Review on Multiple‐Degree‐of‐Freedom Cross‐Scale Piezoelectric Actuation Technology

Piezoelectric actuation technology has been widely used in various precise‐oriented fields. Its notable advantages include high resolution, rapid response speed, output force with high density, and immunity to electromagnetic interference. Characteristics of cross‐scale and multiple‐degree‐of‐freedom (multi‐DOF) output motions are of utmost importance in the context of micro‐/nanopositioning technology. For decades, researchers have been working to develop various piezoelectric devices that exploit these important properties. In this review, a comprehensive review of recent research efforts in the field of cross‐scale multi‐DOF piezoelectric drive technology is provided. To commence, it provides an in‐depth exploration of the unique advantages associated with piezoelectric actuation, demonstrating them through comparative analyses with alternative actuation methods. Subsequently, the complexity of piezoelectric cross‐scale motion is introduced, and the multi‐DOF piezoelectric motion is classified in detail. Furthermore, the practical applications of multi‐DOF cross‐scale piezoelectric actuation technology are systematically elucidated, highlighting its versatility and suitability in real‐world environments. Finally, an in‐depth discussion that addresses the challenges encountered in the field is provided, and the prospective directions for further developments in piezoelectric actuation technology are outlined. This scholarly contribution plays an important role in guiding future research and innovative initiatives.


Introduction
Precision actuation technology is one of the most important technologies in micro/nano machining and assembly, biological manipulation, optical pose adjustment, and other precision fields.[3] The stroke index determines the motion workspace; the larger the stroke, the larger the workspace; the motion resolution index determines the motion accuracy, so the high motion resolution is the premise of achieving high-precision positioning; the DOF index is expected to be enough, because enough number of DOF can obtain stronger flexibility.Generally, the millimeterscale stroke, nanometer-scale resolution, and multi-DOF characteristics are simultaneously required in ultraprecision application fields.
Precision actuation technologies can be mainly classified into electromagnetic actuation, electrostatic actuation, electrothermal actuation, magnetostrictive actuation, and piezoelectric actuation according to the actuation principle, as shown in Figure 1.
Electromagnetic actuation technology [4][5][6][7] converts electric energy into mechanical energy based on the electromagnetic effect, which can achieve large motion stroke, but it is easily susceptible to external electromagnetic interference and requires additional electromagnetic protection for devices; in addition, the structure for multi-DOF actuation is complex, because multi-DOF actuation needs multiple one-DOF actuators and other auxiliary devices, leading to the system with large volume and mass.Electrostatic actuation [8][9][10][11] uses the interaction of attractive and repulsive forces between charges to actuate the electrodes to generate motion, which has the advantages of fast response, low power consumption, and simple structure, but it needs high requirements for the actuation voltage and the environmental condition; in addition, the pull-in effect is unavoidable, which results in a shortened life span of the actuators.Based on the thermoelectric conversion principle, electrothermal actuation [12][13][14][15] uses the elastic deformation of the material itself after heating to achieve micro-displacement and force output, which has the advantages of low actuation voltage and no electromagnetic interference, but it needs good thermal insulation condition; in addition, the existing thermal lag leads to slow response speed.Magnetostrictive actuation [16][17][18][19] can realize force and micro-displacement output based on the magnetostrictive positive effect, which has the advantages of fast response speed and large stroke, but it is easily susceptible to external electromagnetic interference; in addition, the unavoidable eddying effect results in low working efficiency.Based on the inverse piezoelectric effect, piezoelectric actuation [20][21][22][23][24] converts electrical energy into mechanical energy, namely, the polarized piezoelectric ceramic components produce nanoscale mechanical deformations under the action of an external electric field.Piezoelectric actuation technology has the advantages of high resolution, output force with high density, fast response speed, and no electromagnetic interference.[27] Therefore, piezoelectric actuation has gradually become the core technology in ultraprecision engineering fields.
In this comprehensive review, we provide a detailed overview of piezoelectric actuation technology in four key aspects: crossscale actuation, multi-DOF characteristics, application fields, as well as the existing problems and prospects of piezoelectric actuation technology.Section 2 elaborates on the complexities of cross-scale characteristics, along with a comprehensive classification of piezoelectric actuation methods to achieve cross-scale motion.Section 3 offers an extensive overview of multi-DOF piezoelectric actuation technology; classifies it based on series, parallel, series-parallel structural configurations; and describes the methodology to achieve multi-DOF parallel piezoelectric actuation with a single actuator.Furthermore, Section 4 explores diverse applications of multi-DOF cross-scale piezoelectric actuation technology.Finally, in Section 5, we address both the current challenges and the promising prospects inherent in piezoelectric actuation technology.

Cross-Scale Piezoelectric Actuation 2.1. Cross-Scale Characteristic
Cross-scale characteristic [28] is defined as the characteristic that balances large stroke and high resolution, which is the key performance of many precision devices.Generally, macromotionmicromotion platform integrates the advantages of macromotion and micromotion, and can simultaneously obtain large stroke, high velocity, and motion resolution.For example, macromotion is generated by a coarse stage consisting of leadscrews or ball screws, micromotion is usually actuated by the piezoelectric actuator, the voice coil motor, or the microelectromechanical systembased actuator, which can compensate for positioning errors resulting from the coarse stage.Yabui et al. proposed a dual-stage actuator of head positioning control system in hard disk drives, [29] which was composed of a voice coil motor for macromotion and a piezo actuator for micromotion.Kwon et al. proposed a coarse/fine dual-stage manipulator, [30] which achieved the 200 Â 100 mm macromotion with large stroke characteristic based on the servomotor and the 100 Â 100 μm micromotion with nano-scale resolution characteristic based on the piezoelectric actuation platform.Pahk et al. proposed an ultraprecision positioning system with a servomotor and a piezoelectric actuator, [31] a ball-screw-based servomotor was used as the global stage and a piezoelectric actuator as the microstage, which achieved the large stroke with 200 mm and the high positioning accuracy within 10 nm.Song et al. proposed a coarse-fine dual stage with high-speed and ultraprecise characteristics, [32] the fine stage with the resolution of 10 nm actuated by a voice coil motor tracked the designed trajectory, and the coarse stage with the stroke of 300 mm actuated by permanent-magnet linear synchronous motor tracked the trajectory of the fine stage to prevent its motion saturation.Kawashima et al. proposed a coarse/fine dual-positioning stage using pneumatic actuators, [33] where the coarse movement was actuated by a pneumatic cylinder with air bearings and the long stroke was up to 100 mm, the fine movement was actuated by pneumatic bellows and the motion resolution was minimized to 20 nm.Zhu et al. proposed a magnetically levitated parallel actuated dual-stage motion system for six-axis precision positioning, [34,35] which consisted of a 6-DOF maglev primary stage for coarse positioning and a 2-DOF planar motion flexurebased secondary stage for fine positioning, and the dual-stage motion system had the stroke of 5 mm and the resolution of 150 nm.Chun et al. proposed a novel dual-mode motion mechanism capable of achieving nanopositioning on a monolithic linear motion platform, [36] where the coarse motion with the stroke of 1 μm was actuated by a piezoelectric motor and the fine motion with the resolution of 2.5 nm was actuated by a fluidic pressure-fed mechanism.

Piezoelectric Actuation Technology
Although the aforementioned macromotion-micromotion platforms can achieve cross-scale characteristic, their structures and control methods are always complicated due to the structure integration and the control switch of macro-and microdevices.Different from the traditional macroactuation-microactuation technology using two types of actuators, piezoelectric actuation technology can achieve cross-scale characteristic based on simple structure and control method.Based on the inverse piezoelectric effect, the polarized piezoelectric ceramics can produce nanoscale mechanical deformations under the influence of external electric fields.By combining friction-pair transmission forms, large stroke motion can be achieved in different actuation modes.Therefore, piezoelectric actuation technology can achieve crossscale actuation characteristics in multiple actuation modes.In addition, the piezoelectric actuation technology has some promising advantages, such as no electromagnetic interference, simple and flexible structure.Piezoelectric actuation modes mainly include ultrasonic actuation, [37][38][39][40][41][42] direct actuation, [43][44][45][46] inchworm actuation, [47][48][49][50][51][52] and inertia actuation [53][54][55][56] according to the operating principle.

Piezoelectric Ultrasonic Actuation
Ultrasonic actuation is one of the piezoelectric actuation technologies, and its working frequency is always set over 20 kHz, which can obtain large velocity up to meter-scale per second.According to the way of realizing elliptical motion of the stator, the ultrasonic actuation can be classified into traveling wave actuation, standing wave actuation and hybrid mode actuation, as shown in Figure 2.
The traveling wave actuation means that piezoelectric ceramics in the elastic stator are used to excite traveling bending vibration waves, so that the driving foot on the driving surface of the elastic stator can generate elliptical trajectories with microscale amplitudes, and the large stroke motion of the mover can be achieved by superimposing actuation displacement of the periodic elliptical trajectory.Based on a radial bending mode of a thick ring, a traveling wave ultrasonic motor was proposed, [57] and the traveling wave was generated by 20 lead zirconium titanate (PZT) stacks and 20 block springs nested alternately into 40 slots cut in the ring's outer surface; the vibration amplitudes of surface particles were 4.1 and 3.9 μm in circumferential and radial directions, respectively; and the ultrasonic motor achieved the maximum velocity and torque of 146 r min À1 and 1.0 N•m under the frequency of 19.85 kHz, respectively.The smallest ultrasonic motor using a cube with a side length of 0.5 mm was proposed, [58] its vibration mode was generated by three waves along the circumference of a hole in its stator, and the ultrasonic motor achieved the angular velocity of 123 rad s À1 and the peak torque of 0.2 μN m.Based on the solution-deposited thin-film lead zirconate titanate and wafer-scale microelectromechanical system fabrication techniques, bidirectional rotary motion of a millimeter-scale traveling wave ultrasonic motor was achieved; [59] the rotary velocity was up to 1730 r min À1 with a diameter of 2 mm.A rotary traveling wave ultrasonic motor with double vibrators was proposed, [60] which  [63] Copyright 2018, AIP Publishing.d) The standing wave ultrasonic motor by Park et al.Reproduced with permission. [66]Copyright 2012, Elsevier.e) The standing wave ultrasonic motor by Dabbagh et al.Reproduced with permission. [68]Copyright 2017, Elsevier.f ) The travelling wave ultrasonic motor by Chen et al.Reproduced with permission. [57]Copyright 2014, IEEE.g) The travelling wave ultrasonic motor by Liu et al.Reproduced with permission. [61]Copyright 2012, Elsevier.h) The travelling wave ultrasonic motor by Ma et al.Reproduced with permission. [62]Copyright 2020, IEEE.i) The hybrid-actuated ultrasonic motor by Jian et al.Reproduced with permission. [75]Copyright 2017, Elsevier.j) The hybrid-actuated ultrasonic motor by Liu et al.Reproduced with permission. [77]Copyright 2015, Elsevier.k) The hybrid-actuated ultrasonic motor by Yan et al.Reproduced with permission. [78]Copyright 2016, Elsevier.
used the elastic body of the stator and rotor to generate corresponding traveling waves to force each other forward in the contact zone; the vibration amplitude of the stator was up to 1.42 μm and the ultrasonic motor achieved the rotary velocity more than 30 r min À1 under the frequency of 47.5 kHz.Liu et al. proposed a square-type rotary ultrasonic motor with four driving feet, [61] where the elliptical motion on the driving tip was generated by superimposing longitudinal vibrations of the bolt-clamped transducers; both the particle vibration amplitudes on the driving feet in horizontal and vertical directions achieved 5.3 μm, and the ultrasonic motor achieved no-load velocity of 71 r min À1 and the maximum torque of 12.3 N•m under the voltage of 200 V rms .Ma et al. proposed a rotary traveling wave ultrasonic motor based on the B (0, 5) axial bending mode of a ring-shaped stator, [62] which used four groups of piezoelectric ceramics embedded in the stator to generate a bending traveling wave; average axial and circumferential amplitudes were 1.14 and 0.94 μm, respectively; and the ultrasonic motor achieved the output velocity of 53.86 r min À1 under the voltage of 250 V p-p , the frequency of 24.86 kHz, and the preload of 0.69 N.
The standing wave actuation means that piezoelectric ceramics in the stator elastomer are used to excite bending vibration standing waves, so that the driving teeth arranged at a specific position of the standing wave can generate elliptical trajectories with the microscale amplitude, and the large stroke motion of the mover can be achieved by superimposing actuation displacement of the periodic elliptical trajectory.A standing-wave bidirectional linear ultrasonic motor with a high thrust-weight ratio was proposed, [63] which used modes B1 and B2 to achieve bidirectional movement through a single-phase excitation signal; the ultrasonic motor with the size of 13 Â 5.8 Â 5 mm 3 achieved the thrust-weight ratio of 134.69; the vibration amplitudes of the driving foot were 0.19 and 0.05 μm in horizontal and longitudinal directions, respectively; and the maximum velocities of 158 mm s À1 at 58.917 kHz in the B1 mode and 137 mm s À1 at 113.581 kHz in the B2 mode, respectively.A multimode single vibrator piezoelectric motor with a sandwiched structure was proposed, [64] which used two orthogonal bending modes to actuate a piezoelectric plate; the ultrasonic achieved the maximum velocity and torque of 80 rpm and 2 mN m under the voltage of 104 V p-p , respectively.Chen et al. [65] developed a standing wave linear ultrasonic motor operating in in-plane expanding and bending modes; the maximum step displacements of the stator were 0.28 μm in transverse direction at the resonant frequency of 88.8 kHz and 0.23 μm in longitudinal direction at the resonant frequency of 89.4 kHz, respectively; and the maximum velocity was up to 310 mm s À1 under the voltage of 250 V p-p and the frequency of 89 kHz.Some standing wave ultrasonic motors with tubular structure were designed.He et al. [66,67] used a single vibration bending mode of a piezoelectric tube to construct a rotary tubular ultrasonic motor based on the brass-PZT square tube, which used one driving signal to excite vibration in a single bending mode to generate reciprocating diagonal trajectories of teeth, and the rotor was actuated by the tangential forces along the same circumferential direction, and the bidirectional motion was achieved by simply switching the bending direction.Dabbagh et al. [68] proposed a compact tubular ultrasonic motor actuated by a single-phase source, which achieved the maximum velocity and torque of 59 rpm and 0.28 mN m at the voltage of 80 V p-p .
The hybrid mode actuation [69][70][71][72][73][74] means that the piezoelectric ceramics in the stator composite elastomer are used to excite the vibration modes of the same frequency, where one vibration mode is used to provide positive pressure between the stator and the mover, and the other vibration mode provides driving force by means of the friction between the stator and the mover, so that the mover can generate linear or rotary motion.A clamped V-type linear ultrasonic motor [75] was proposed for an absolute gravimeter based on a new clamping method with sufficient tangential rigidity and the ability to facilitate preloading, which achieved the maximal thrust and velocity of 43 N and 1400 mm s À1 , respectively.A bonded V-shaped linear ultrasonic motor [76] with large thrust-weight ratio was proposed, which was operated in the coupled longitudinal-bending mode, and the coupled longitudinal-bending mode of the V-shaped transducer with a flexible joint provided higher vibration efficiency and more convenient adjustment.Liu et al. [77] proposed a single-foot T-shaped linear piezoelectric motor, which used two orthogonal longitudinal vibration modes to generate the elliptical trajectory of driving foot, where the horizontal displacement actuated the runner and the vertical displacement provided the preloading force.Yan et al. [78] proposed a bonded structure ultrasonic motor based on bending-bending mode, which was easier to assemble and adjust compared with the bolt-clamped-type ultrasonic motor.A bonded-type crossbeam ultrasonic motor [79] used two orthogonal first bending vibrations to generate elliptical trajectories of the two driving feet, and the symmetric structure of the ultrasonic motor successfully solved the problem of mode frequency degeneracy.A 2-DOF ultrasonic motor [80] was developed based on a longitudinal-bending hybrid sandwich transducer, which achieved the motion in X direction by the hybrid modes of the second longitudinal and fifth bending vibrations of the motor, and the motion in Y direction by the composition of two orthogonal fifth bending vibrations; the proposed ultrasonic motor achieved the maximum output forces of 24 and 22 N in X and Y directions, respectively.And then Liu et al. [81] used two parallel longitudinal-bending hybrid piezoelectric actuators to develop a 2-DOF linear piezoelectric stepping platform, which achieved the motion in X direction by the hybrid of the vertical and horizontal bending motions, and the motion in Y direction by vertical bending and longitudinal hybrid motions of two actuators.The characteristics of some ultrasonic motors with different working principles are listed and compared in Table 1.

