Acoustic shape-morphing micromachines

Domain: physics
Published: 2026-02-02
Editorial outcome: minor_revision

Abstract
Shape-morphing mechanisms help organisms adapt to their environment and have inspired applications in advanced systems. Designing microrobots that are both miniaturized and capable of fast shape changes is challenging, as performance can be weakened at small scales. Ultrasound offers advantages such as fast response, repeatability, and programmability, making it suitable for enabling shape-morphing microrobots. Here, we introduce an acoustic micromachine composed of two microbubbles connected by a microhinge. Acoustic-field excitation generates interaction forces between the bubbles, enabling complete micromachine deformation within milliseconds. We also present design principles for programmable acoustic deformation, enabling both forward and inverse design, precise control, and information storage. By tuning the excitation amplitude, the micromachine can switch between multiple modes. As proof of concept, microlotus and microbird structures are demonstrated with controllable and stable performance.

Introduction
Shape-morphing mechanism enables organisms to adapt to the environment, enhancing their chances of survival. For example, a pillbug defends itself against external threats by rolling its body into a tight sphere1. At the microscale, microorganisms achieve locomotion or predation through dynamic shape changes; for example, the spasmoneme in Vorticella can contract within milliseconds2 (see Fig. 1a). Owing to their excellent environmental sensitivity and adaptability, these critical morphing mechanisms are widely applied to various macroscopic-scale systems, including robotic systems3,4, wearable devices5,6, medical devices7–9, artificial muscles6,10, and materials science11,12. However, most existing designs cannot maintain their superior shape-morphing characteristics while miniaturizing the structures. These designs often require tethered connections to external sources13,14, significantly limiting their microscale applicability. Moreover, with increasing static friction and adhesion forces, surface forces, such as van der Waals and electrostatic forces, become predominant at the microscale. Consequently, small-scale structures typically maintain rigidity, showing high susceptibility toward fracture formation15,16, thereby rendering the design of microscale variants highly challenging.

With rapid advancements in smart functional materials17, micro/nano manufacturing technologies18,19, precise manipulation20–22, and multiphysics driving strategies23–25, research on design frameworks and methodologies rooted in microscale shape-morphing mechanisms has seen substantial progress. These designs leverage characteristics, such as strong electrostatic adsorption, huge surface tension, and high area-mass ratio, endowing microrobots with advantages including high permeability, low immune rejection, and high local efficiency. As a result, they demonstrate significant potential across a range of fields, including biomedical engineering26,27, microfluidics28, and microactuation29,30. Besides, multiphysics field-driven methods are designed and used to control small untethered robots by using various stimuli, such as chemical gradients31–34, light35–39, heat40–43, electric static fields30,44–47, and magnetic fields48–51. Although these designs address the challenges associated with microscale effects, substantial limitations exist. For example, pH-responsive hydrogel materials exhibit limited sensitivity and slow response because they can only react within a specific pH range. The choice of solvent can influence the behavior and applications of a material, thereby constraining its potential utilization52. Consequently, the application of pH-responsive hydrogel deformation systems is limited for scenarios requiring rapid, repeatable, and frequency-programmable deformations. Shape memory alloys or polymers are commonly used as temperature-responsive deformable materials. However, their morphing mechanisms exhibit long response times and are difficult to miniaturize53. Furthermore, heating may be unsuitable or require stringent control in biological or temperature-sensitive environments. Photoresponsive morphing structures are constrained by environmental factors and photoresponsive materials are active within a limited wavelength range. Additionally, the scattering and reflection of light restrict the functionality and repeatability of photoresponsive morphing mechanisms54. Consequently, optically-actuated deformation systems are well-suited for environments with ample illumination, but are less applicable in scenarios that require actuation through opaque or highly scattering materials. Although deformation structures driven by electric and magnetic fields have attracted considerable attention11,55, complex preprogramming, including predesigned magnetic moments, multilayer structures, and multistep processes, are required to produce micromachines compatible with such approaches. Furthermore, scaling down may lead to the failure or significant deterioration of the underlying physical mechanisms governing such designs.

Ultrasound fields exhibit several properties, such as high penetration, flexibility, low cost, and biocompatibility, and can generate significant power. Acoustic actuation methods based on sharp edges and microbubble-induced oscillations can generate intense local pressure gradients and fluid flows56–59. For instance, ultrasound-activated artificial ciliary bands mimic biological cilia to generate volumetric flow for cargo transport57, while bubble-based microrobots demonstrate efficient propulsion through biological environments with the ability to adhere to soft tissues58. Despite exciting prospects, the use of acoustics in transformable micromachines has received minimal attention60. Controllable deformations at the microscale can be generated in micromachines using acoustics technology. These mechanisms can be miniaturized, remotely controlled, wirelessly operated, and rapidly fabricated for rapid and reversible switching within tens of milliseconds60. However, this deformation mechanism relies on differences in geometry and material stiffness, which makes it slow and power-hungry. Moreover, it struggles to reconfigure complex three-dimensional (3D) shapes or maintain stable deformation across different states. Therefore, research on the mechanisms, driving methods, and control techniques of acoustic micromachines is currently in the nascent stage, and a comprehensive theoretical framework for such systems has not been reported.

In this study, we designed an acoustic shape-morphing micromachines (ASMs) (see Fig. 1b) that can alter their shape within 10 ms under acoustic-field stimulation and rapidly return to their initial state on acoustic-field removal. These micromachines comprise a pair of identically sized microbubbles connected by flexible microhinges. On acoustic field exposure, microbubble oscillation induces deformation within milliseconds; the forces and torques required for this deformation are generated by secondary acoustic radiation forces between the microbubbles and the flow induced by their oscillations. This can be continuously tuned by varying the exciting acoustic-field voltage. Additionally, this study proposes a modular design approach for deformable micromachines based on their rapid response, ultrafast deformation, large deformation angles, and programmability properties. The motion of these machines can be predicted using Denavit-Hartenberg (DH) parameters, which can explain 2D-to-2D and 2D-to-3D deformations. Subsequently, the potential of the proposed method for 3D-to-3D deformation is analyzed. The results offer different design paradigms for a wider range of applications at the microscale in various fields, including soft robotics, flexible electronics, microfluidics, smart materials, and adaptive optics.

Results
Design and Characterization of ASMs
Microbubbles are widely used as microscale acoustic tools. Compared with other tools, such as sharp-edged structures61, microbubbles exhibit frequency response characteristics under external acoustic-field stimulation62. Additionally, interaction forces exist between different microbubbles63. These mechanisms offer greater flexibility in the design and characterization of microbubble-based micromachines, thereby enhancing their potential multifunctionality. Supplementary Figs. S1 and S3 show the working schematic and fabrication process of the ASM, respectively. Micromachines with hinges of varying lengths, ranging from 4 to 16 μm, width within the range of 0.5–3 μm, and a uniform height of 57.5 μm in the Z-direction were manufactured in this study. The deformable angle between the two microbubbles ranged from 0° to 75°. Supplementary Fig. S7 shows the rigid structure of the ASMs and Young’s modulus of their flexible microhinges measured using an atomic force microscope (see Supplementary Note 1 and Supplementary Fig. S7 for details). Detailed information on the fabrication process is presented in the Materials and Methods section.

