal between the corresponding driving electrode and the ground electrode, specific modes such as longitudinal vibration, bending vibration around the Y-axis, or bending vibration around the Z-axis can be selectively excited.

[0060] The piezoelectric actuator 3-2 adopts a stacked structure to flexibly adapt to the needs of different application scenarios for displacement output range, mechanical response characteristics and spatial constraints.

[0061] The flexible hinge 2 is fixed to the end platform 1 and the amplitude rod 3-1 by an integral molding method.

[0062] The flexible hinge 2 is biaxially symmetrical.

[0063] The vibration platform is installed and fixed by the amplitude rod 3-1 bracket to achieve efficient coupling of vibration energy and stable support of the system.

[0064] The axes of the four actuation units 3 are parallel to each other.

[0065] Reference Figure 4 The translational vibration along the Y-axis of the end platform 1 is excited by the Z-axis bending ceramic group of the four piezoelectric actuators 3-2 when an in-phase alternating voltage signal is applied and the frequency matches the bending resonant mode around the Z-axis. Reference Figure 5 There are two ways to excite the rotational vibration of the end platform 1 around the Z-axis: one is to excite it by applying an in-phase alternating voltage signal to the four piezoelectric actuators 3-2 around the Z-axis bending ceramic group, and the frequency matches the bending resonant mode around the Z-axis; the other is to excite it by applying an in-phase alternating voltage signal to the two piezoelectric actuators 3-2 on one side of the XZ plane, and applying another alternating voltage signal with a phase difference of 180 degrees to the former to the two piezoelectric actuators 3-2 on the other side of the XZ plane, and the frequencies of both signals match the longitudinal vibration mode. Reference Figure 6 The excitation methods for the rotational vibration of the end platform 1 around the X-axis include the following four: The first method involves applying an alternating voltage signal to the ceramic assemblies of the two piezoelectric actuators 3-2 that bend around the Z-axis on one side of the XY plane; and applying another alternating voltage signal to the ceramic assemblies of the other two piezoelectric actuators 3-2 that bend around the Z-axis on the other side of the XY plane. This signal is 180 degrees out of phase with the first signal, and the frequencies of both signals are matched with the bending vibration mode frequency around the Z-axis, thereby effectively exciting the rotational vibration of the end platform 1 around the X-axis. The second method is as follows: On one side of the XZ plane, an alternating voltage signal is applied to the bending vibration ceramic groups around the Y-axis in the two piezoelectric actuators 3-2; on the other side of the XZ plane, another alternating voltage signal is applied to the bending vibration ceramic groups around the Y-axis in the other two piezoelectric actuators 3-2. This signal is 180 degrees out of phase with the first signal, and the frequencies of both signals are matched with the bending vibration mode frequency around the Y-axis, thereby effectively exciting the rotational vibration of the end platform 1 around the X-axis. The third method: In a piezoelectric actuator 3-2 located on the positive half-axis of the Y-axis on one side of the XY plane, an alternating voltage signal is applied to the ceramic assembly that bends and vibrates around the Z-axis; In a piezoelectric actuator 3-2 located on the negative half-axis of the Y-axis on the other side of the XY plane, another alternating voltage signal is applied to the ceramic assembly that bends and vibrates around the Z-axis. This signal is 180 degrees out of phase with the first signal, and the frequencies of both signals are matched with the bending vibration mode frequency around the Z-axis. This excitation method can also excite the rotational vibration of the end platform 1 around the X-axis. The fourth method: In a piezoelectric actuator 3-2 located on one side of the XZ plane at the positive half-axis of the Y-axis, an alternating voltage signal is applied to the ceramic assembly that bends and vibrates around the Y-axis; In a piezoelectric actuator 3-2 located on the other side of the XZ plane at the negative half-axis of the Y-axis, another alternating voltage signal is applied to the ceramic assembly that bends and vibrates around the Y-axis. This signal is 180 degrees out of phase with the first signal, and the frequencies of both signals are matched with the bending vibration mode frequency around the Y-axis. This excitation method can also be used to excite the rotational vibration of the end platform 1 around the X-axis. Reference Figure 7 The translational vibration along the Z-axis of the end platform 1 is excited by the bending ceramic group around the Y-axis in the four piezoelectric actuators 3-2 when an in-phase alternating voltage signal is applied and the frequency matches the bending resonant mode around the Y-axis. Reference Figure 8 There are two ways to excite the rotational vibration of the end platform 1 around the Y-axis: one is to excite it by applying an in-phase alternating voltage signal to the four piezoelectric actuators 3-2 around the Y-axis bending ceramic group, and the frequency matches the bending resonant mode around the Y-axis; the other is to excite it by applying an in-phase alternating voltage signal to the two piezoelectric actuators 3-2 on one side of the XY plane, and applying another alternating voltage signal with a phase difference of 180 degrees to the former to the two piezoelectric actuators 3-2 on the other side of the XY plane, and the frequencies of both signals match the longitudinal vibration mode. Reference Figure 9 The translational vibration along the X-axis of the end platform 1 is excited by the longitudinal vibration ceramic group in the four piezoelectric actuators 3-2 when an in-phase alternating voltage signal is applied and the frequency matches the longitudinal vibration resonant mode.