Piezoelectric Direct Actuation
Direct actuation can directly achieve motion output based on the inverse piezoelectric effect, as shown in Figure 3, but its stroke is short, which is about 0.1% of the length of excitation ceramics, so the flexible hinge amplification mechanism is always used to obtain large output displacement, which can be amplified to hundred micron scale, but the structure stiffness will be reduced at some extent.
A compact piezo-actuated flexure stage [82] achieved large stroke of 97.32 μm and high resolution of 10 nm in vertical direction, where an orthogonal compound bridge-type amplification mechanism was introduced to amplify the output displacement, and the displacement amplification ratio was up to more than 6.Yang et al. [83] proposed a compact piezoelectric nanopositioning mechanism based on the pile-up structure, which achieved the large amplification ratio of up to 13.3 and the high resonant frequency of 1211 Hz; the proposed positioning mechanism achieved the resolution of 40 nm and the output displacement of 29.5 μm.Based on the dual-stacked bridge-type amplification mechanism, [84] a piezo-actuated nanopositioning stage with low coupling and high amplification characteristics was designed, which achieved the stroke of 127 μm with the resolution of 20 nm under the amplification ratio of 8.9.In addition, the team also designed other micro/nanopositioning platforms based on the direct-actuation principle and flexure-hinge amplification mechanisms. [85,86]Large workspace was obtained by multilevel amplification mechanisms, [87,88] including four leverage mechanisms, two Scott-Russell mechanisms, and a Z-shaped flexurehinge mechanism, the proposed micro/nanopositioning stage with the resolutions of 70 nm achieved the strokes of 1140 Â 320 μm 2 and the displacement amplification ratio of 13.0.Based on a hybrid actuation mechanism, [46] including a half bridge-type mechanism and two symmetric Scott-Russell mechanisms, a parallel XY nanopositioning platform with totally decoupled characteristic was proposed, the output displacement was amplified by two-level displacement amplification mechanisms, and the amplification ratios along X and Y axes were up to 5.2 and 5.4, respectively.An actuator-internal micro/ nanopositioning stage was developed, [89] which used the Chen et al. [57] Travelling wave 19.85 146 r min À1 4.1/3.91.0 N mm Φ90 Â 67 Mashimo et al. [58] Travelling wave 950 1175 r min À1 0.011 0.2 mN mm 0.5 Â 0.5 Â 0.5 Dong et al. [60] Travelling wave 47.5 >30 r min À1 1.42 0.75 N m ≈Φ30 Â 45 Liu et al. [61] Travelling wave 23   [82] Copyright 2019, IEEE.c) The mechanism by Yang et al.Reproduced with permission. [83]Copyright 2020, IEEE.d) The stage by Zhang et al.Reproduced with permission. [84]Copyright 2016, Springer-Verlag.e) The stage by Zhu et al.Reproduced with permission. [87]Copyright 2016, AIP Publishing.f ) The stage by Wang et al.Reproduced with permission. [89]Copyright 2019, IEEE.
compound bridge arm configuration and compact flexure-hinge structure to obtain large stroke and high lateral stiffness; the proposed stage achieved the resolution of 8 nm, and the displacement amplification ratio of 5.46/5.37 in X/Y-axis directions, respectively.

Piezoelectric Inchworm Actuation
Inchworm actuation is regarded as a bionic actuation, which imitates the motion of the inchworm insect, and it can simultaneously obtain large stroke and high-resolution characteristics; [48,[90][91][92][93][94][95] in general, it contains two clamping units and one feeding unit, as shown in Figure 4, so it has complex structure.
To simplify the complicated structure and control system, Ma et al. [49] developed a walker-pusher inchworm actuator actuated by two piezoelectric stacks with the characteristics of large carrying capacity and no backward motion, the proposed actuator achieved the maximum velocity of 0.471 mm s À1 and the carrying load of 6.1 kg.Based on the three-jaw-type clamping mechanism, Deng et al. [96] proposed a compact inchworm piezoelectric actuator, which actuated an output shaft to realize linear motion based on the automatic centering and guidance functions of the three-jaw-type clamping mechanism; the proposed actuator achieved the maximum velocity of 155.5 μm s À1 and the thrust force of 12.3 N. Different from the traditional structure of the inchworm actuator, the clamping switching was achieved by only one piezoelectric actuator based on flexible supported baffles, and a high-speed bidirectional inchworm actuator using two piezoelectric actuators was developed, [97] which achieved the maximum velocity of 5.1 mm s À1 and the thrust force of 1.6 N. To solve the problems of complex control and uneven friction, a magnetorheological elastomer (MRE) was used as the material of clamping unit, and a piezoelectric inchworm actuator with high-positioning accuracy and large output force was proposed, [98] which used an MRE-capillary-cover sandwich structure to achieve rigid-to-elastomeric clamping, so that the feeding motions were performed.Ghenna et al. [99] proposed a compact inchworm piezoelectric linear motor with high integration flexibility and blocking force, which consisted of an actuation mechanism and two doubled clamping mechanisms; the proposed motor achieved the maximum velocity of 2.9 μm s À1 under the voltage of 80 V and the frequency of 1.25 Hz.Ling et al. [100] developed a pusher-type inchworm piezoelectric actuator based on an asymmetric driving and clamping configuration, the proposed actuator used a lever amplification mechanism and a hexagonal output shaft to increase the step and enhance the load capacity, respectively.

Piezoelectric Inertial Actuation
The inertia actuation uses sawtooth voltage signal with different duty cycles to excite the piezoelectric ceramics, generating alternating slow and rapid deformation, and large stroke can be obtained by accumulating step motions achieved by alternate stick and slip motions, [101][102][103][104][105][106] which consists of inertial impact actuation and inertial stick-slip actuation, as shown in Figure 5.The essence of the inertial actuation is the friction force change between the maximum static friction force and the sliding friction force.
Based on the inertial stick-slip actuation principle, a vertically moving nanopositioning stage was developed, [107] which achieved the stroke of 22 mm with upward and downward positioning accuracy of 7 and 5 nm, respectively; in addition, the maximum upward and downward velocities were, respectively, 0.77 and 2.70 mm s À1 .Qin et al. used a composite flexible hinge to actively control the contact force between the driving foot and the slider, and solved the contradiction between large load capability and displacement backward suppression; [108] the proposed inertial actuator achieved the maximum velocity of 4.1 mm s À1 under the frequency of 370 Hz and the maximum load of 70 g under the frequency of 200 Hz, respectively.Zhang et al. [109] proposed a stick-slip piezoelectric actuator with the characteristics of high resolution, large velocity, and driving force, which used the coupling motion of a triangular driving mechanism to generate the clamping effect of the stick phase and the releasing effect of the slip phase, so the proposed actuator achieved 11 times larger driving load and 3 times higher driving velocity.Based on the combination of a lever flexible hinge and a triangular flexible hinge, a stick-slip piezoelectric actuator was designed, and the motion stroke and velocity were amplified by the lever flexible hinge, and the load capacity was improved by the clamping force transmitted by the triangular flexible hinge. [110]Based on the bending-bending hybrid mode, Deng et al. [111] developed an inertial piezoelectric actuator bending independently in the horizontal and vertical directions, where the horizontal bending pushed the slider to move step by step and the vertical bending adjusted the friction force in the driving process.The proposed actuator achieved the maximum velocity of 350 μm s À1 under the voltage of 400 V p-p and the frequency of 250 Hz.Based on the parasitic motion generated by a rhombus-type flexure-hinge mechanism, an actuator was developed, [112] which achieved the maximum carrying load of 135 g, and the maximum velocity of 13.08 mm s À1 under the voltage of 100 V p-p and the frequency of 570 Hz.
In summary, the ultrasonic actuation works on the resonant state of system, and it can achieve large velocity, but its displacement resolution is limited to micrometer or sub-micrometer scales in general, and there are severe wear and heating problems, which means that it cannot work continuously for a long time.Compared with the ultrasonic actuation, the direct actuation, the inchworm actuation, and the inertial actuation can be classified as the nonresonant actuation, and the characteristics of some nonresonant motors with different working principles are listed and compared in Table 2.The direct actuation can obtain nanoscale even sub-nanoscale resolution, but its stroke is limited, generally a few micrometers.Combining with the flexible hinge amplification mechanism, the piezoelectric direct actuation can obtain the stroke with 100 μm range.The inchworm actuation can simultaneously obtain large stroke and high resolution, but it has large size, complex structure, and control system in general.The inertial actuation can simultaneously obtain these characteristics of large stroke and high resolution, and it has simple and compact structure, but the problem of displacement backward usually exists, which has an impact on the motion stability.In summary, these four piezoelectric actuation methods can achieve the cross-scale motion characteristic and solve some macromotion-micromotion problems, as shown in Figure 6.
Some companies have commercialized a series of precision actuators based on the piezoelectric actuation principle, such as Physik Instrumente (PI) in Germany, Harbin Core Tomorrow Science & Technology Co., Ltd., in China, Newport in the USA and so on.PI company has developed many types of cross-scale positioning platforms, which can satisfy different requirements and have been widely applied in the industrial microassembly, measurement, and medical devices.For example, the XY piezoelectric motion platform U-751.24 can achieve the strokes of 25 Â 25 mm and the motion resolution of 0.3 μm, which can be used in the microscope, biotechnology, and laboratory automation.The piezoelectric motion platform P-611.ZS can achieve linear motion along Z axis with the stroke of 100 μm  [107] Copyright 2020, Springer-Verlag.d) The actuator by Qin et al.Reproduced with permission. [108]Copyright 2019, Elsevier.e) The actuator by Zhang et al.Reproduced with permission. [109]Copyright 2019, IEEE.f ) The actuator by Deng et al.Reproduced with permission. [111]Copyright 2018, Elsevier.g) The actuator by Gao et al.Reproduced with permission. [112]Copyright 2019, AIP Publishing.and the resolution of 0.2 nm, which can achieve highly accurate positioning.The linear actuator N-310.16 can achieve the stroke of 125 mm and the resolution of 0.03 nm.Harbin Core Tomorrow Science & Technology has also produced many types of cross-scale positioning platforms.For example, the piezoelectric platform P78A.Z200K can achieve linear motion along Z axis with the stroke of 200 μm and the resolution of 3 nm, and it can be used in the vacuum environment.XY65P83S K À1 is a macroplatform-microplatform, which can achieve linear motions along X and Y axes; the macromotion with the stroke of 13 mm is generated by a hand micrometer, and the micromotion with the resolution of 0.5 nm is actuated by a piezoelectric mechanism.The piezoelectric positioning platform P11.X100K can achieve the stroke of 100 μm and the resolution of 1.0 nm, which can be used in nanometer imprinting technology.