The characterization of the manufactured ASMs was experimentally investigated using a setup comprising an acoustic manipulation region and a piezoelectric transducer (PZT) adjacent to a glass slide (see Supplementary Fig. S2). The PZT was connected to a signal generator through an amplifier to produce an acoustic field with adjustable amplitude and frequency. The dynamic deformation of the ASMs was observed using a microscope and camera. An acoustic field with a voltage amplitude varying within the range of 0–60 V and a working frequency of 102-104 kHz, matching the resonance frequency of the experimental setup, was applied during the analysis. Further experimental details are provided in the Materials and Methods section.

A microbubble pair with identical diameters is a crucial component of ASMs as it determines the deformation capability of the entire device. When the acoustic field traverses the liquid medium and reaches the micromachine, acoustic streaming effects occur between the pair of microbubbles; secondary acoustic radiation forces induces attraction between the bubbles. Simultaneously, the microhinges contract, causing the two microbubbles to approach each other until complete contact, as shown in Fig. 2a, b. The ASMs manufactured in this study showed a fully folded shape within 5–10 ms, as indicated by the experimental results (see Supplementary movie S1). This dynamic deformation was controlled by the acoustic pressure; once the acoustic field was turned off, the ASMs rapidly returned to its original shape, as shown in Fig. 2c, d. Through structural design, the deformation in the XY-plane could be extended to the ZX-plane, as shown in Fig. 2e. After deformation of the ASMs, their microscopic images showed defocusing along the Z-axis, as illustrated in Fig. 2f, g. Notably, this dynamic deformation is regulated by the excitation voltage of the external acoustic field, which can be adjusted using a signal generator. The Materials and Methods section provides a detailed characterization of the acoustic pressure distribution generated by our setup, as well as the operational lifetime of the microbubbles in the ASM.

To further understand the mechanisms underlying shape morphing, the dynamic mechanisms of micromachines in an acoustic field were investigated. According to bubble acoustics, acoustically excited bubbles function as acoustic sources when they approach each other63,64. Because the distance between the bubbles is significantly smaller than the wavelength of the ultrasound in the experimental setup, the acoustic radiation force generated by the background acoustic field can be assumed to not cause relative displacement between the microbubbles. Therefore, the secondary forces acting on the micromachine comprised the interaction forces between the bubbles, resistance induced by acoustic streaming, and secondary acoustic radiation forces. As identical bubbles produce the same acoustic streaming, the interaction force between them is attractive, causing the adjacent microbubbles to move closer to each other. The total force acting on the microbubbles can be expressed as follows:

F B=F U+F S+F R (1)

where F U, F S, and F R represent the acoustic radiation force, thrust from the flow, and drag force exerted on a bubble by the flow generated by the neighboring bubbles, respectively. As the distance between the bubbles is comparable to the bubble size, which is significantly smaller than the wavelength of sound waves, in this study, we assumed that F R did not depend on the distance between the microbubbles65. Therefore, we have |F R|=|F S|. Given that acoustic streaming is a second-order effect, its resulting thrust remains substantially smaller than the secondary acoustic radiation force at low-to-moderate drive levels with the microbubble approaching. According to the force balance equation64,66, the above equation can be rewritten as

F B − F U=B*G (2)

r2 1
G= 1 (3)
L2[(1−ω2 0=ω2)2+δ2 0]

where G>0 represents the attraction between the microbubbles. As shown in the Fig. 2a, r 1 represents the radius of the identical microbubble pairs, L denotes the distance between the microbubbles, ω 0 is the natural frequency of the microbubble pair, and ω is the acoustic excitation frequency. Moreover, δ 0 denotes their total damping constants. B is a scalar related to the excitation amplitude and does not change the sign of the force. Equation (3) indicates that the sign of the interaction force between the identical microbubbles remains constant, regardless of the changes in the acoustic excitation frequency. Therefore, the identical microbubbles tend to attract each other. However, the complex interaction forces between microbubbles of different sizes can result in attraction or repulsion depending on the acoustic excitation frequency. Details regarding theoretical development, verification, and simulations of the model are provided in the Supplementary Information (see Supplementary Notes 2, 3 and Supplementary Fig. S4).

An intriguing phenomenon was observed on investigating the dynamics of the manufactured ASMs using high-magnification microscopy. As the two microbubbles were driven by a variable-amplitude acoustic field, the deformation amplitude of the micromachine changed with variations in the acoustic-field amplitude. The deformation amplitude of the micromachine remained constant at a constant acoustic-field amplitude. The introduction of tracer particles into the liquid generates microvortices in the surrounding fluid, as illustrated by the simulated streamlines in Supplementary Fig. S5, leading to rapid oscillation of the microbubbles. As the distance between the two microbubbles decreased, as per Equation (3), their interaction force increased significantly. Consequently, the microbubbles progressively attracted each other, inducing microhinge folding, resulting in a nonlinear reduction in the angle between the two microbubbles, as shown in Fig. 2h.

A series of experiments was conducted to optimize the microhinge structure of the ASMs for efficient transformation by varying their microhinge length, angle, and width. The deformation angle of the micromachine was significantly influenced by the microhinge width and length. At the microhinge length of 10 μm and an excitation voltage of 25 V, a 25% reduction in the microhinge width (from 2 to 1.5 μm) resulted in a 445% increase (from 11° to 60°) in the maximum deformable angle, as shown in the Fig. 2i, possibly owing to a reduction in stiffness. Similarly, at the microhinge width of 1.5 μm, an increase of 33% in the microhinge length (from 6 to 8 μm) led to a substantial 100% increase (from 30° to 60°) in the maximum deformable angle. For microhinge lengths below 10 μm, the acoustic radiation force dominated the total force. The secondary acoustic radiation force reduces markedly with increased inter-microbubble distance. Under our experimental conditions, its attenuation upon microbubble separation 1/L2 thereby the streaming-induced thrust to become predominant. Consequently, when the microhinge length exceeded 10 μm, the magnitude of the acoustic radiation force decreased, and the thrust from the fluid became dominant, causing the sign of the total force to switch, resulting in the microbubbles beginning to repel each other, as shown in Fig. 2k.