[0066] The vibration platform of this invention is based on an orthogonal centrally symmetrical layout of four actuation units 3, enabling high-frequency micro-vibration output with a total of six degrees of freedom: three-way translation along the X, Y, and Z axes and three-way rotation around the X, Y, and Z axes. Thanks to its strict central symmetry and biaxial mirror symmetry structure, the coupling between degrees of freedom is significantly reduced, resulting in high modal purity. This makes it suitable for advanced applications such as complex spatial trajectory generation, multidimensional micro / nano fabrication, high-precision biological cell manipulation, microrobot actuation, and omnidirectional active vibration suppression.

[0067] Those skilled in the art will understand that the above description is merely a preferred embodiment of the present invention, and the features described in the various embodiments and / or claims of this disclosure can be combined or combined in various ways, even if such combinations or combinations are not explicitly described in this disclosure. This is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0068] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if these modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include these modifications and modifications.

Claims

1. A multidimensional vibration platform with a four-sandwich piezoelectric actuator arranged in a co-directional, centrally symmetrical configuration, characterized in that, The multidimensional vibration platform includes an end platform (1), a flexible hinge (2), and an actuation unit (3). The actuation unit (3) integrates multiple sub-components, each of which includes at least an amplitude rod (3-1), a piezoelectric actuator (3-2), an end cap (3-3), and a first bolt (3-4). The end platform (1) is centrally symmetrically arranged, and the end platform (1) includes two mutually orthogonal mirror symmetric planes, which are planes passing through their geometric center points and parallel to the XZ plane and the XY plane, respectively; the central symmetric arrangement of the end platform (1) matches the orthogonal symmetric arrangement of the four actuation units (3); The four actuation units (3) are arranged in a symmetrical manner with the geometric center of the end platform (1) as the symmetry reference, and are orthogonally symmetrically arranged at 90-degree intervals in the horizontal plane; the sub-components inside each actuation unit (3) are collinear along the vibration transmission direction axis and are axially pre-tightened by the first bolt (3-4); The amplitude transformer (3-1) is a variable cross-section rod with parallel end faces at both ends. One end has a larger contact area, while the other end has a smaller contact area. The end with the larger contact area has an internal threaded hole. The piezoelectric actuator (3-2) has parallel end faces and an axial through hole. The end cap (3-3) has parallel end faces and an axial through hole. One end face of the piezoelectric actuator (3-2) is in contact with the upper end face of the end cap (3-3), and the other end face is in contact with the amplitude transformer (3-1). The end face of the section with the larger contact area is in contact with the end face; the first bolt (3-4) passes through the axial through hole of the end cover (3-3) and the through hole of the piezoelectric actuator (3-2) in sequence, and is screwed into the internal thread hole of the end with the larger contact area of ​​the cross-section of the amplitude rod (3-1) to achieve axial fastening of the three; the axes of the first bolt (3-4), the end cover (3-3) and the piezoelectric actuator (3-2) are collinear, and the head end face of the first bolt (3-4) is in contact with the lower end face of the end cover (3-3); The thin end of the amplitude rod (3-1) is connected to the lower end face of the flexible hinge (2), and the upper end face of the flexible hinge (2) is fixedly connected to the lower end face of the end platform (1); the amplitude rod (3-1) and the piezoelectric actuator (3-2) are both provided with brackets for installation and fixation in the circumference, so as to realize the overall constraint of the platform and the efficient coupling of vibration energy.