Multi-DOF Piezoelectric Actuation
The output DOF is one of the key parameters of the positioning platform, which plays an important role in the ability to adjust the pose; the more the output DOFs, the stronger the flexibility of the positioning platform, such as, in the field of space optical pose adjustment, the pose of the sub-mirror needs to be adjusted by a six-DOF positioning platform, so multi-beam light can be adjusted to con-focus and co-phasing state; in the field of biomedical engineering, aiming at the fine manipulation of the complex morphological organisms; the more DOFs of the puncture device, the higher the operation flexibility and the larger the workspace; in the field of micro/nanomanufacturing, the flexibility of the tool or workpiece depends on their DOF number, which has a great influence on the processing technology.Therefore, research on the multi-DOF piezoelectric actuation technology is very necessary for the development of the precision operation field.Generally, the number of DOF can be expanded by connecting multiple one-DOF mechanisms in series, parallel, or seriesparallel; in addition, multi-DOF output can be also achieved by a single piezoelectric actuator, which has the ability of generating multidirectional actuation trajectories.

Series Multi-DOF Piezoelectric Actuation
A series mechanism refers to the sequential connection of several one-DOF mechanisms, and the output motion of each front mechanism is the input of the rear mechanism.The outputs with multi-DOF can be achieved by combining multiple single-DOF Wu et al. [82] Direct-actuated 373 97.32 μm -58 Â 20 Â 15.5 Yang et al. [83] Direct-actuated 1211 29.5 μm -138 Â 88 Â 25 Zhang et al. [84] Direct-actuated 200 127 μm -69 Â 69 Â 69 Zhu et al. [87] Direct-actuated 185-225 1140/320 μm -195 Â 130 Â 22 Wang et al. [89] Direct-actuated 285.8 55.4/53.2μm -160 Â 160 Â 12 Ma et al. [49] Inchworm-actuated 19 471.0 μm s À1 11.76 N 61 Â 29 Â 7 Deng et al. [96] Inchworm-actuated 40 155.5 μm s À1 12.3 N Φ34 Â 40 Sun et al. [97] Inchworm-actuated 60 5100 μm s À1 1.6 N -Lu et al. [98] Inchworm-actuated 24 1250.4μm s À1 0.42 N 100 Â 100Â-Ghenna et al. [99] Inchworm-actuated 1.25 2.9 μm s À1 5 N 100 Â 16 Â 7 Ling et al. [100] Inchworm-actuated 650 44 690 μm s À1 0.6 N 110 Â 106 Â 10 Pan et al. [107] Inertial-actuated 1000 0.77/2.7 mm s À1 72 g 24 Â 12 Â 30 Qin et al. [108] Inertial-actuated 370 4.1 mm s À1 70 g 80 Â 60 Â 20 Zhang et al. [109] Inertial-actuated 3500 46.67 mm s À1 4000 g 140 Â 100 Â 37 Deng et al. [111] Inertial-actuated 250 0.35 mm s À1 5880 g Φ58 Â 71 Gao et al. [112] Inertial-actuated 570 13.08 mm s À1 135 g 75 Â 108 Â 31 mechanisms in series.Combining a linear inchworm actuator and a rotary inchworm actuator in series, Hua et al. [113] proposed a 2-DOF series linear-rotary inchworm actuator, where all flexible hinges for clamping and driving were integrated into a monolithic stator; the actuator achieved the maximum velocities of 482 μm s À1 and 0.01 rad s À1 , the resolutions of 19 nm and 0.3 μrad, and dynamic forces and torque of 39.2 and 0.38 N m in linear and rotary directions, respectively.Li et al. [114] proposed a series inchworm-actuated 2-DOF piezoelectric positioning platform, which achieved linear and rotary motions with large stroke and high resolution.And then the team developed a piezoelectric platform for 3D cellular bio-assembly system based on the Z-shaped flexure hinges and the parallel six connecting rods structure. [115]Lee et al. [116] proposed a series piezoelectric 2-DOF compliant platform using an automatic optical inspection system, which achieved linear motions along X and Y directions; where two orthogonal platforms were integrated into a 2-DOF structure, and this approach took the advantages of expansion of more DOFs.Pinskier et al. [117] designed a haptic-enabled modular flexure-based manipulator, which consisted of two one-DOF translational modules connecting in series; the manipulator achieved the motion strokes of 39.1 and 42.1 μm in X-and Y-axis directions, respectively.Based on the triangle amplification mechanism, Liu et al. [118] designed a series nanopositioning platform with large stroke and bidirectional symmetrical output characteristics, which achieved the strokes of 41.6 and 42.9 μm in X-and Y-axis directions, respectively.Li et al. proposed a compact 2-DOF series piezo-actuated positioning stage with the size of 55 Â 55 Â 30 mm 3 based on the parasitic motion of flexure-hinge mechanism and inertial actuation principle. [119]The positioning stage achieved large stroke of 19 Â 19 mm 2 and the first resonant frequency of 1900 Hz; in addition, the velocities along the positive and negative direction of X-and Y axes are 1499, 1180, 1648, and 1403 μm s À1 under the voltage of 100 V and the frequency of 100 Hz, respectively.Oubellil et al. proposed a 3-DOF nanorobotic system integrating scanning electron microscope, [120] which was composed of three inertial-actuated single-DOF platforms in series; a switch control strategy was designed to achieve the appropriate transition between the coarse positioning with large stroke and the fine positioning with high accuracy.Zhang et al. proposed a 2-DOF piezoelectric rotary-linear actuator with large stroke and high driving force based on inertial actuation principle, [121] which achieved linear and rotary motion resolutions of 26 nm and 0.019°and the maximum driving force/torque of 2.09 N/12.20 N mm, respectively.Rong et al. [122] proposed a 3-DOF XYZ compact nanopositioner with the size of 24 Â 24 Â 70 mm 3 consisting of three stick-slip inertial stages in series, which achieved the resolution of 10 nm in X/ Y/Z-axis directions and the maximum vertical carrying capacity of 70 g.Howald et al. proposed a piezoelectric inertial stepping motor with spherical rotor, [123] which achieved 3-DOF rotary motions; the angular step resolution was less than 4.8 μrad.Some series piezo-actuated platforms have been commercialized as shown in