Notably, the excitation voltage required for complete deformation increased with an increase in the initial ASM angle, as shown in Fig. 2j. The micromachine deformation time was investigated at different widths and excitation voltages. Upon only varying the external excitation voltage, the micromachine required 50–60 ms to deform completely. On full deformation, the deformation time decreased significantly with increasing excitation voltage; rapid deformation (8 ms) occurred at 60 V. Thin and long microhinges showed relatively low stiffness, and soft hinges generated greater acoustic forces, leading to more pronounced deformation. Moreover, by adjusting the laser intensity, the degree of microhinge cross-linking could be controlled by selectively enhancing the stiffness differential between the rigid link and soft hinge. These varied options for stiffness modulation provide exciting possibilities for designing and programming transformable micromachines and microrobots.

Design and Encoding of 2D ASMs
Unlike traditional 3D printing, shape-morphing micromachines should address complex forward and inverse design problems, making the model design crucial for precise experimentation. Considering the degrees of freedom and programmability of the ultrasonic deformation module, a modular design approach was used to analyze the forward and inverse kinematics of the target structure by defining the DH parameters associated with the deformation, which adhere to the principle of superposition. Any complex transformation can be described using only these four physical parameters in a closed-form analytical manner67.

[T]=[XY 1][Z 1][XY 2][Z 2]...[XY n][Z n] (4)

Here, T denotes the transformation positioning the terminal link of the final building module. This transformation allows the frame structure to undergo curved motion around a defined axis.

[XY i]=Trans xy (R x i)Trans y (d i)Rot xy (θ xy i)Rot xy (α xy i) (5)

[Z i]=Trans z i(d i)Rot z i(θ z i) (6)

where d i, α i, R i, θ i represent the DH parameters. In combination with the micromachine units described above, the DH parameters can be used to define the morphology planning principles of the modular system, as shown in Fig. 3a–i. Figure 3a–e shows the simulated rotational motion of micromachine units encoded using θ i. These micro-units were rigidly connected to each other to avoid inter-unit deformation interactions and ensure the validity of the superposition principle. The rotation angle of the micro units rotating around the Z-axis, determined by θ z i, can be adjusted by tuning the exposure dose during the manufacturing process. Figure 3f, g indicate that the radius of rotation, R i, can be changed by connecting deformed micro units to the fixed micro units. Figure 3h shows the micro unit offset along the Z-axis (d i), which was used to construct the deformed morphology, and Fig. 3i shows that a coordinate system can be reconstructed by rotating the micro cell in the XY-plane (α i). Together, these four DH parameters can be used to formulate the morphological planning rules for the modularized system. The details regarding the theoretical development, validation, and simulations of the model are provided in the Supplementary Information (see Supplementary Fig. S11, Supplementary Tables S1, and S2, respectively).

According to the aforementioned rules, any 2D shape can be converted into a finite number of ASM modules. Here, the DH parameters were derived from inverse kinematics, and switching rules were constructed between the target and initial morphologies according to Equation (4), as shown in Fig. 4a. Figure 4d shows the details of the structure. Considering the deformation designs of the chain and wave to be the target and initial morphology, respectively, θ i is the only variable parameter in the morphing design. Figure 4b, c show the experimental results of the chain-to-arc conversion (see Supplementary movie S2). Under the excitation voltage of 23 V, the chain structure folded sequentially, and the deformation of the four modules produced a deformation effect of up to 233°; complete folding and release occurred within 2003 and 742 ms, respectively, as shown in Fig. 4e. In the subsequent experiments, prior to the completion of folding, the response time increased with increasing voltage. When the excitation voltage exceeded the critical voltage of 23 V, at which full folding occurs, the time required for full folding gradually decreased with increasing voltage, finally requiring only 95 ms for a complete chain-to-arc deformation at the excitation voltage of 50 V. Additionally, Fig. 4f, i show transformations from chains to rolls, honeycombs, ‘S’s, and waves (see Supplementary movies S3–S6), confirming the versatility and generality of the proposed design approach.

Notably, multimodule micromachines that can store information can comprise modular unit assemblies (see Fig. 5). Multiple tailored configurations can be developed by encoding target traits according to the reverse-design method. Therefore, different information edits were implemented on the chain structure to enable the ASM to store the corresponding information. Here, the letters were encoded ‘N’, ‘W’, ‘P’, and ‘U’ (representing Northwestern Polytechnical University) in the chained 2D-ASM, as shown in Fig. 5a. The deformation process of each letter, which is the driving region of the deformed structure that gradually bends to the pre-edited position under the action of an externally stimulated acoustic field, was subsequently characterized, as shown in Fig. 5b–e and Supplementary movie S7. Thus, the ASM concept of information coding allows the creation of complex shape-coding systems with customized 2D transformations by tuning the design and layout of the deforming micro units.

Complex 3D-ASM
Blooming microlotus. To analyze the applicability of acoustic ASM technology, complex configurations of ASM in 3D space (labeled 3D-ASM) were investigated. In the aforementioned deformable micromodules, the interaction forces between bubbles under varying acoustic-field intensities enable them to maintain a stable state in any deformed configuration. Here, the deformation direction of the micromodules was adjusted to extend the deformation degrees of freedom along the Z-axis to design an acoustically driven microlotus inspired by the blooming of natural lotus flowers (see Fig. 6a). To address the constraints between structures, the flower comprised four petals connected to the center by ASM micromodules (see Fig. 6b). The driving force for structural deformation comprised interaction forces between a pair of identical acoustic-field-activated microbubbles. The deformation direction of the micromodules was configured to be along the Z-axis, resulting in a maximum deformation angle of 60° (see Supplementary movie S8). The deformation process was assessed in chronological order using one flower petal at a time. Unlike other deformation methods, such as those involving pH52, thermal53 and photonic stimuli54, the deformation of the microlotus designed in this study could be halted at any moment and maintained in its current configuration by fixing the excitation voltage. On removing the ultrasonic excitation signal, the flowers rapidly returned to their initial state (see Supplementary Fig. S6). At the same time, the deformed microlotus could resist the external interference. On exposing the deformed microlotus to significant disturbances using a microprobe, the shape of the flower was restored within A few milliseconds (see Supplementary Note 5 and Supplementary Fig. S8). This deformation method, which enabled the rapid opening and closing of the flower while maintaining its current state at any moment, could enable the precise 3D microscale-manipulation of microparticles, cells, or microrobots. We demonstrate a micromanipulation task where the magnetic cargo is delivered along a fixed track to a target location by the microlotus. The cargo is released upon the cessation of the acoustic excitation, as shown in Supplementary Fig. S15.