2. The four-sandwich piezoelectric actuator co-directional centrally symmetrical arrangement multidimensional vibration platform according to claim 1, characterized in that, The end platform (1) is implemented using a planar structure with dual-axis symmetry, namely a circle, a square or a cross, to ensure that the XZ plane and the XY plane are mirror symmetric.

3. The four-sandwich piezoelectric actuator co-directional centrally symmetrical arrangement multidimensional vibration platform according to claim 1, characterized in that, The piezoelectric actuator (3-2) is any one of a longitudinal vibration ceramic group, a bending vibration ceramic group around the Y-axis, and a bending vibration ceramic group around the Z-axis. Each ceramic group is provided with a driving electrode and a ground electrode. By applying an alternating voltage signal between the corresponding driving electrode and the ground electrode, specific modes of longitudinal vibration, bending vibration around the Y-axis, or bending vibration around the Z-axis are excited.

4. The four-sandwich piezoelectric actuator co-directional centrally symmetrical arrangement multidimensional vibration platform according to claim 2, characterized in that, The piezoelectric actuator (3-2) is one of the following structures: stacked, surface mount, piezoelectric tube, or any combination thereof.

5. The four-sandwich piezoelectric actuator co-directional centrally symmetrical arrangement multidimensional vibration platform according to claim 1, characterized in that, The flexible hinge (2) is fixed to the end platform (1) and the amplitude rod (3-1) by means of threaded connection, adhesive bonding, welding or integral molding.

6. The four-sandwich piezoelectric actuator co-directional centrally symmetrical arrangement multidimensional vibration platform according to claim 1, characterized in that, The flexible hinge (2) adopts a dual-axis symmetric or universal structure to transmit the axial linear motion and multi-directional bending deformation output by the actuation unit (3), and adapts to the six-degree-of-freedom motion requirements of the end platform (1).

7. The four-sandwich piezoelectric actuator co-directional centrally symmetrical arrangement multidimensional vibration platform according to claim 1, characterized in that, The vibration platform is installed and fixed by any one of the following methods: amplitude rod bracket, piezoelectric actuator bracket, or a combination of the two, to achieve coupling and stable support of vibration energy.

8. The four-sandwich piezoelectric actuator co-directional centrally symmetrical arrangement multidimensional vibration platform according to claim 1, characterized in that, The axes of the four actuation units (3) are arranged parallel to each other; the included angle between any two axes is less than 90 degrees.

9. The four-sandwich piezoelectric actuator co-directional centrally symmetrical arrangement multidimensional vibration platform according to claim 1, characterized in that, The geometric center point, XZ symmetry plane and XY symmetry plane of the end platform (1) in the vibration platform simultaneously satisfy central symmetry and mirror symmetry.

10. An excitation method for a multidimensional vibration platform with a four-sandwich piezoelectric actuator arranged in a co-directional, centrally symmetrical configuration, characterized in that... The excitation method is based on the four-sandwich piezoelectric actuator co-directional, centrally symmetrically arranged multidimensional vibration platform described in claim 3, and the method includes the following steps: The translational vibration of the end platform (1) along the X-axis is excited by the longitudinal vibration ceramic group in the four piezoelectric actuators (3-2) when an in-phase alternating voltage signal is applied and the frequency matches the longitudinal vibration resonant mode; The translational vibration of the end platform (1) along the Y-axis is excited by the bending ceramic group around the Z-axis in the four piezoelectric actuators (3-2) when an in-phase alternating voltage signal is applied and the frequency matches the bending resonant mode around the Z-axis; The translational vibration of the end platform (1) along the Z-axis is excited by the bending ceramic group around the Y-axis in four piezoelectric actuators (3-2) when an in-phase alternating voltage signal is applied and the frequency matches the bending resonant mode around the Y-axis.