Parallel-Type Multi-DOF Piezoelectric Actuation
A parallel mechanism is defined as a closed-loop mechanism with two or more DOFs actuated in parallel, where the mover and the fixed platform are connected by at least two independent motion sequences.The parallel-type multi-DOF piezoelectric platforms have been studied a lot.In the review, the parallel-type multi-DOF piezoelectric actuation technology is introduced according to different actuation methods, as shown in Figure 8.
Based on the proposed Z-shaped flexure hinges, [124] a parallel 2-DOF piezo-actuated fast tool servo platform was proposed, which achieved completely decoupled servo motions of the cutting tool in both the X-and Z-axis directions.Zhu et al. proposed a 2-DOF piezo-actuated parallel-kinematic micro/nanopositioning platform with multilevel amplification, [87,88] which consisted of two Scott-Russell mechanisms, four leverage mechanisms, and a Z-shaped flexure-hinge mechanism; the displacement amplification ratio was 13.0 and the strokes of 1140 Â 320 μm 2 were achieved; the first resonant frequencies along X and Y axes were 184.9 and 224.7 Hz, respectively; and the coupling errors were only 0.87% and 1.75% in two directions.A parallel XY nanopositioning platform with totally decoupled kinematics was proposed based on a novel hybrid actuation mechanism; [46] the hybrid hinge mechanism consisted of a half bridge-type mechanism and two symmetric Scott-Russell mechanisms, which were used for two-level displacement amplification and adjusting the output displacement direction; the amplification ratios along X and Y axes were 5.2 and 5.4, respectively; in addition, the coupling error was less than 1%.A parallel 2-DOF inertial-actuated piezoelectric positioning stage with size of 160 Â 160 mm 2 was proposed, [89,125] which used an arch-shape bridge-type amplification mechanism based on single notch circular flexure hinges to compensate the positioning error of coarse stage; high lateral stiffness and compact structure were achieved simultaneously based on the compound bridge arm configuration and compact flexure-hinge structure; the strokes of the stage were 55.4 Â 53.2 μm 2 and the resolution was 8 nm.Wang et al. proposed a 2-DOF parallel nanopositioning scanner with novel compound decoupling-guiding mechanism, [126] which used the combination of separated prismatic joint and parallelogram to reduce the parasitic displacement, and an amplifier and a symmetrical configuration were used to achieve decoupled motion with large stroke.The scanner obtained the working range of 40.2 Â 42.9 μm 2 with the positioning resolution of 10 nm and the coupling error of less than 0.6%.Qin et al. [127] proposed a decoupled 2-DOF monolithic mechanism with size of 187 Â 187 Â 20 mm 3 , and the statically indeterminate leaf parallelograms were used to reduce the coupling error between different DOFs and amplify the output displacement; the strokes of the platform were 82 Â 82 μm 2 , the first resonant frequency was 423 Hz, and the coupling error was less than 1%.Tian et al. proposed a novel flexure-based XY nanopositioning platform with a three-stage amplification mechanism; [128] the Scott-Russell mechanism, leverage mechanism and half bridge-type mechanism were arranged in series or parallel to achieve the amplification ratio of 12.7; the workspace was 126.54 Â 126.92 μm 2 and the first resonant frequency was 157.9 Hz.
Wu et al. proposed a novel piezo-actuated XY parallel stage with the size of 87.2 Â 87.2 Â 32 mm 3 for nanopositioning applications, [129] which provided the workspace of 212.48 Â 219.24 μm 2 with a resolution of 7 nm; the first resonant frequencies were 64.03/54.75Hz and the coupling errors were 5.19%/1.36%along X and Y axes, respectively.Zhang et al. [84] proposed a 2-DOF piezo-actuated parallel nanopositioning stage with low coupling and high amplification characteristics based on the dual-stacked bridge-type amplification mechanism, which achieved the stroke of 127 μm with a resolution of 20 nm and the amplification ratio of 8.9; the size of the positioning stage was 68.5 Â 68.5 Â 68.5 mm 3 , and the first resonant frequency was 222.2 Hz.In addition, the team also designed other 2-DOF  [113] Copyright 2014, Hindawi Publishing.b) The inchworm stage by Li et al.Reproduced with permission. [114]Copyright 2015, Elsevier.c) The direct-actuated-type XY stage by Li et al.Reproduced with permission. [115]Copyright 2017, MDPI.d) The direct-actuated-type XY stage by Lee et al.Reproduced with permission. [116]Copyright 2016, Elsevier.e) The direct-actuated-type XY stage by Pinskier et al.Reproduced with permission. [117]Copyright 2016, Elsevier.f ) The direct-actuated-type XY stage by Liu et al.Reproduced with permission. [118]Copyright 2016, Elsevier.g) The inertial XY stage by Li et al.Reproduced with permission. [119]Copyright 2020, IOP Publishing.h) The inertial XYZ stage by Oubellil et al.Reproduced with permission. [120]Copyright 2019, Elsevier.i) The inertial Zθ z stage by Zhang et al.Reproduced with permission. [121]Copyright 2006, AIP Publishing.j) The inertial XYZ stage by Rong et al.Reproduced with permission. [122]Copyright 2011, Elsevier.k) U-723.micro/nanopositioning platforms based on direct-actuation principle and flexure-hinge amplification mechanisms. [85,86]Huang et al. [45] optimized and designed a flexure-based XY positioning platform with size of 130.9 Â 130.9 mm 2 based on the finiteelement response surface method; the hybrid leaf spring and right circular hinges were used to increase the motion stroke and reduce the coupling error; the proposed platform achieved the stroke of 125 Â 125 μm 2 with the coupling error of less than 0.6% and the first resonant frequency of 740 Hz.Tang et al. [130] proposed a 2-DOF parallel nanopositioning stage with large stroke and low crosstalk characteristics and the size of 285 Â 285 mm 2 , which achieved the workspace of 1.035 Â 1.035 mm 2 and the coupling error of less than 0.5% in both X and Y axes, and the bandwidth and positioning accuracy in closed-loop condition were 119.6 Hz and 400 N m, respectively.Zhao et al. proposed a high-precision XY monolithic compliant mechanism for lens micro-adjustment, [131] which used 1RR-2RRR configuration to achieve the workspace of large than AE25 Â AE25 μm 2 with the coupling error of 0.91% and 0.72% in X and Y axes, respectively; the first resonant frequency was 212 Hz, and the resolutions along X and Y axes were AE4 and AE7 nm under the closed-loop condition, respectively.Zhong et al. proposed a 2-DOF parallel piezoelectric platform to improve the precision positioning accuracy of image stabilization mechanism; [132] the proposed platform achieved the workspace of 103.9 Â 104.8 μm 2 with the coupling error of less than 7.5% in X-and Y-axis directions and the first resonant frequency of 160 Hz.Polit et al. proposed a parallel piezo-actuated XY nanopositioning platform for high-rate micro/nanomanufacturing, [133] which achieved the first resonant frequency of 2000 Hz and the strokes of 15 Â 15 μm 2 with the resolution of 1 nm.Yang et al. proposed a parallel XY nanopositioning stage with multiple actuation modes, [134] which achieved the resolution of 27 nm and the first resonant frequency of 1570 Hz, and the coupling errors were less than AE20 μm in both X and Y axes. Lee et al. proposed a novel XY nanopositioning stage using a compliant parallel mechanism with small crosstalk and yaw motion, [135] which used parallelogram guides and leaf springs to compensate the coupling error and prevent the motion yaw; the stage with the size of 150 Â 150 Â 30 mm 3 achieved the stroke of 120 Â 120 μm 2 with the coupling error of 0.77 Â 0.435 μm 2 in both X and Y axes; the first resonant frequency was 200 Hz and the resolution was 3 nm.Yong et al. proposed a flexure-based XY compliant stage for fast nanoscale positioning, [136] which achieved the workspace of 25 Â 25 μm 2 in X-and Y-axis directions and had high dynamics characteristic to perform high-speed and precise scanning tasks under the frequency of 400 Hz.
Liang et al. [137,138] proposed a 2-DOF parallel monolithic compliant rotary platform for high accuracy pose adjustment, which used three Hooke's joints and two bridge-type mechanisms to achieve decoupling motion and large stroke, respectively; the proposed rotary platform achieved the maximum rotary angles of 2.04 and 2.12 mrad with the coupling error of 2.03% and 2.09% in X and Y axes, respectively; the settling time was 40 ms and the resolutions in both X and Y axes were 5 μrad.Chen et al. proposed a novel 2-DOF fast steering mirror based on three parallel piezoelectric actuators arranged in triangles, [139,140] which achieved the rotary strokes of 2.558°and 4.495°with the first resonant frequencies of 1036.8 and 654 Hz around X and Y axes, respectively.Jing et al. proposed a piezo-actuated two-axis mirror-scanning mechanism based on the flexure-hinge amplification mechanism, [141] which achieved large stroke of 54.8 Â 50.5 mrad around X and Y axes, respectively.Shao et al. proposed a 2-DOF piezoelectric fast steering mirror with cross-axis decoupling capability, [142] which achieved the tilt range of AE7 mrad with the coupling error of less than 2% in both axes; and the bandwidths of both axes were higher than 810 Hz.Dong et al. proposed a space-qualified piezoelectric fast steering mirror, [143] which was used for the tip-tilt correction of small jitter of the satellite platform in the image stabilization system of space astronomical telescopes based on high-resolution and large-bandwidth characteristics.Zhu et al. proposed a 2-DOF piezo-actuated fast steering mirror for laser beam tracking, [144] which was used to maintain precise pointing control.Zhang et al. studied the pointing performance of a piezoelectric fast steering mirror under shock and random vibration, [145] which verified the deviation angle of the proposed fast steering mirror during vibration.Zhong et al. proposed a high-bandwidth piezoelectric fast steering mirror with a permanent magnet preload force mechanism for optical scanning, [146] where a preload force mechanism based on permanent magnets was used to avoid additional dynamics induced by flexure hinges.Kim et al. proposed a 2-DOF piezoelectric laser scanner with large steering angle and fast response characteristics, [147] which achieved tilting angle of 21 Â 21 mrad 2 with the resolution of 13.57μrad and the frequency of 200 Hz. Park et al. proposed a 2-DOF piezoelectric fast laser scanner with the size of Φ28 Â 22 mm 3 based on three-point direct-actuation method, [148] which was used for beam adjustment in laser processing system to realize ultraprecision machining.Chang et al. [149] proposed a novel 2-DOF piezo-actuated fast steering mirror with high stiffness and good decoupling characteristic, which achieved rotary motions around X/Y axis by differential push-pull structure with four piezoelectric stack actuators arranged in cross and orthogonal state and enough lateral stiffness to overcome large lateral force by anti-shear structure; the piezoelectric platform with the first resonant frequency of 4578 Hz achieved the rotary angles of 2.33 Â 2.25 mrad with the resolution of 0.28 μrad and the coupling error of less than 0.75%.Shao et al. proposed a compact precision tilt positioning mechanism for inter-satellite optical communication, [150] which used three piezoelectric actuators and the elastic deformation of a flexure ring to achieve tilt motions.Fang et al. proposed a 2-DOF piezo-actuated fast steering mirror for incoherent laser beam combination, [151] which achieved the tilting range of 4 mrad with the first resonant frequency of 250 Hz.
Clark et al. [152] proposed a parallel 2-DOF linear-angular precision positioning stage based on the flexure-hinge amplification mechanism and piezoelectric direct-actuated method, which achieved the strokes of 10.31 μm and 535.8 μrad along X axis and around Z axis.Zhang et al. [153] proposed a small bipedal trans-scale precision positioning stage with small size and high flexibility; the stage with the size of 15 Â 10 Â 9.5 mm 3 achieved the linear and rotary velocities of 3.553 mm s À1 and 462.72 mrad s À1 under the voltage of 150 V and the frequency of 1500 Hz.Gao et al. [154] proposed a 2-DOF precision positioning stage generating linear-rotary motions along and around Z axis based on inertial actuation principle, which used the magnetic force to hold the moving element and stabilize the driving condition; the proposed stage achieved the strokes of 12 mm and 360°with the resolutions of 0.5 μm/10 00 , and the maximum velocities of 16 mm s À1 and 10.5 rpm.Peng et al. proposed a micro-stage with the size less than 1 cm 3 for linear-rotary positioning, [155] which achieved the strokes of 3.8 mm/unlimited and the maximum velocities of 5.7 mm s À1 /26 rpm along/around Z-axis based on inertial actuation principle, respectively.And then the team proposed a second-generation linear-rotary micro-stage with the size of 11 Â 11 Â 5.7 mm 3 for millimeter-scale positioning, [156] which was obtained by optimizing and miniaturizing the mechanical components of the previous stage.Chang et al. [157] proposed a precise linear-rotary positioning stage for optical focusing based on the stick-slip actuation principle, which achieved linear stroke of 5 mm and unlimited rotary stroke, the upward and downward linear resolutions of 82.32 and 86.26 nm, and the clockwise and anticlockwise rotary resolutions of 3.90 and 3.85 μrad, respectively.And then the excitation signal was optimized, [158] which was replaced with an alternate actuation signal, and the characteristics of carrying load capacity and the smoothness of cross-scale motion in vertical direction were improved greatly.Li et al. proposed a compact 2-DOF precision piezoelectric positioning platform based on the inchworm actuation principle, [114] which achieved the linear and rotary resolutions of 0.15 μm and 0.23 μrad, the largest linear and rotary velocity of 105.31 μm s À1 and 3521.7 μrad s À1 , the largest output force and torque of 4.9 N and 0.294 N m, respectively.Sun et al.
proposed a piezoelectric 2-DOF linear-rotary inchworm actuator with large stroke and high resolution, [159] where two clamping flexure modules were used to alternately hold the actuator shaft, the linear/rotary driving flexure module were used to provide the driving force and torque, respectively.The proposed actuator achieved the maximum velocities of 1450 μm s À1 and 34 270 μrad s À1 , the resolutions of 0.049 μm and 10.3 μrad, the maximum output force and torque of 11.8 and 73.5 N mm in linear and rotary motions, respectively.Aforementioned paralleltype 2-DOF stages include linear, rotary, and linear-rotary motion stages, as shown in Figure 9.
Wang et al. proposed a 4-DOF nanopositioning stage based on a six-branched-chain compliant parallel mechanism, [160] which used three types of uniaxial and one type of biaxial notch flexure hinges to achieve the nanoscale motion guiding and decoupling; the proposed stage achieved the output stiffness of 0.172 N μm À1 and the first resonant frequency of 368 Hz.Zhu et al. proposed a piezo-actuated monolithic compliant rotary spatial vibration system, [161] which achieved three decoupled translational vibrations with high working bandwidth and was arranged on the rotating spindle of a machine to assist diamond cutting system; the strokes of the spatial vibrator were up to 11.067, 10.100, and 12.254 μm along X/Y/Z-axis directions.A piezo-actuated 3-DOF compliant mechanism was designed to achieve the translational motions along X/Y/Z-axis directions, [162] which achieved large strokes of 84 Â 84 Â 50 μm 3 based on the bridge-type mechanisms, low coupling errors of less than 0.012%, 0.012%, and 0.08% of X/Y/Z-direction based on the dual-leaf parallelogram  [87] Copyright 2016, AIP Publishing.b) The direct-actuated XY linear stage by Wu et al.Reproduced with permission. [129]Copyright 2018, Elsevier.c) The direct-actuated XY linear stage by Zhang et al.Reproduced with permission. [84]Copyright 2016, Springer-Verlag.d) The direct-actuated XY linear stage by Yang et al.
hinges mechanisms and mirror symmetric configuration.Li et al. [163] proposed a parallel flexure-based XYZ micropositioning stage with good decoupling characteristic, which achieved the resolution of 38 nm in micropositioning applications.A parallel 3-DOF micro/nanostage for vibration-assisted milling was proposed, [164] which used a compound differential branch chain to solve the poor stiffness of traditional branch chains and large deflection errors; the stage achieved the strokes of 41.9 Â 34.3 Â 28.2 μm 3 along X/Y/Z directions, and the maximum coupling error of 0.53%; and the machining experiments of typical structural surfaces verified the effectiveness of the proposed stage for vibration-assisted milling.Based on a multi-objective optimal approach, a planar parallel 3-DOF nanopositioner was designed, [165] which achieved the first resonant frequency of 664 Hz and the linear and rotary strokes of 63 μm Â 69 μm Â 2.4 mrad along X-and Y-axis directions and around Z direction.Based on L-shape levers and half-bridge structure, a novel XYZ micro/nanopositioner with an amplifier was proposed, [166] which used a concave input mechanism with the function of location restriction to reduce the coupling errors; the input coupling was below 1% and the output coupling was less than 2%; the positioner achieved the workspace of 128.1 Â 131.3 Â 17.9 μm 3 with the amplification ratios in X/Y axis of 8.54 and 8.58.Cai et al. proposed a 3-DOF piezoelectric positioning stage, [167,168] which used three T-shape flexible hinge mechanisms to provide excellent planar motion capability with high stability and guarantee the outstanding dynamics characteristics; the stage achieved the translational and rotational motion strokes of 6.9 μm Â 8.5 μm Â 289 μrad, the linear resolutions of 50 nm along both X and Y axes, and the rotary resolution of 1.25 μrad around Z axis.A low-mobility XYZ flexure parallel mechanisms with large displacement and decoupled kinematics structure were proposed, [169] which used notch hinges to achieve large displacement more than 1 Â 1 Â 1 mm 3 and small crossaxis error less than 1.9% in the decoupled X/Y/Z-axis translational motions; under the robust controller, the positioning error was less than AE 0.1 μm, and the settling time was shortened to 0.1 s or so.Based on the bridge-type displacement amplification mechanism, Ghafarian et al. developed two precise XYZ micromanipulators, [170,171] where a parallel monolithic micromanipulator with the characteristics of nanoscale accuracy, high bandwidth, and large workspace was proposed, which achieved the workspace of 124.4 Â 116.4 Â 129.4 μm 3 , the first resonant frequency of 456.6 Hz, and the resolutions of 23 Â 24 Â 18 nm along X/Y/Z axis, respectively.Tian et al. proposed a 3-DOF spatial deployable compliant nanopositioning platform based on a three-stage amplification mechanism, [172] which achieved the strokes of 177.33 Â 179.30Â 17.45 μm 3 with the resolution of 5 nm in X/Y/Z-axis directions, where the motion amplification ratios in the X/Y axis were 10.19 and 10.3.These direct-actuated parallel-type multi-DOF piezoelectric stages are shown in Figure 10.