Figure 6c shows that the deformation time of the microlotus gradually decreased with increasing voltage. Under an external acoustic-field activation voltage of 30 V and frequency of 103 kHz, a maximum time of 621 ms was required for complete structural deformation (from the ‘bloom’ state to the ‘bud’ state). The resultant net force and net torque caused the micromachines to undergo transformation with a negative Poisson’s ratio of approximately -1 (refer to Supplementary Note 4 and Supplementary Figs. S9 and S10 for calculation method and results). The time required for complete deformation decreased with increasing excitation voltage. At the acoustic-field activation voltage of 50 V, complete structural deformation occurred within 138 ms, resulting in a 77.8% reduction in response time as compared with that at the excitation voltage of 30 V. Figure 6e shows the optical images of the microlotus deformation process at the excitation voltage and frequency of 40 V and 103 kHz, respectively. Projection curves of the microlotus in the XY-plane at different deformation angles were used to correlate the optical images of the system with the degree of deformation (see Fig. 6d).

During the bubble’s stable period, we cyclically actuated the microlotus at 103 kHz using sinusoidal voltages from 25 to 50 V. One cycle was defined as a full petal deformation and relaxation. By measuring cycle time and total bubble lifetime (see Supplementary Fig. S16), we estimated the maximal actuation cycles for each voltage. At 25 V, 545 cycles were possible before bubble shrinkage began. At 35 V, the actuation was faster, yielding 1403 cycles, though shrinkage accelerated slightly under stronger drive. At 50 V, despite larger deformation amplitude, the total lifetime dropped and the cycle count fell to 1136. These results reveal a trade-off: higher voltages yield faster and greater deformation but shorten microbubble longevity.

Multiflight-mode microbird. Varying the deformation direction can result in advanced deformation behaviors, and the deformation amplitude can be tuned by adjusting the maximum deformation angle between the microbubbles within the ASM. Figure 7c shows two ASM units with different deformation directions oriented along the Z-axis while being distributed at different orientations in the XY-plane. Arbitrary deformation poses were assigned to each component by adjusting the deformation direction and amplitude of each ASM. As a proof-of-concept, an origami-type microbird was designed in this study to mimic the different flight modes of real birds (see Fig. 7a) by specifically arranging ASMs on the five body parts of the microbird (i.e., the head, body, tail, and a pair of wings). The corresponding electron microscopy image is shown in Fig. 7b. Two possible deformation directions and one stationary state existed at the wings or joints of the microbird. Editing the configurations of the ASMs on different parts of the microbird resulted in four distinct morphological changes, namely, ‘flapping,’ ‘taking off,’ ‘turning,’ and ‘hovering’ (see Fig. 7d and Supplementary movie S9). The microbird showed various deformation behaviors: in the ‘flapping’ mode, both the wings folded simultaneously in phase and in the same direction; in the ‘taking off’ mode, the head and tail rose, while the wings folded downward; in the ‘turning’ mode, the wings folded in different directions; and in the ‘hovering’ mode, only the tail folded relative to the body. Thus, the ASM can be used as a foundational structural module to design a wider range of micro deformable micromachines with diverse structural configurations, geometric dimensions, and deformation directions.

Methods
Preparations of Materials
Acrylic ester (AAm, 99%), N-isopropylacrylamide (NIPAAm, 98%), ethyl lactate (EL, 98%), polyvinylpyrrolidone (PVP, average molecular weight, 1,300,000), N,N-dimethylformamide (DMF, 99.5%), 4,4’-bis(diethylamino)benzophenone (EMK, 97%), Dipentaerythritol pentaacrylate (DPEPA, 98%), and triethanolamine (TEA, 99%) were purchased from Aladdin Chemicals. All chemicals were used directly as received.

Preparation of hydrogel precursor
In a typical procedure, NIPAAm and AAm were added to EL solution and stirred vigorously for 30 min. PVP was added to adjust the photoresist viscosity to Adjust the density of the cross-linked network in the material after polymerization. After complete dissolution, the above solution, DPEPA cross-linker, TEA photosensitizer, and the EMK/DMF photoinitiator solution were mixed and stirred overnight to ensure the complete mixing of each component in the solution. Once made, the photoresist was stored in yellow light condition to prevent unnecessary exposure before use.

In this study, NIPAAm served as a copolymeric component within the hydrogel network rather than as a thermoresponsive actuator. All experiments were conducted at room temperature (22°C ± 3°C), well below the hydrogel’s lower critical solution temperature (LCST) (~32°C). Moreover, copolymerization with non-thermosensitive monomers (e.g., AAm) further elevates the LCST, ensuring no phase transition or change in hydrophilicity. Consequently, the material exhibits stable mechanical properties without temperature-induced deformation.

Fabrication of micromachine
Micromachine were fabricated by two-step sequential printing, using a commercial two-photon direct laser writing system (MPD-PPI, YZQ instruments). 3D models were built using the AutoCAD software and exported as STL format files. The STL files were converted into General Writing Language by the slicing software and loaded into the fabrication software for printing.

Before the first printing, the borosilicate glass square substrate (22×22 mm, 0.13 to 0.17 mm thick; Thermo Fisher Scientific Inc.) was rinsed using isopropanol, followed by nitrogen purging and oxygen plasma treatment, to serve as the printing substrate. To make certain printed microstructure pinned to the borosilicate glass, the substrate must be cleaned and locally surface-treated so the printed polymer forms a strong attachment.

Subsequently, a drop of IP-L resist was placed on the center of the substrate using a pipette, which was printed with a commercially available 3D laser lithography system (MPD-PPI, YZQ instruments) with a 60x/1.42 oil immersion objective (Olympus). During the first printing, the laser power (40 mW) and scanning speed ("8000 μm/s”) were set to cross-link the IP-L resist. After the first printing, the sample was immersed separately in SU-8 developer and IPA for 8 min and 5 min, respectively, for development, and then dried under nitrogen.

The IP-L resist was dropped on the existing structure on the glass substrate, which was placed back in the DLW system in the same position as the first printing. Before the second printing, the center of the printing stage was adjusted with the fabrication software through the integrated camera in the printing system to align with the existing structure. During the second printing, the laser power (40 mW) and scanning speed ("4000 μm/s”) were set to cross-link the hydrogel. The laser power and scanning speed were modulated dynamically to achieve desired stiffness and hardness. After the second printing, the sample was developed in IPA two times for 8 minutes and then dried under nitrogen. After the second fabrication, the flexible part and the rigid part are connected together.

Acoustic device
The acoustic system is established on a glass slide of 75mm*25 mm*1mm, where the transducer (Murata) is connected to the epoxy resin (Devocon). Once the microchannels and other microstructures are fabricated and cleaned on the acoustic device (IPA, Aladdin), they are transferred to the microscope stage. Upon immersion of the device into deionized water, small air pockets were naturally trapped within the microcavities due to incomplete wetting of the hydrophobic cavity surfaces. The cavity geometry (diameter=50 μm) and high contact angle prevented full liquid infiltration, resulting in air entrapment. The trapped air was stabilized by surface tension pinning at the cavity rim, leading to the formation of persistent microbubbles within the device.