Zesch et al. proposed a piezoelectric
XYθ z micro/nanorobot, [173] which achieved the resolution of 10 nm, the maximum velocity of 60 rpm, and the powerless holding torque of 0.9 mN m.Li et al. proposed a micro-piezo-actuated focusing mechanism with rapid response, [174] high-precision positioning, and large stroke characteristics, which achieved the maximum thrust force of 562.5 N and the maximum actuation torque of 1.16 N m, respectively.Morita et al. proposed a 3-DOF parallel XYθ z link mechanism based on the impact actuation principle, [175] which achieved linear motions along X/Y axis and rotary motion around Z axis; the positioning error was 18.6 μm in the point-positioning test and the deviations of the position and rotary angle were À5.34 μm and À50 mdeg, respectively.A 3-DOF XYθ z tripedal microrobotic platform with unlimited stroke and sub-micrometer accuracy was designed, [176] which achieved unconstrained and omnidirectional sample positioning; the platform achieved strokes of 3 mm Â 3 mm Â 20°.Fuchiwaki et al. [177] developed a compact 3-DOF inchworm mechanism with low-inertia characteristic for omnidirectional precise positioning, which consisted of four piezoelectric actuators and a pair of electromagnets.The proposed mechanism improved the maximum velocity without the slip motion and achieved the movement like an inchworm with the resolution less than 10 nm.Wu et al. [178] used one piezoelectric actuator to design a novel XYθ z mechanism based on the inchworm actuation principle and a monolithic flexure-hinge mechanism, which performed operation in narrow space of microsystem.A novel 3-DOF miniature-step mobile robot with high-resolution characteristic was proposed based on the inchworm principle, [179] which used a piezoelectric actuator, a rhombic flexure-hinge mechanism, and four electromagnetic legs to achieve translation and rotation motions with large stroke.Shi et al. proposed a ring-type 3-DOF ultrasonic motor with high torque and compact structure characteristics, [180] which achieved rotary motions around X/Y/Z axis actuated by the elliptic trajectories of driving feet tips generated by the simultaneous excitation of two orthogonal axial bending modes and a radial bending mode of the ring stator, where the ring stator consisted of four driving feet uniformly arranged in the inner circumference of the ring stator.Mizuno et al. proposed a 3-DOF sandwich-type spherical ultrasonic motor with high torque characteristic, [181] which used a multimode annular vibrating stator to achieve the maximum torque of 1.48, 1.48, and 2.05 N m around X/Y/Z axis, respectively.Aoyagi et al. proposed a disk-type 3-DOF ultrasonic motor, [182] which achieved the maximum torques of 91, 91, and 69.7 mN•m in the X/Y/Z-axis rotation directions based on the sandwich structure, respectively.Hoshina et al. [183] proposed a compact 3-DOF spherical ultrasonic motor actuation system with high responsiveness and accuracy, which was successfully used for camera orientation in pipe inspection.
Based on the Stewart structure and the direct-actuation principle, [184][185][186][187] 6-DOF Stewart nanoscale platforms were proposed, which achieved some merits of compact structure, high stiffness, and strong carrying capacity.Yang et al. [188] proposed a 6-DOF manipulator for a handheld instrument with the size of Φ28.5 Â 126 mm 3 , which used a Gough-Stewart piezoelectric platform to perform active tremor compensation during microsurgery, which achieved the workspace of Φ4 Â 4 mm and the side load capacity up to 0.25 N. Ghafarian et al. [189] [190,191] which used six piezoelectric actuators and the passive joints constructed by flexure-hinge mechanisms; the pointing mechanism achieved the advantages of high accuracy, large force and high frequency response characteristic, and the merits of frictionless, gapless, and good stability based on the transmission mechanism constructed by the flexible hinge mechanism; the pointing mechanism achieved motion strokes of 100 μm Â 116 μm Â 33 μm Â 0.066°Â 0.07°Â 0.2°with the linear resolution of 5 nm and the rotary resolution of 5 Â 10 À5 °.Kang et al. proposed a flexure-based 6-DOF parallel nanopositioning stage for precise optics alignment; [192] the stage with the size of Ф350 Â 120 mm 3 achieved the first resonant frequency of 396.1 Hz and the strokes of 4 mm Â 4 mm Â 4 mm Â 4°Â 4°Â 4°with linear resolution of 15 nm and rotary resolution of 0.14 arcsec.Zhang et al. proposed a 6-DOF micropositioning mechanism for real-time adjustment of lithography projection lens posture, [193] which achieved the translation and rotation stroke of more than 50 μm and 200 μrad, respectively.Zhang et al. [194] proposed a novel 6-DOF micro/nanopositioning system with the characteristics of high resolution, high repeatability, and low parasitic motions, which consisted of three identical limbs including two symmetrical six prismatic-universal-spherical branches; the proposed positioning platform with the size of Ф264 Â 148.4 mm 3 achieved the first resonant frequency of 188.84 Hz and the strokes of 80 μm Â 80 μm Â 60 μm Â 400 μrad Â 400 μrad Â 600 μrad with the linear and rotary resolutions of 5 nm and 100 nrad, respectively.Yu et al. [195] proposed a bioinspired hexapod piezoelectric robot integrating multiple characteristics of high precision, long stroke, and strong carrying capability, which achieved the unlimited strokes of in-plane motions, the linear/ rotary resolutions higher than 4 nm/0.2μrad, and the carrying capacity of 10 kg.Based on the multi-axis distributed-electrode excitation of PZT/Si unimorph T-beams, a 6-DOF piezoelectric microvibratory stage was proposed, [196] which achieved linear strokes larger than AE7.5 μm, rotary angles larger than AE0.5°, and the first resonant frequency of 900 Hz.Qin et al. proposed a 6-DOF piezoelectric micromechanical vibration platform, [197] which was constructed by four folded beams and excited by 32 partitioned electrodes based on PZT film; the damping and fatigue experiments verified that the proposed platform possessed large driving capability and good stability in inertial measurement units.Lee et al. proposed a flat-type 6-DOF piezoelectric stage for positioning error compensation in the optical measurement system, [198] which achieved the linear and angular resolution of 0.02 μm and 0.1 arcsec, respectively.Ellis et al. [199] proposed a versatile 6-DOF sample stage working in ultrahigh vacuum base pressure environment, whose working temperatures ranged from the room temperature to 1500 °C.Varadarajan et al. proposed a dual-purpose positioner-fixture for precision 6-DOF positioning and precision fixturing, [200] where the combination of positioner and fixture characteristics achieved the precise adjustment of the fixtured position/orientation.The parts of parallel-type 6-DOF piezoelectric stages are shown in Figure 11.

Series-Parallel Hybrid-Type Multi-DOF Piezoelectric Actuation
A series-parallel hybrid mechanism refers to a mechanism that combines series and parallel mechanisms, which integrates the advantages and disadvantages of both, as shown in Figure 12.Chang et al. proposed a cross-scale 6-DOF piezoelectric stage based on the inertial actuation principle, [201] which solved the problem that few existing 6-DOF stages took the characteristics of large range, high resolution, and low coupling into account together.The proposed stage achieved the strokes of 5 mm Â 5 mm Â 5 mm Â 68°Â 68°Â 360°, the resolutions of 22.6 nm Â 18.9 nm Â 12.4 nm Â 0.12 μrad Â 0.13 μrad Â 0.40 μrad, and the coupling error of less than 5.03% in the 6-DOF motions.Gaunt et al. proposed a 6-DOF positioner for optical components, [202] which was a hybrid mechanism constructed by two 3-DOF parallel mechanisms in series; the proposed positioner achieved the strokes of 4 mm Â 4 mm Â 4 mm Â 4°Â 4°Â 10°with the resolutions of 10 μm Â 10 μm Â 10 μm Â 6 0 Â 6 0 Â 14 0 .Cai et al. proposed a direct-actuation 6-DOF piezoelectric precision positioning platform consisting of two 3-DOF parallel mechanisms in series, [203,204] where the upper platform achieved the linear motions along X/Y axis and the rotary motion around Z axis; the lower platform achieved the linear motion along Z axis and the rotary motions around X/Y axis; the 6-DOF platform with the size of Ф150 Â 143 mm 3 achieved the first resonant frequency of 586.3 Hz and the strokes of 8.2 μm Â 10.5 μm Â 13.0 μm Â 224 μrad Â 105 μrad Â 97 μrad with the resolutions of 31 nm Â 25 nm Â 7 nm Â 20 nrad Â 25 nrad Â 0.8 μrad.Chen et al. proposed a piezo-actuated 6-DOF series-parallel positioning system with high-precision and low-coupling characteristics for space optics alignment, [205] which consisted of triple cascade sub-platform; where the first stage realized the rotary motions around X/Y axis and the translation motion along Z axis; the second stage was completely decoupled parallel mechanism, which achieved the translation motions along X/Y axis; the third stage was redundantly actuated 1-DOF mechanism achieving the rotary motion around Z axis; each substage was actuated by displacement amplifiers and the flexure-hinge mechanism eliminated the friction and backlash; the proposed 6-DOF platform with the size of Ф650 Â 158 mm 3 achieved the first resonant frequency of 19.45 Hz and the strokes of 1 mm Â 1 mm Â 1 mm Â 600 00 Â 600 00 Â 600 00 with the motion resolutions of 0.5 μm Â 0.5 μm Â 1 μm Â 0.5 00 Â 0.5 00 Â 0.5 00 .Xu et al. proposed a 6-DOF piezo-actuated adjustment device, which consisted of an upper stage and a lower stage; where the upper stage included four vertically placed rhombus displacement amplification mechanisms with the structure of central antisymmetric arrangement, which achieved the rotary motions around X/Y axis and the linear motion along Z axis; the lower stage included four horizontally placed rhombus displacement amplification mechanisms with the structure of central antisymmetric arrangement, which achieved the rotary motion around Z axis and the linear motions along X/Y axis.The device achieved 6-DOF high-precision adjustment based on these characteristics of frictionless, simple control, and compact structure.Chao et al. proposed a dexterous 6-DOF manipulator serially connected by two compliant parallel stages, [206] where the upper stage of 3-RPS mechanism achieved rotary motions of X/Y axis and translation motion of Z axis, and the lower stage of a 3-RRR mechanism achieved rotary motion of Z axis and translation motions of X/Y axis.Lin et al. proposed a piezo-actuated 6-DOF micropositioner based on a compliant mechanism and ten piezoelectric actuators, [207][208][209] which consisted of the upper stage achieving the rotary motion around Z axis, the middle stage achieving the rotary motions around X/Y axis and the linear motion along  [188] Copyright 2015, IEEE.b) The stage by Ghafarian et al.Reproduced with permission. [189]Copyright 2018, IEEE.c) The stage by Du et al.Reproduced with permission. [190]Copyright 2014, IEEE.d) The stage by Kang et al.Reproduced with permission. [192]Copyright 2012, AIP Publishing.e) The stage by Zhang et al.Reproduced with permission. [194]opyright 2019, IEEE.f ) The stage by Yu et al.Reproduced with permission. [195]Copyright 2021, Wiley-VCH.g) The stage by Aktakka et al.Reproduced with permission. [196]Copyright 2013, Elsevier.h) The stage by Ellis et al.Reproduced with permission. [199]Copyright 2013, AIP Publishing.
Z axis, and the lower stage achieving the linear motions along X/Y axis; the micropositioner with the size of 241 Â 241 Â 67 mm 3 achieved the strokes of 111.38 μm Â 111.38 μm Â260.06 μm Â 4.58 mrad Â 4.58 mrad Â 2.71 mrad.Wang et al. proposed a 6-DOF series-parallel optic-fiber-positioning stage, [210] which consisted of a 3-DOF series mechanism and a 3-DOF parallel mechanism in series.6-DOF motions for precise laser beam positioning were achieved by both disc-and cylinder-type actuators, [211] where one transducer was used to rotate the mirror around three axes, another transducer was used to position the mirror in the plane, and these two ultrasonic actuators were connected by the hyperelastic material.The disc-type actuator achieved the angular and translation resolutions of 10 μrad and 1 μm, and the cylindertype actuator achieved the angular and translation resolutions of 20 μrad and 5 μm.Dong proposed a compliant ultraprecision 6-DOF parallel positioner based on the coarse/fine dual architecture, [212] which achieved large strokes of 10 mm Â 10 mm Â 10 mm Â 6°Â 6°Â 6°with the linear resolution of 40 nm and the rotary resolution of 2.0 μrad, and the finepositioning platform achieved the linear repeatability of 10 nm and the rotary repeatability of 0.2 μrad.Woody et al. proposed a dual-stage tip-tilt steering mechanism, [213] which consisted of a coarse platform and a fine platform; the fine motion platform had high frequency response to reduce following errors of the coarse platform, and the coarse platform had large range to compensate the shortage of the fine motion platform.
The CEDRAT company in France has developed different series of piezoelectric fast steering mirrors with multiple DOFs for satellite-ground communication systems, which were used in high-precision imaging systems, such as positioning, micro-scanning, pixel offset and jitter compensation.The Physik Instrumente (PI) company in Germany has developed many kinds of multi-DOF-positioning platforms, which have been used in the fields of industrial microassembly, measurement, and biomedical equipment.Based on the inertial actuation principle and series-parallel structure, PI developed some novel 6-DOF positioning platforms, such as, the Q-821.140with the size of 79.5 Â 72.9 Â 48 mm 3 achieving the motion strokes of 12 mm Â 12 mm Â 6 mm Â 12°Â 12°Â 33°and the resolutions of 10 nm Â 10 nm Â 20 nm Â 0.9 μrad Â 0.9 μrad Â 0.9 μrad, the Q-845.140with the size of 173.9 Â 163.7 Â 77 mm 3 achieving the motion strokes of 14 mm Â 14 mm Â 10 mm Â 14°Â 14°Â 16°and the resolutions of 6 nm Â 6 nm Â 20 nm Â 0.9 μrad Â 0.9 μrad Â 0.9 μrad.Harbin Core Tomorrow Science & Technology Co., Ltd., has developed a series of multi-DOF positioning devices, which have achieved sub-nanometer resolution and nanoscale positioning accuracy and have been wildly used in the fields of beam scanning and precision positioning, such as, the 6-DOF positioning stage of N90.XYZTR5 with the motion  [201] Copyright 2022, Elsevier.b) The stage by Cai et al.Reproduced with permission. [204]Copyright 2018, Elsevier.c) The stage by Chen et al.Reproduced with permission. [205]Copyright 2019, IEEE.d) The stage by Lin et al.Reproduced with permission. [208]Copyright 2020, MDPI.e) The stage by Bansevicius et al.Reproduced with permission. [211]Copyright 2019, Hindawi.f ) The stage by Dong et al.Reproduced with permission. [212]Copyright 2006, IEEE.g) The stage by Woody et al.Reproduced with permission. [213]Copyright 2006, Elsevier.strokes of 50 μm Â 50 μm Â 25.6 μm Â 1.28 mrad Â 1.28 mrad Â 1.96 mrad and the resolutions of 0.08 nm Â 0.08 nm Â 0.2 nm Â 0.04 μrad Â 0.04 μrad Â 0.06 μrad, XD801, XF801, and other positioning stages.