Localized stiction of the movable structures was then overcome using a micromanipulator equipped with a metallic probe, which carefully released them without disturbing adjacent features. Then, the piezoelectric transducer is connected to the signal generator through an amplifier (ATA-2032 High Voltage Amplifier, Aigtek), with the purpose of generating a tunable frequency sound field in the liquid. The entire device is mounted under a microscope (CM4000, HangZhou BoNa Optoelectronics Co., Ltd.).

The transducer and acoustic chamber were securely mounted on a glass slide, with their position and orientation relative to the work area remaining unchanged throughout the experimental process. The design and calibration of the integrated acoustic chamber-transducer assembly were aimed at ensuring a reproducible and Uniform acoustic field. Furthermore, the experimental setup remained unaltered between trials, thereby maintaining a spatially homogeneous acoustic field. The specific positional relationship is illustrated in the Supplementary Fig. S14a. Acoustic field simulations under this configuration were also performed, as shown in the Supplementary Fig. S14b. It can be observed that when the printed structure is positioned at the center of the acoustic chamber—a condition readily achievable in two-photon direct laser writing fabrication—it is subjected to a uniform acoustic field under 103 kHz ultrasound excitation.

We characterized the microbubble lifetime in deionized water and PBS buffer, as shown in Supplementary Fig. S13. It was observed that in the absence of ultrasonic excitation, the microbubble maintained its volume without change for 25 min in deionized water. Under ultrasonic excitation at 25 V (exceeding the minimum actuation voltage for complete deformation of the ASM), the operational duration of the microbubble decreased to 8 min, as shown in Fig. S13a. Using PBS buffer as the liquid medium can increase the lifetime of the microbubble. Without ultrasonic excitation, the microbubble maintained a constant volume for 64 min, representing a 156% increase compared to its lifetime in deionized water. Under 25 V ultrasonic excitation, the working time reached 29 min, a 263% increase over that in deionized water, as presented in Fig. S13b. Thus, through experimental configuration, sufficient operational time for the ASM can be secured, during which the microbubble volume remains constant. Under our experimental conditions, this ensures that the ASMs maintain in-phase vibrations and ultimately undergo mutual attraction under ultrasonic excitation.

Imaging and data analysis
Experiments were conducted on a microscope (CM4000, HangZhou BoNa Optoelectronics Co., Ltd.). The microscope was equipped with a camera and the recorded frequencies were analyzed using software. Recording frame rates range from 50 to 1000 frames per second (fps). Recorded footage is analyzed in ImageJ.