Multi-DOF Parallel Piezoelectric Actuation Based on a Single Actuator
Except from above traditional structure forms, multi-DOF actuation can be achieved based on a single piezoelectric actuator which has the ability of generating multidimension actuation trajectories.Deng et al. proposed a compact piezoelectric XY platform with the size of 100 Â 100 Â 93.5 mm 3 based on a single actuator, [214] which achieved the large stroke of 15 Â 15 mm 2 and the positioning resolution better than 400 nm; the platform achieved the carrying capacity of 20 kg, and the maximum velocities along X and Y axes were 2.13 and 3.11 mm s À1 under the voltage of 400 V p-p and the frequency of 600 Hz, respectively.Tian et al. proposed a decoupled 2-DOF inertial positioning stage with large stroke, [215] which consisted of a clamping mechanism used to adjust the normal force at the friction interface and a hybrid decoupling configuration used to eliminate the coupling error.Shimizu et al. [216] proposed an XY micro/nanopositioning stage with the size of 24 Â 24 Â 5 mm 3 based on the stick-slip actuation principle, which used the leaf springs to guide the X/Y directional motions of moving plate; the proposed stage achieved range of AE1 Â AE1 mm 2 with the resolution of 10 nm in X/Y directions.Zhang et al. proposed a 2-DOF pointing mechanism based on a bending-bending hybrid piezoelectric actuator with the ability to generate two orthogonal DOFs; [217] the pointing mechanism achieved the rotary velocities of 153 and 154 mrad s À1 around X and Y axes under the voltage of 400 V p-p and the frequency of 460 Hz, respectively; the motion resolutions were 2.49 and 2.52 μrad in both directions, respectively.Gao et al. proposed a small 2-DOF robotic spherical joint based on a bonded-type piezoelectric actuator, [218] which achieved the rotary motions with large stroke around two orthogonal axes based on the stick-slip principle; the proposed device achieved the rotary velocities of 1.03 and 1.14 rad s À1 with the resolutions of 4.64 and 4.76 μrad around X and Y axes under the voltage of 400 V p-p and the frequency of 750 Hz, respectively.And then, the team also proposed a 2-DOF micro/nanomanipulator with compact structure based on a single miniature piezoelectric tube actuator, [219] which achieved the maximum rotary velocities of 0.171 and 0.169 rad s À1 , the rotary resolutions of 0.54 and 0.57 μrad around X and Y axis, respectively.Based on a cross-orthogonal-axis structure, Chang et al. proposed a 2-DOF piezoelectric posture alignment mechanism with low coupling characteristic, [220] which achieved the range of rotation angles of AE68°Â AE68°, the rotary resolutions of 0.09 μrad, and the coupling errors of 4.69% and 3.86% around X/Y axis, respectively.Deng et al. proposed a 2-DOF piezoelectric arched needle insertion device for precise manipulation of biological tissues, [221] which achieved linear and rotary motions along/around Z axis based on inertial actuation principle; the device achieved the step displacement of 2.47 μm and 0.56 mrad with the maximum velocities of 382 μm s À1 and 201 mrad s À1 along/around Z axis under the voltage of 120 V and the frequency of 250 Hz, respectively; the maximum insertion force was tested as 32 mN.Wang et al. proposed a linear-rotary piezoelectric positioning stage, [222] which used a double-octagon driving module to generate rectangular driving trajectories of a surface to achieve linear and rotary motions; the stage achieved the strokes of 50 mm Â 360°with the resolutions of 19.85 nm and 1.32 μrad; the maximum velocities and load capacities were 1023.4 μm s À1 Â 98.21 mrad s À1 and 10.78 Â 13.72 N, respectively.Han et al. used a single piezoelectric tube stator with two independent electrodes to design a compact linear-rotary impact motor, [223] which achieved the linear and rotary strokes of 2.17 μm and 599.98 μrad under the voltage of 720 V p-p ; the linear/rotary velocities of 6.3 mm s À1 /1.21 Â 10 6 μrad s À1 and the maximum output force/torque of 0.45 N/0.80 mN m were obtained, respectively.Blackford et al. proposed a 2-DOF piezo-actuated inertial slider micropositioner for cryogenic applications, [224] which achieved the linear and rotary motions by activating the longitudinal and bending modes of the piezo tube, respectively; the proposed micropositioner achieved step sizes from 10 to 3000 nm and the maximum velocity of 0.2 mm s À1 .Blackford et al. [225] proposed a 2-DOF piezoelectric tube device to achieve remote micropositioning in the vertical and horizontal directions in cryogenic application fields, which achieved a minimum step size of less than 20 nm and the largest velocity of 0.2 mm s À1 in vertical direction relative to gravity.
Liu et al. proposed a rotatable and deployable sleeve mechanism using a 2-DOF longitudinal-bending composite piezoelectric actuator; [226] the actuator used a single driving foot to push the inner sleeve with linear, rotary, or spiral stretching motions; the deployable sleeve mechanism achieved the maximum linear and rotary speeds of 530 mm s À1 and 240°s À1 under the voltage of 300 V p-p and the frequency of 22.35 kHz; the motion resolutions of the inner sleeve were tested to be 2 μm and 0.0014°, respectively.Mashimo proposed a linear-rotary ultrasonic motor for endovascular diagnosis and surgery, [227] which achieved the linear motion excited by T 1 and T 2 modes and the rotary motion excited by R 3 mode based on a 3.5 mm cubic stator; the motor achieved the linear velocity of 50 mm s À1 and the output force of 0.01 mN under the voltage of 42 V rms and the frequency of 306 kHz, and the rotary velocity of 260 rpm and the output force of 0.1 mN m under the voltage of 42 V rms and the frequency of 270 kHz.Wang et al. [228] developed a linear-rotary ultrasonic motor inspired by the bionic motion principles of the earthworms, which achieved linear motion along X axis by combing the fifth-order bending and the second-order longitudinal vibration modes, and the rotary motion around the X axis by combing two orthogonal bending vibration modes; the ultrasonic motor was used for optical focusing and achieved the maximum linear and rotary velocities of 57.6 mm s À1 and 3319.6 rpm, respectively.The parts of parallel-type piezoelectric stages based on a single actuator are shown in Figure 13.
In summary, the methods of DOF expansion include four types, which are series type, parallel type, series-parallel type, and the single piezoelectric actuator with multidimension actuation ability.The characteristics of multi-DOF piezoelectric platforms based on these four expansion methods are listed and compared in Table 3.For the series multi-DOF piezoelectric platforms, the mechanism DOF is easily expanded by adding the single-DOF mechanism at the output end, large stroke motions, and the simple control method are also easily obtained.However, there is accumulated error in the output, which has a great impact on the positioning accuracy.The parallel multi-DOF piezoelectric platforms have compact structure and can achieve high positioning resolution, but their strokes are limited in the range of dozens to hundreds of micrometers.The series-parallel hybrid multi-DOF piezoelectric platforms are constructed by several mechanisms in series and parallel, so the advantages and disadvantages of series and parallel mechanisms are also integrated together.The method of DOF expansion achieved by a single piezoelectric actuator is different from the traditional structure forms, and it has the characteristics of simple and compact structures.

The Applications of Multi-DOF Cross-Scale Piezoelectric Actuation Technology
With the development of precision engineering technology, piezoelectric actuation technology has gradually permeated into various fields, such as micro/nanomanufacturing, optical posture adjustment, biomedical manipulation, vibration suppression, microrobots, and so on, as shown in Figure 14.

Micro/Nanomanufacturing Field
In some precise manufacturing fields, such as microelectronics manufacturing, ultraprecision cutting processing, microsystem integration, and assembly, the restricted response speed, limited stroke, and resolution characteristics of positioning platforms have emerged as significant bottlenecks in achieving high-quality product. [229,230]These limitations directly impact the precision, efficiency, and controllability of the manufacturing processes.
Piezoelectric actuation has the advantages of high resolution, fast response speed, output force with high density, and no electromagnetic interference, which has been applied in ultraprecision manufacturing fields since the last century.Koga et al. [231] developed a precise positioning stage actuated by six piezoelectric actuators, which was used in a ten-axis stage to achieve precision positioning of the wafer stage and perform the precision operation of quarter-micrometer X-Ray lithography.Ultrasonicassisted machining technology is one of the methods for achieving high-precision machining, which applies the ultrasonic piezoelectric actuator to assist processing.The ultrasonic vibration can lead to intermittent cutting, which has the advantages of small cutting force, low cutting temperature, slight tool wear, and easy chip removal, so the component with characteristics of small shape error and surface roughness can be obtained, and the tool life can also be expanded.Du et al. [232,233] proposed a longitudinalbending hybrid piezoelectric transducer, which was used to assist the milling tool to manufacture the component with the material of titanium alloy.High-precision milling surface was achieved by longitudinal vibration and bending vibration of the milling tool which simultaneously affected the ironing effect and the intermittent cutting effect; compared with the conventional milling and longitudinal vibration-assisted milling, the cutting force decreased by 39.3% and 27.2%, and the surface roughness decreased by 85.2% and 54.5%, respectively.Zhu et al. [124] proposed a piezoelectric 2-DOF decoupled fast tool servo assisting diamond turning, which achieved the servo motions of the cutting tool along X/Z-axis directions; the surface with scattering homogenization microstructure was obtained by the pseudo-random vibrations in the radial direction.

Optical Adjustment Field
The posture adjustment of the laser beam is the most important technology in the field of precise optical engineering, [234] which requires fast response speed, large rotary angle, and high motion resolution.Piezo-actuated fast steering mirrors use the piezoelectric actuator to adjust the direction of laser beam, which can offer the advantages of compact structure, fast dynamic response, high scanning accuracy, and immunity to electromagnetic interference, so the piezoelectric fast steering mirror has gradually been used in the field of optical adjustment.To solve the problem that large external vibration acceleration and lateral force caused damage to the PZT stack, Chang et al. [149] developed a novel 2-DOF piezo-actuated fast steering mirror with high stiffness and good decoupling characteristic, which had enough lateral stiffness to overcome large lateral force based on an anti-shear structure.Based on a bonded-type piezoelectric composite beam, Zhang et al. [235] proposed a two-axis piezoelectric tilting mirror with  [214] Copyright 2020, IEEE.b) The stage by Shimizu et al.Reproduced with permission. [216]Copyright 2013, Elsevier.c) The stage by Zhang et al.Reproduced with permission. [217]Copyright 2019, IEEE.d) the stage by Gao et al.Reproduced with permission. [218]Copyright 2021, IEEE.low capacitance for optical-assisted micromanipulation, which reduced the requirement for power amplifier.A 2-DOF piezoelectric fast steering mirror [236] was developed to solve the problems of small optical aperture and stroke in space laser communication and lidar systems, which achieved rotary stroke of 4.7 mrad.Csencsics et al. [237] proposed a novel piezoelectric fast steering mirror with good tracking performance for highspeed scanning, which achieved the angular stroke of 4.8 mrad.Dong et al. proposed a space-qualified piezoelectric fast steering mirror, [143] which was used to correct the tip and tilt of the small jitter of the satellite platform in the image stabilization system of the space telescopes, based on the characteristics of high resolution and large bandwidth.Zhong et al. proposed a highbandwidth piezoelectric fast steering mirror with a permanent magnet preload force mechanism for optical scanning, [146] where the preload force mechanism was used to avoid additional dynamics induced by flexure hinges.Kim et al. [238] proposed a piezoelectric fast steering mirror with high-resolution and high-speed tilting capability, which was used to compensate the distortion of the optical axis in the portable spectroscopic sensor; the fast steering mirror can achieve the steering range of 0.56°, the resolution of 1.27 mrad and the natural frequency of 282 Hz.Shao et al. proposed a compact precision tilt positioning mechanism for inter-satellite optical communication, [150] which used three piezoelectric actuators and the elastic deformation of a flexure ring to achieve the tilt movement.
A series of piezoelectric fast steering mirrors with different sizes and performance have been developed by many companies, such as the Newport Company and the Ball Aerospace Company in USA, the PI company in Germany, the CEDRAT company in France, Harbin Core Tomorrow Science & Technology Co., Ltd., in China, which have been wildly used in laser communication and aerospace docking systems.

Biomedical Manipulation Field
[241] At present, the commercialized da Vinci surgical robots can perform laparoscopic surgeries and urological surgeries with the requirements at the milli-scale accuracy, but it is difficult for complex morphological organisms to perform precision operations with the nanoscale accuracy.
the flexible hinge mechanism, which effectively improved the puncture performance of the device and reduced the cell deformation.Yu et al. [243] developed a minimally invasive intraocular surgery system consisting of a piezoelectric device achieving linear motion of the end of puncture device, and the implantation and removal of the intravascular liquid tube of the mouse eyeball were performed without external damage.Huang et al. [244] proposed a piezoelectric cell injector used for automated suspended cell injection, which required only a small piezo stack to efficiently carry out the cell injection process and relocated the piezo oscillation actuator to the injector pipette, effectively eliminating any vibration effects on other components of the micromanipulator.Dai et al. [245] proposed a method of automated piezoassisted sperm immobilization to enhance efficacy of cell membrane ablation and sperm orientation control, the study designed a piezo drill consisting of two orthogonal vibration modules to generate controlled micropipette vibration along axial and lateral axes, and the results showed that sperm orientation control by the piezo drill achieved an error of 1.4°and a time cost of 2.5 s.Xu et al. [246,247] developed a new force-sensing cell microinjector with novel compliant small-stiffness mechanism, which enabled both a high sensing sensitivity and large loading capability.The fusion designs of PZT stack and flexible mechanism achieved puncture strokes of hundreds of micrometers and high force resolution for straight needles.Deng et al. [221] developed a 2-DOF inertial piezoelectric micropuncture device for precise manipulation of biological tissues, which achieved linear and rotary motions along/around Z axis based on the inertial actuation principle; the puncture device achieved the stroke of several centimeters and the puncture force of 32 mN.

Vibration Suppression Field
The structure vibration problems caused by the external environment have an important impact on the normal operation of the system, [248,249] where the positioning accuracy will be reduced in precision tracking system, the machining quality will be worse, or the comfort of passengers will be affected in the field of road traffic, even the fatigue damage resulted from structure vibration can endanger human safety.Due to the advantages of wide frequency range, output force with high density, compact structure and high electromechanical conversion efficiency, piezoelectric actuators have been widely used for equipment vibration suppression and noise control.Thinh et al. [250] studied free vibration suppression control of a glass fiber/polyester laminated composite plates bonded with piezoelectric patches.Lu et al. [251] developed an embedded piezo-compensator to effectively eliminate the disturbance in all-radial directions of the circular cross-section cantilever beam.Li et al. [252] designed a piezoelectric stack actuator installed at the root of cantilever beam and used a hybrid proportional integral derivative and filtered-x least mean square (PID-FxLMS) algorithm combining the feedback FxLMS algorithm and PID controller to improve the vibration control efficiency of piezoelectric cantilever beam.Zou et al. [253] used a piezoelectric smart platform to actively isolate the low-frequency broadband multidirectional vibration; the piezoelectric platform can isolate vibration from 0 to 3000 Hz in multiple directions under the coordination of the optimal control algorithm.Zhang et al. [254] used a piezoelectric phononic rod to generate the active tunable isolations of more than 20 dB at low frequencies from 500 Hz to 14 kHz by controlling the excitation voltages of piezoelectric elements.Song et al. [255] proposed an active-passive vibration isolator including the active part of a piezoelectric actuator and the passive part of a damping buffer, which achieved vibration isolation from 5 to 500 Hz and solved the problem of high-precision equipment's positioning and control accuracy.Billon et al. [256] used a piezoelectric bending suspension with a negative capacitance shunt to perform vibration isolation, and the suspension consisted of a piezoelectric component and a mechanical amplifier.Wang et al. [257] designed a six-axis orthogonal vibration isolation platform with piezoelectric actuators to actively isolate vibration, which satisfied the demands of heavy payload, small installation space, and multi-DOF vibration isolation and effectively reduced the vibration response of payload within the target frequency range of 20-200 Hz.
resolution, and large dead movement zone.260] Piezoelectric microrobots have advantages of compact structure with millimeter-scale size, high motion resolution, and no electromagnetic interference, which can transport the samples with large stroke and high accuracy, and perform precise operations in complex and narrow environments.Wang et al. [261] developed a miniature biped piezoelectric robot with a patch-type beam structure, which achieved linear motion with large stroke under the low frequency and voltage, and could perform transport tasks in narrow environments.And then, the team proposed a small and agile ring-shaped tripodal piezoelectric robot, [262] which achieved the linear and rotary motions actuated by standing and traveling mechanical waves based on the propagation of mechanical waves on the rigid ring-shaped structure.Li et al. [41] proposed a miniature quadrupedal piezoelectric robot, which realized nanoresolution and high speed based on the quasi-static and resonant motions, respectively.A miniature piezoelectric robot was developed, [263] which used three unconventional inertial impact modes (diagonal, jumping, and resonant inertial impact modes) to achieve the performance improvement in both resolution, single step value, and motion speed; and the piezoelectric robot achieved the resolution of 0.5 μm under the diagonal inertial impact mode, the maximum single step of 63.1 μm under the jumping inertial impact mode, and the fastest speed of 24.8 mm s À1 under the resonant inertial impact mode.Deng et al. [264] developed a hexapod miniature piezoelectric robot, which used a circular arrangement and a triangular gait scheme to achieve high repeatability of step displacements, low lateral coupling, and small posture change of large stroke motions; in addition, the piezoelectric robot had strong load capacity, the carrying capability was up to 800 g, which was more than 38 times its own weight.Bansevicius et al. [265] introduced detailedly the piezoelectric kinematic pairs with multiple DOFs in a miniature piezoelectric robot with high resolution, and a piezoelectric robot with 15 DOFs was proposed.Fan et al. [266] developed a small-scale piezoelectric walking robot actuated directly by eight pieces of piezoelectric bimorph actuators, which avoided using the displacement amplification mechanism to minimize the overall weight and complexity; the piezoelectric robot consisted of four inner legs and four outer legs, and achieved bidirectional motions under the excitation of two square wave signals with a phase difference of 180°.Hariri et al. [267] proposed a standing wave actuated piezoelectric miniature robot, which used a single piezoelectric patch with free boundary conditions at each end, and rigidly attached legs to generate bidirectional motion.Hu et al. [268] developed a new insect-scale piezoelectric robot with asymmetric structure, which worked at six vibration modes under the actuation of two pieces of piezoelectric ceramics and achieved two kinds of linear motion and four kinds of circular motion; the piezoelectric robot achieved a maximum velocity of 97 mm s À1 with integrated drive device of 45.7 g under the voltage of 100 V p-p .

Problems and Prospects of Piezoelectric Actuation Technology
While piezoelectric actuation technology has attracted significant attention in numerous precision-oriented fields, it is essential to address specific technical challenges that require further research to advance the field of piezoelectric actuation technology. 1) Nonlinearity output characteristics of piezoelectric actuators: owing to the inherent properties of piezoelectric materials, such as hysteresis and creep behaviors, the accurate prediction and control of piezoelectric actuator outputs pose a formidable challenge, potentially compromising the overall system performance.Consequently, the pursuit of novel piezoelectric materials characterized by enhanced energy density, superior temperature stability, and reduced hysteresis and creep becomes imperative.2) Lifecycle of piezoelectric actuators: while the lifecycle of a PZT stack can extend up to one billion cycles, it is essential to recognize that certain factors, such as depolarization, fatigue, temperature fluctuations, and environmental conditions, may lead to property degradation.Therefore, it is imperative to conduct research focusing on the property development and long-term stability of piezoelectric actuators.3) High-power voltage necessity: typically, achieving the desired displacement entails the application of high-power voltage to excite piezoelectric actuators, which presents challenges in terms of safety and energy efficiency.Furthermore, the demand for amplifiers with substantial amplification ratios and high-power voltage further contributes to increasing system dimensions, cost, and complexity.Therefore, there is an urgent need for research focused on piezoelectric actuators that can operate effectively with low-power voltage requirements.4) Miniaturization and integration: a piezoelectric actuation system consists of a mechanical body, a power amplifier, a sensor, and a control system.The prerequisite for the widespread adoption of piezoelectric actuators is the miniaturization and integration of these systems, and thus the expansion of application for piezoelectric actuation technology.Consequently, it is imperative to engage in research of integrated multifunctional piezoelectric actuation systems, which are characterized by compact structures and the utilization of advanced control algorithms.

Conclusion
First, this review provides an initial exposition by categorizing precise actuation methods, thereby elucidating the merits of piezoelectric actuation technology.Second, a detailed exposition on piezo-actuated cross-scale motion is presented in granular detail, encompassing various piezoelectric actuation methodologies such as ultrasonic actuation, direct actuation, inchworm actuation, and inertia actuation.Subsequently, the review delves into the intricacies of multi-DOF piezoelectric actuation technology, meticulously discussing structure forms such as series, parallel, series-parallel configurations, and the realization of multi-DOF parallel piezoelectric actuation based on a single actuator.In addition, the applications of multi-DOF cross-scale piezoelectric actuation technology were introduced in brief, including micro/ nanomanufacturing, optical posture adjustment, biomedical manipulation, vibration suppression, microrobot fields.Finally, the study addresses the challenges faced and outlines the prospects of piezoelectric actuation technology.
While extensive research on piezoelectric actuation technology has been conducted both domestically and internationally, many challenges still exist.For instance, the energy conversion efficiency of piezoelectric materials remains relatively low.Therefore, researchers must focus on enhancing the energy conversion efficiency to more effectively harness energy generated by mechanical vibrations or pressure changes in future applications.Additionally, the structural design of piezoelectric systems must consider the mechanical strength of individual components to reduce the risk of breakage resulting from stress concentration, vibration, or external impact.The implementation of robust mechanical structures plays a pivotal role in enhancing system reliability and reducing the potential for fatigue and damage.Another important aspect concerns the material properties and stability of piezoelectric actuators.Some commonly used piezoelectric materials can degrade or become unstable over long periods of use or under extreme environmental conditions.The development of new piezoelectric materials and friction materials can significantly enhance the life cycle and reliability of piezoelectric systems.Therefore, researchers should dedicate efforts to develop more stable, reliable, and durable piezoelectric materials that meet the requirements of practical engineering applications.
Piezoelectric technology involves many disciplines, including materials science, physics, and electronic engineering, but sometimes there is a lack of interdisciplinary cooperation.Closer multidisciplinary cooperation can drive innovation in piezoelectric actuation technology and facilitate the integration of expertise in different fields.Solving these problems requires the joint efforts of researchers around the world to promote broader application of piezoelectric actuation technology in various fields.