Numerical Simulation
The interaction forces between microbubbles were analyzed and calculated using commercial software MATLAB. The numerical simulation reported in this work was performed using the commercial multiphysics finite element software COMSOL. Two-dimensional simulations were conducted using triangular elements, while three-dimensional simulations were conducted using tetrahedral elements to simplify the meshing process. We assumed the acoustic field to be a linearized first-order field of the Navier-Stokes equations, and the acoustic flow field to be a time-averaged second-order field describing system disturbances. We used P 1–P 2 composite elements to measure pressure and velocity, where P 1 and P 2 represent triangular elements with 1st and 2nd order Lagrange polynomials, respectively. Direct solvers were employed for both first and second-order equation systems to obtain solutions.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript reports the development of an Acoustic Shape-Morphing Micromachine (ASM) capable of ultrafast and reversible morphological reconfiguration under acoustic-field actuation. The ASM architecture consists of a pair of isodiametric microbubbles interconnected by a compliant microhinge, wherein shape transformation is driven by secondary acoustic radiation forces and acoustic streaming flows generated in the inter-bubble region. The authors present a comprehensive design framework that enables precise modulation of deformation kinetics, angular displacement, and structural stability, and introduce a modular design methodology applicable to both forward and inverse kinematic modeling. This framework supports the fabrication of ASMs with fully programmable 2D and 3D morphologies, as well as integrated information-encoding functionalities. The study offers potentially significant implications for the future design of shape-morphing micromachines in domains such as soft robotics, microfluidics, and adaptive microstructures. I recommend the manuscript for publication, contingent upon the authors’ satisfactory response to the following technical comments.\n\nComments:\n1. While acoustic streaming generated by oscillating microbubbles typically propagates radially away from the bubble surface, prior studies have demonstrated that even subtle variations in excitation frequency or bubble volume can induce a reversal in streaming direction. A more detailed and mechanistically rigorous exposition is warranted to clarify how such streaming flows, in conjunction with secondary acoustic radiation forces, effectuate morphological reconfiguration of microscale structures. Although the present work effectively demonstrates the practical feasibility of employing acoustically driven microbubbles for microscale structural deformation, the fundamental physico-mechanical underpinnings of these transformations—rooted in bubble oscillatory dynamics—are not yet sufficiently elucidated.\n2. Related to the above, in cases where the bubble volume is sufficiently small, transient shifts in its resonance frequency could undermine the reproducibility or fidelity of the intended deformation response. Further clarification is requested on the protocols employed for precise generation of such small-volume bubbles, and on the temporal stability of their volume during operation. In addition, previous investigations have shown that both the oscillation amplitude of microbubbles and the magnitude of the resultant acoustic streaming and secondary radiation forces vary with the spatial offset from the piezoelectric transducer (PZT). It would be of interest to determine whether similar spatially dependent phenomena were observed in the present experiments, and if so, how they were accounted for in the design and analysis.\n3. The originality and conceptual ingenuity of the reported research are noteworthy. To facilitate a more rigorous and objective evaluation of the work’s novelty, it would be advantageous for the authors to provide a concise synopsis of their prior related studies and to delineate explicitly the principal advancements and distinctive contributions of the present investigation relative to those earlier efforts.", "reviewer_2": "This work reported a novel technique to deform microrobots to demonstrate novel modality and control of the microrobot shape by implementing bubble-based acoustic streaming with deformable hinges. Though acoustically driven micro robots is a well-established field, I have yet to see demonstrated the shape-changing of micro robots with acoustics. With this technique of acoustic shape-morphing of micromachines they demonstrated x-, y-, and z-axis deformation, complex 2D shape deformation, and complex 3D shape deformation. With the development of this technology, they also laid the theoretical framework for designing the structures to develop the end design (design is not necessarily my field of expertise, but the demonstration of their designs appear sound). The reported technique demonstrates good performance and versatility in design and performance. The quality of writing and demonstration of applicability of shape-morphing micro robotics is lacking within the manuscript. I recommend the following manuscript for publication in Nature Communications with the following revisions.\n\nComments:\n1. The lack of attention for acoustic driven deformation does not merit increased attention, as mentioned in your abstract. Please articulate why shape-changing microrobots is important.\n2. There are several errors in the writing and consistency of formatting within the manuscript. Please increase the quality of the writing of the manuscript, particularly in the methods, abstract, figure captions, and supplemental information.\n3. I’m not sure if acoustic microrobots is in the nascent stage, as mentioned in the introduction. There are several papers in this field that have discussed the mechanisms, driving methods, and control techniques of acoustically driven micro robots, including the following.\na. Helical acoustic driven – Yong Deng et al. An acoustically controlled helical microrobot.Sci. Adv.9,eadh5260(2023).DOI:10.1126/sciadv.adh5260\nb. Multi-modal – Dillinger, C., Nama, N. & Ahmed, D. Ultrasound-activated ciliary bands for microrobotic systems inspired by starfish. Nat Commun 12, 6455 (2021). https://doi.org/10.1038/s41467-021-26607-y\nc. Microbubble micro-robot – J. G. Lee, R. R. Raj, C. P. Thome, N. B. Day, P. Martinez, N. Bottenus, A. Gupta, C. Wyatt Shields IV, Bubble-Based Microrobots with Rapid Circular Motions for Epithelial Pinning and Drug Delivery. Small 2023, 19, 2300409. https://doi.org/10.1002/smll.202300409\nd. Literature review on the topic – Xiao Y, Zhang J, Fang B, Zhao X, Hao N. Acoustics-Actuated Microrobots. Micromachines (Basel). 2022 Mar 20;13(3):481. doi: 10.3390/mi13030481. PMID: 35334771; PMCID: PMC8949854.\ne. Literature review on the topic – https://pubs.rsc.org/en/content/articlelanding/2024/lc/d4lc00566j#!divAbstract\n4. I think your report on shape-morphing micromachines is novel, but that is not described or evaluatied in the introduction. Please re-shape your introduction to discuss this critical component of your work.\n5. Mechanism description is unclear. What do you mean by resistance induced by acoustic streaming in line 133? Is secondary acoustic radiation force or acoustic streaming the main driving mechanism of your platform?\n6. Is the microhinge thickness referring to the width of the microhinge? It appears that the z-parameter remains constant while the y-axis is what is being altered. Please clarify.\n7. It appears that the Fig. 2k x-axis is incorrect. Shouldn’t it be micro-hinge length?\n8. There appears to be some inconsistencies in the reference of figures in the results section (Fig. 2I, line 170). Please double check the entire manuscript to ensure that there are no errors.\n9. In line 260-262, it is claimed that 3D microscale manipulation of microparticles, cells or microbots could be achieved. Can you demonstrate this? Demonstrating an application with your technology would bolster the quality of your manuscript.\n10. It is unclear how bubbles were entrapped within your fabricated devices in the methods section, please elaborate.\n11. What is the life cycle of your microrobots? How many times can the micro lotus deform and relax before it no longer responds? How does the cycle life of your microrobot change with voltage? Including this data would help show repeatability and longevity of your microrobot system.\nSmall comments\n1. The syntax for Fig. X (Y) is inconsistent. Please ensure that these are uniform throughout.", "reviewer_3": "In this work the authors harness the significant acoustic forces that can be generated by oscillating microbubbles, yielding repeatable actuation of microstructures. This was used to generate programmed designs via actuation, including the generation of shapes/patterns, actuation in a variety of system architectures, and multi-step motions. This is highly novel and interesting work, however the authors are advised to address the following comments in order to better elucidate the mechanisms and experimental details utilized in this work.\n1. The authors might provide a comparison of the mechanisms between the microbubble-based ASM approach here and the approach used in previous work (ref. 68), highlighting advantages and performance characteristics compared to this previous work.\n2. How important is the relative size of the bubbles? It’s stated that they need to be identical, however any Bjerknes/inter-bubble forces would in principle still be acting even with a differential bubble size (though the magnitude may be different). Some sensitivity analysis, even if analytical, would be helpful in elucidating the importance of bubble size.\n3. Is there any impact of acoustic radiation forces between the microbubble and any adjoining/nearby surfaces?\n4. Fig. 2 can include more experimental detail in the caption, e.g. voltage, thickness and length for given results (e.g. 2J could state the length and thickness for this data, 2I and 2J could state voltage).\n5. Based on the text Fig. 2K appears to show the deformation as a function of length, but the axis says thickness. Moreover, more detail and discussion on why the deformation angle inverts for longer hinges is warranted (noting that Eqn. 2 appears to rule out acoustic streaming).\n6. To be clear, in transitioning between equation 1 and 2 it appears that the streaming/drag forces are cancelling each other out. More explicit and justified language in this section would be useful.\n7. More detail on the choice of materials is warranted, notably the phase-changing heat-sensitive polymer NIPAAm. Is there any importance to the phase-change behaviour of this material to the effects that have been observed? Moreover, what was the temperature of the system being examined, and how might have this been controlled? The mechanical properties of the hinge material might be strongly impacted by temperature if NIPAAm is used.\n8. Is “NIPAAm” the same as “PNIPAAm”? I wonder what the standard acronym for this is, as I’ve seen many iterations of this elsewhere.\n9. More detail on the fabrication process, specifically how some elements are bonded/pinned to a surface, and how some are released and thus free to move around the pinned elements, is warranted.\n10. Additionally, can the authors clarify if any of the systems shown were free-floating? What would the overall mass density of a given element be, and would it thus float or sink in water?\n11. How were the authors able to achieve long-lasting and uniform microbubbles? Or do these shrink/grow over time, and was there any way to modulate their size after they were immersed?\n12. Line 160: should clarify here that this is a simulation\n13. Line 57 of SI: (?,?)"}, "author_response": "---------------------------------------------------------------------------\nResponse to the Reviewers’ Comments --#NCOMMS-25-54681A\n--------------------------------------------------------------------------\nManuscript #NCOMMS-25-54681A\n“Acoustic shape-morphing micromachines”\nResponse to the Reviewer 1\nGeneral comment: This manuscript reports the development of an Acoustic Shape-Morphing\nMicromachine (ASM) capable of ultrafast and reversible morphological reconfiguration under\nacoustic-field actuation. The ASM architecture consists of a pair of isodiametric microbubbles\ninterconnected by a compliant microhinge, wherein shape transformation is driven by\nsecondary acoustic radiation forces and acoustic streaming flows generated in the inter-bubble\nregion. The authors present a comprehensive design framework that enables precise\nmodulation of deformation kinetics, angular displacement, and structural stability, and\nintroduce a modular design methodology applicable to both forward and inverse kinematic\nmodeling. This framework supports the fabrication of ASMs with fully programmable 2D and\n3D morphologies, as well as integrated information-encoding functionalities. The study offers\npotentially significant implications for the future design of shape-morphing micromachines in\ndomains such as soft robotics, microfluidics, and adaptive microstructures. I recommend the\nmanuscript for publication, contingent upon the authors’ satisfactory response to the following\ntechnical comments.\nResponse: We thank the reviewer for the careful and thoughtful feedback on our manuscript,\nwhich help improve the quality of our manuscript. We have carefully revised the manuscript\nbased on the suggestions. Please check the following point-by-point responses for details.\nBelow, reviewer’s comments are presented with purple italics to distinguish from our response.\nChanges and additions in the manuscript are highlighted in blue type.\nComment 1: While acoustic streaming generated by oscillating microbubbles typically\npropagates radially away from the bubble surface, prior studies have demonstrated that even\nsubtle variations in excitation frequency or bubble volume can induce a reversal in streaming\ndirection. A more detailed and mechanistically rigorous exposition is warranted to clarify how\nsuch streaming flows, in conjunction with secondary acoustic radiation forces, effectuate\nmorphological reconfiguration of microscale structures. Although the present work effectively\n1\ndemonstrates the practical feasibility of employing acoustically driven microbubbles for\nmicroscale structural deformation, the fundamental physico-mechanical underpinnings of these\ntransformations—rooted in bubble oscillatory dynamics—are not yet sufficiently elucidated.\nResponse: We thank the reviewer for their insightful remarks regarding the mechanical basis\nof the ASM deformation and the underlying microbubble dynamics. In response, we have\nexpanded our discussion to elucidate how the combined action of acoustic streaming and\nsecondary acoustic radiation forces effectuates the morphological reconfiguration of the\nmicrostructures.\nWe have noted the phenomenon raised by the reviewer, wherein variations in excitation\nfrequency or microbubble volume can lead to a reversal in the direction of acoustic streaming.\nFor instance, Doinikov observed that acoustic scattering between microbubbles of different\nsizes can cause an increase in their natural frequencies, which may in turn reverse the sign of\nthe secondary acoustic radiation force[R1]. Specifically, when the driving frequency exceeds the\nnatural frequencies of both microbubbles, the natural frequency of the smaller microbubble in\nan approaching pair may rise above the driving frequency as the inter-microbubble distance\ndecreases, thereby changing the force from attractive to repulsive. Conversely, when the driving\nfrequency lies between the natural frequencies of the two microbubbles, the natural frequencies\nof both microbubbles may increase as they approach each other. If the natural frequency of the\nlarger microbubble surpasses the driving frequency, the force may switch from repulsive to\nattractive. It is important to emphasize that such sign reversals are more likely to occur when\nthe driving frequency is sufficiently close to the natural frequencies of the microbubbles.\nFurthermore, under high-intensity acoustic fields, strong driving amplifies the\nmicrobubbles' radiation fields, causing multiple scattering effects—which are typically\nnegligible—to become dominant. This shift significantly alters the phase relationship between\nthe microbubbles, which can also result in a reversal in the sign of the secondary acoustic\nradiation force[R2].\nThe distances between microbubbles are significantly smaller than the acoustic\nwavelength in all our prototypes. The secondary forces that act on the ASM are thrust ( ), drag\nforce exerted on a microbubble by the flow generated by the neighboring microbubbles ( ),\n𝐹𝑆\nand secondary acoustic radiation force ( ) (also known as secondary acoustic radiation force\n𝐹𝑅\nor secondary Bjerknes force). Consequently, the secondary acoustic radiation force is\n𝐹𝑈\nproportional to the time-averaged product of the volume velocities of the two microbubbles\nunder the standard monopole approximation[R3, R4]. The secondary acoustic radiation force\nfor identical microbubbles, instead of in the original text, can be written as:\n𝐹𝑈\n𝑭𝑩 2\n2\n𝑟1 1\nrepresents the radius of th𝐹e 𝑈 ~iden 2 tical micr 2 obu 2 bb 2 le 2 pai 2 rs. denotes the distance between\n1 𝐿 [(1−𝜔0/𝜔 ) +𝛿0]\nthe microbubbles, is the natural frequency of the microbubble pair, and is the acoustic\n𝑟 0 𝐿\nexcitation frequency. Moreover, denotes their total damping constants. Consequently, the\n𝜔 0 𝜔\nsecondary acoustic radiation force grows markedly with reduced inter-microbubble distance.\n𝛿\nUnder our experimental conditions, its amplification upon microbubble approach ( )\n2\nthereby establishes it as the dominant term.