Figure 2 .
Figure 2. Piezoelectric ultrasonic actuation.a) Working principle of travelling wave actuation; b) working principle of standing wave actuation; and c) the standing wave ultrasonic motor by Fan et al.Reproduced with permission.[63]Copyright 2018, AIP Publishing.d) The standing wave ultrasonic motor by Park et al.Reproduced with permission.[66]Copyright 2012, Elsevier.e) The standing wave ultrasonic motor by Dabbagh et al.Reproduced with permission.[68]Copyright 2017, Elsevier.f ) The travelling wave ultrasonic motor by Chen et al.Reproduced with permission.[57]Copyright 2014, IEEE.g) The travelling wave ultrasonic motor by Liu et al.Reproduced with permission.[61]Copyright 2012, Elsevier.h) The travelling wave ultrasonic motor by Ma et al.Reproduced with permission.[62]Copyright 2020, IEEE.i) The hybrid-actuated ultrasonic motor by Jian et al.Reproduced with permission.[75]Copyright 2017, Elsevier.j) The hybrid-actuated ultrasonic motor by Liu et al.Reproduced with permission.[77]Copyright 2015, Elsevier.k) The hybrid-actuated ultrasonic motor by Yan et al.Reproduced with permission.[78]Copyright 2016, Elsevier.

Figure 3 .
Figure 3. Piezoelectric direct actuation.a) Working principle of piezoelectric direct actuation; b) the stage by Wu et al.Reproduced with permission.[82]Copyright 2019, IEEE.c) The mechanism by Yang et al.Reproduced with permission.[83]Copyright 2020, IEEE.d) The stage by Zhang et al.Reproduced with permission.[84]Copyright 2016, Springer-Verlag.e) The stage by Zhu et al.Reproduced with permission.[87]Copyright 2016, AIP Publishing.f ) The stage by Wang et al.Reproduced with permission.[89]Copyright 2019, IEEE.

Figure 5 .
Figure 5. Piezoelectric inertial actuation.a) Working principle of inertial impact actuation; b) working principle of inertial stick-slip actuation; and c) the actuator by Pan et al.Reproduced with permission.[107]Copyright 2020, Springer-Verlag.d) The actuator by Qin et al.Reproduced with permission.[108]Copyright 2019, Elsevier.e) The actuator by Zhang et al.Reproduced with permission.[109]Copyright 2019, IEEE.f ) The actuator by Deng et al.Reproduced with permission.[111]Copyright 2018, Elsevier.g) The actuator by Gao et al.Reproduced with permission.[112]Copyright 2019, AIP Publishing.

Figure 7 .
The company of PI in Germany produced a series of multi-DOF positioning platforms with series structure, such as the U-723.25 linear platform with the strokes of 22 Â 22 mm 2 in X and Y directions, the M-Y00 linear platform with the maximum velocity of 5 mm s À1 and output thrust force of 20 N. The company of Mechanics produced a large number of series positioning platforms, such as the MS.015.0402 with the size of 15 Â 7 Â 15 mm 3 and the strokes of 3.5 Â 3.5 mm 2 in X and Y directions, the MS.015.0403 with the size of 15 Â 7 Â 15 mm 3 and the strokes of 3.5 Â 3.5 Â 3.5 mm 3 in X, Y, and Z directions.The company of New Scale Technology also produced a series of multi-DOF positioning platforms connecting multiple 1-DOF stages in series, such as the M3-LS-U2-10 linear platform with the strokes of 10 Â 10 mm 2 in X and Y directions, the M3-LS-3.4-15linear platform with the strokes of 15 mm in X, Y, and Z directions, the M3-LS-1.8-6linear platform with the strokes of 6 mm in X, Y, and Z directions.

Figure 7 .
Figure 7. Series piezoelectric devices.a) The inchworm stage by Hua et al.Reproduced with permission.[113]Copyright 2014, Hindawi Publishing.b) The inchworm stage by Li et al.Reproduced with permission.[114]Copyright 2015, Elsevier.c) The direct-actuated-type XY stage by Li et al.Reproduced with permission.[115]Copyright 2017, MDPI.d) The direct-actuated-type XY stage by Lee et al.Reproduced with permission.[116]Copyright 2016, Elsevier.e) The direct-actuated-type XY stage by Pinskier et al.Reproduced with permission.[117]Copyright 2016, Elsevier.f ) The direct-actuated-type XY stage by Liu et al.Reproduced with permission.[118]Copyright 2016, Elsevier.g) The inertial XY stage by Li et al.Reproduced with permission.[119]Copyright 2020, IOP Publishing.h) The inertial XYZ stage by Oubellil et al.Reproduced with permission.[120]Copyright 2019, Elsevier.i) The inertial Zθ z stage by Zhang et al.Reproduced with permission.[121]Copyright 2006, AIP Publishing.j) The inertial XYZ stage by Rong et al.Reproduced with permission.[122]Copyright 2011, Elsevier.k) U-723.25 XY linear platform by PI; l) the M-Y00 XY linear platform by PI; m) the MS.015.0402XY platform by Mechanics; n) the MS.015.0403XYZ platform by Mechanics; o) the M3-LS-3.4-15XYZ linear platform by New Scale Technology; p) the M3-LS-1.8-6XYZ linear platform by New Scale Technology; and q) the M3-LS-U2-10 XY linear platform by New Scale Technology.
Figure 7. Series piezoelectric devices.a) The inchworm stage by Hua et al.Reproduced with permission.[113]Copyright 2014, Hindawi Publishing.b) The inchworm stage by Li et al.Reproduced with permission.[114]Copyright 2015, Elsevier.c) The direct-actuated-type XY stage by Li et al.Reproduced with permission.[115]Copyright 2017, MDPI.d) The direct-actuated-type XY stage by Lee et al.Reproduced with permission.[116]Copyright 2016, Elsevier.e) The direct-actuated-type XY stage by Pinskier et al.Reproduced with permission.[117]Copyright 2016, Elsevier.f ) The direct-actuated-type XY stage by Liu et al.Reproduced with permission.[118]Copyright 2016, Elsevier.g) The inertial XY stage by Li et al.Reproduced with permission.[119]Copyright 2020, IOP Publishing.h) The inertial XYZ stage by Oubellil et al.Reproduced with permission.[120]Copyright 2019, Elsevier.i) The inertial Zθ z stage by Zhang et al.Reproduced with permission.[121]Copyright 2006, AIP Publishing.j) The inertial XYZ stage by Rong et al.Reproduced with permission.[122]Copyright 2011, Elsevier.k) U-723.25 XY linear platform by PI; l) the M-Y00 XY linear platform by PI; m) the MS.015.0402XY platform by Mechanics; n) the MS.015.0403XYZ platform by Mechanics; o) the M3-LS-3.4-15XYZ linear platform by New Scale Technology; p) the M3-LS-1.8-6XYZ linear platform by New Scale Technology; and q) the M3-LS-U2-10 XY linear platform by New Scale Technology.

Figure 9 .
Figure 9. Parallel-type 2-DOF piezoelectric stages.a) The direct-actuated XY linear stage by Zhu et al.Reproduced with permission.[87]Copyright 2016, AIP Publishing.b) The direct-actuated XY linear stage by Wu et al.Reproduced with permission.[129]Copyright 2018, Elsevier.c) The direct-actuated XY linear stage by Zhang et al.Reproduced with permission.[84]Copyright 2016, Springer-Verlag.d) The direct-actuated XY linear stage by Yang et al.Reproduced with permission.[134]Copyright 2020, IEEE.e) The direct-actuated XY linear stage by Lee et al.Reproduced with permission.[135]Copyright 2017, Springer-Verlag.f ) The direct-actuated XY linear stage by Yong et al.Reproduced with permission.[136]Copyright 2009, IEEE.g) The direct-actuated θ X θ Y rotary stage by Liang et al.Reproduced with permission.[137]Copyright 2020, IEEE.h) The direct-actuated θ X θ Y rotary stage by Jing et al.Reproduced with permission.[141]Copyright 2015, IOP Publishing.i) The direct-actuated θ X θ Y rotary stage by Dong et al.Reproduced with permission.[143]Copyright 2018, Optica Publishing Group.j) The direct-actuated θ X θ Y rotary stage by Zhong et al.Reproduced with permission.[146]Copyright 2020, Elsevier.k) The direct-actuated θ X θ Y rotary stage by Park et al.Reproduced with permission.[148]Copyright 2012, IOP Publishing.l) The direct-actuated θ X θ Y rotary stage by Chang et al.Reproduced with permission.[149]Copyright 2021, Elsevier.m) The inertial-actuated linear-rotary stage by Zhang et al.Reproduced with permission.[153]Copyright 2021, Springer.n) The inertial-actuated linear-rotary stage by Gao et al.Reproduced with permission.[154]Copyright 2010, Elsevier.o) The inertial-actuated linear-rotary stage by Chang et al.Reproduced with permission.[157]Copyright 2022, Elsevier.p) The inertial-actuated linear-rotary stage by Li et al.Reproduced with permission.[114]Copyright 2015, Elsevier.q) The inertial-actuated linear-rotary stage by Sun et al.Reproduced with permission.[159]Copyright 2015, Elsevier.

Figure 11 .
Figure 11.Parallel-type 6-DOF piezoelectric stages.a) The stage by Yang et al.Reproduced with permission.[188]Copyright 2015, IEEE.b) The stage by Ghafarian et al.Reproduced with permission.[189]Copyright 2018, IEEE.c) The stage by Du et al.Reproduced with permission.[190]Copyright 2014, IEEE.d) The stage by Kang et al.Reproduced with permission.[192]Copyright 2012, AIP Publishing.e) The stage by Zhang et al.Reproduced with permission.[194]Copyright 2019, IEEE.f ) The stage by Yu et al.Reproduced with permission.[195]Copyright 2021, Wiley-VCH.g) The stage by Aktakka et al.Reproduced with permission.[196]Copyright 2013, Elsevier.h) The stage by Ellis et al.Reproduced with permission.[199]Copyright 2013, AIP Publishing.

Figure 12 .
Figure 12.Series-parallel-type 6-DOF piezoelectric stages.a) The stage by Chang et al.Reproduced with permission.[201]Copyright 2022, Elsevier.b) The stage by Cai et al.Reproduced with permission.[204]Copyright 2018, Elsevier.c) The stage by Chen et al.Reproduced with permission.[205]Copyright 2019, IEEE.d) The stage by Lin et al.Reproduced with permission.[208]Copyright 2020, MDPI.e) The stage by Bansevicius et al.Reproduced with permission.[211]Copyright 2019, Hindawi.f ) The stage by Dong et al.Reproduced with permission.[212]Copyright 2006, IEEE.g) The stage by Woody et al.Reproduced with permission.[213]Copyright 2006, Elsevier.h) The stage developed by CEDRAT company; i) the Q-821.140stage developed by PI company; j) the Q-845.140stage developed by PI company; k) the N90.XYZTR5 stage developed by Coremorrow company; and l) the XF801 stage developed by Coremorrow company.
Figure 12.Series-parallel-type 6-DOF piezoelectric stages.a) The stage by Chang et al.Reproduced with permission.[201]Copyright 2022, Elsevier.b) The stage by Cai et al.Reproduced with permission.[204]Copyright 2018, Elsevier.c) The stage by Chen et al.Reproduced with permission.[205]Copyright 2019, IEEE.d) The stage by Lin et al.Reproduced with permission.[208]Copyright 2020, MDPI.e) The stage by Bansevicius et al.Reproduced with permission.[211]Copyright 2019, Hindawi.f ) The stage by Dong et al.Reproduced with permission.[212]Copyright 2006, IEEE.g) The stage by Woody et al.Reproduced with permission.[213]Copyright 2006, Elsevier.h) The stage developed by CEDRAT company; i) the Q-821.140stage developed by PI company; j) the Q-845.140stage developed by PI company; k) the N90.XYZTR5 stage developed by Coremorrow company; and l) the XF801 stage developed by Coremorrow company.

Figure 13 .
Figure 13.Parallel-type piezoelectric stages based on single actuator.a) The stage by Deng et al.Reproduced with permission.[214]Copyright 2020, IEEE.b) The stage by Shimizu et al.Reproduced with permission.[216]Copyright 2013, Elsevier.c) The stage by Zhang et al.Reproduced with permission.[217]Copyright 2019, IEEE.d) the stage by Gao et al.Reproduced with permission.[218]Copyright 2021, IEEE.e) The stage by Chang et al.Reproduced with permission.[220]Copyright 2021, IOP Publishing.f ) The stage by Wang et al.Reproduced with permission.[222]Copyright 2019, Elsevier.g) The stage by Liu et al.Reproduced with permission.[226]Copyright 2018, IEEE.h) The stage by Mashimo et al.Reproduced with permission.[227]Copyright 2009, IEEE.

Table 1 .
Characteristics of some ultrasonic motors.

Table 2 .
Characteristics of some nonresonant motors.

Table 3 .
Characteristics of multi-DOF piezoelectric platforms based on different expansion methods.