\n1/𝐿\nAcoustic streaming is a second-order mean flow generated within the viscous boundary\nlayer, whose velocity is proportional to the square of the vibration amplitude. The thrust must\nbe transmitted to the microbubble through viscous drag, which in turn governs its translational\nvelocity[R5]. Therefore, the induced thrust force will cause the microbubbles to repel each other.\nGiven that acoustic streaming is a second-order effect, its resulting thrust remains substantially\nsmaller than the secondary acoustic radiation force at low-to-moderate drive levels with the\nmicrobubble approaching [R3, R5, R6]. The thrust can be written as:\n𝐹𝑆~𝜇𝜔𝜑\nthe microbubbles is comparable to the microbubble size, which is significantly smaller than the\n𝜇 𝜑\nwavelength of sound waves, so we assumed that did not depend on the distance between the\nmicrobubbles[R1]. Therefore, we have . \n𝐹𝑅\nThe total force acting on the microbubbles can be expressed as follows:\n|𝐹𝑅| = |𝐹𝑆|\nIn our study, the driving frequ𝐹e𝐵nc=y 𝐹w𝑈a+s s𝐹e𝑆t +at𝐹 𝑅the resonance frequency of identical\nmicrobubbles, and the driving amplitude was maintained at a moderate level (0-60 V), which\nwas well below the threshold for exciting strong nonlinear effects. Therefore, in this work, when\nthe microhinge length connecting the two microbubbles in the ASM is less than 10 μm, the\nsecondary acoustic radiation force dominates the total force, and the microbubbles remain\nmutually attracted under external ultrasound excitation (see Figure 2(K)). However, when the\nmicrohinge length exceeds 10 μm, the secondary acoustic radiation force diminishes—\nconsistent with the aforementioned prediction—and the fluid-induced thrust becomes dominant.\nThis leads to a sign reversal of the net force, resulting in mutual repulsion between the\nmicrobubbles, as shown in Figure 2(K). Consequently, under these conditions, theoretical\nanalysis along with multiple experimental and numerical studies consistently characterize the\n3\nidentical microbubble pair with in-phase vibration and an attractive secondary acoustic\nradiation force at close range, with no sign reversal of the radiation force observed.\nFurthermore, as noted by the reviewer, microbubble lifetime and volumetric change are\nclosely linked to the sign of the secondary acoustic radiation force. Therefore, we characterized\nthe microbubble lifetime in deionized water, as shown in Figure S13(A). It was observed that\nin the absence of ultrasonic excitation, the microbubble maintained its volume without change\nfor 25 minutes. Under ultrasonic excitation at 25 V (exceeding the minimum actuation voltage\nfor complete deformation of the ASM), the operational duration of the microbubble decreased\nto 8 minutes. To enhance microbubble lifetime and thereby extend the working time of the\nASM, we evaluated the microbubble lifetime in PBS buffer, as presented in Figure S13(B).\nWithout ultrasonic excitation, the microbubble maintained a constant volume for 64 minutes,\nrepresenting a 156% increase compared to its lifetime in deionized water. Under 25 V ultrasonic\nexcitation, the working time reached 29 minutes, a 263% increase over that in deionized water.\nFigure S13. Temporal stability of microbubbles. (A) Lifetime of microbubbles in deionized\nwater with and without ultrasonic excitation. (b) Lifetime of microbubbles in PBS buffer with\nand without ultrasonic excitation.\nAdditionally, plasma treatment of the structure prior to experiments (e.g., using\ntetrafluoromethane gas) can increase the hydrophobicity of the structure, which also contributes\nto prolonging microbubble lifetime[R7]. Therefore, both environmental configuration and pre-\nexperimental treatments can effectively extend the microbubble operational time to half an hour\nor longer without volumetric change, thereby ensuring stable operation of the ASM.\nThus, through experimental configuration and pre-treatment procedures, sufficient\noperational time for the ASM can be secured, during which the microbubble volume remains\nconstant. In summary, throughout the stable operational period of the ASM, the maintained\nmicrobubble volume enables the consistent generation of a secondary acoustic radiation force\n4\nwithout sign reversal. Under our experimental conditions, this ensures that the ASMs maintain\nin-phase vibrations and ultimately undergo mutual attraction under ultrasonic excitation.\n[R1] A. Doinikov, S. Zavtrak, On the mutual interaction of two gas bubbles in a sound field.\nPhysics of Fluids 7 (8), 1923–1930 (1995).\n[R2] V. Pandey, Asymmetricity and sign reversal of secondary Bjerknes force from strong\nnonlinear coupling in cavitation bubble pairs. Physical Review E 99 (4), 042209 (2019).\n[R3] N. A. Pelekasis, A. Gaki, A. Doinikov, J. A. Tsamopoulos, Secondary Bjerknes forces\nbetween two bubbles and the phenomenon of acoustic streamers. Journal of Fluid\nMechanics 500, 313–347 (2004).\n[R4] M. Lanoy, C. Derec, A. Tourin, V. Leroy, Manipulating bubbles with secondary Bjerknes\nforces. Applied Physics Letters 107 (21) (2015).\n[R5] M. S. Longuet-Higgins, Viscous streaming from an oscillating spherical bubble.\nProceedings of the Royal Society of London. Series A: Mathematical, Physical and\nEngineering Sciences 454 (1970), 725–742 (1998).\n[R6] N. A. Pelekasis, J. A. Tsamopoulos, Bjerknes forces between two bubbles. Part 1.\nResponse to a step change in pressure. Journal of Fluid Mechanics 254, 467–499 (1993).\n[R7] Y. Xiao, J. Zhang, B. Fang, X. Zhao, N. Hao, Acoustics-actuated microrobots.\nMicromachines 13 (3), 481 (2022).\nTo elucidate the microbubble dynamics mechanism underlying the ASM deformation, and we\nhave thoroughly revised and expanded the theoretical section of the manuscript. The relevant\nparts have already been updated in the revision as follows:\nPage 6, Lines 158 to 160\n“Given that acoustic streaming is a second-order effect, its resulting thrust remains substantially\nsmaller than the secondary acoustic radiation force at low-to-moderate drive levels with the\nmicrobubble approaching.”\nPage 7, Lines 162\n“ ”\n𝐹𝐵 ≈ 𝐹𝑈 = 𝐵 ∗𝐺\n(Supporting information) Page S4, Lines 56 to 85\n5\n“The secondary forces that act on the ASM are thrust , drag force exerted on a microbubble\nby the flow generated by the neighboring microbubbles , and secondary acoustic radiation\n𝐹𝑆\nforce (also known as secondary acoustic radiation force or secondary Bjerknes force).\n𝐹𝑅\nConsequently, the secondary acoustic radiation force is proportional to the time-averaged\n𝐹𝑈\nproduct of the volume velocities of the two microbubbles under the standard monopole\napproximation.\nAcoustic streaming is a second-order mean flow generated within the viscous boundary layer,\nwhose velocity is proportional to the square of the vibration amplitude. The thrust must be\ntransmitted to the microbubble through viscous drag, which in turn governs its translational\nvelocity. Therefore, the induced thrust force will cause the microbubbles to repel each other.\nGiven that acoustic streaming is a second-order effect, its resulting thrust remains substantially\nsmaller than the secondary acoustic radiation force at low-to-moderate drive levels with the\nmicrobubble approaching. The thrust can be written as:\n𝐹𝑆~𝜇𝜔𝜑\nmicrobubbles is comparable to the microbubble size, which is significantly smaller than the\n𝜇 𝜑\nwavelength of sound waves, so we assumed that did not depend on the distance between the\nmicrobubbles. Therefore, we have . \n𝐹𝑅\nThe total force acting on the microbubbles can be expressed as follows:\n|𝐹𝑅| = |𝐹𝑆|\nIn our study, the driving frequency was set at the resonance frequency of identical microbubbles,\n𝐹𝐵 = 𝐹𝑈 +𝐹𝑆 +𝐹𝑅\nand the driving amplitude was maintained at a moderate level (0-60 V), which was well below\nthe threshold for exciting strong nonlinear effects. Therefore, in this work, when the microhinge\nlength connecting the two microbubbles in the ASM is small, the secondary acoustic radiation\nforce dominates the total force, and the microbubbles remain mutually attracted under external\nultrasound excitation. However, when the microhinge length becomes large enough, the\nsecondary acoustic radiation force diminishe and the fluid-induced thrust becomes dominant.\nThis leads to a sign reversal of the net force, resulting in mutual repulsion between the\nmicrobubbles.”\n(Supporting information) Page S7, Lines 133\n“ ”\n𝐹𝑈 = 𝐅𝟏 = 2𝜋𝜌𝐴𝐴∗𝒎𝐺\n(Supporting information) Page S8, Lines 141 to 143\n6\n“Consequently, the secondary acoustic radiation force grows markedly with reduced inter-\nmicrobubble distance. Under our experimental conditions, its amplification upon microbubble\napproach thereby establishes it as the dominant term.”\n1\n2\n𝐿\nPage 6, Lines 140 to 142\n“The Materials and Methods section provides a detailed characterization of the acoustic\npressure distribution generated by our setup, as well as the operational lifetime of the\nmicrobubbles in the ASM.”\nPage 16, Lines 431 to 443\n“We characterized the microbubble lifetime in deionized water and PBS buffer, as shown in\nFigure S13. It was observed that in the absence of ultrasonic excitation, the microbubble\nmaintained its volume without change for 25 minutes in deionized water. Under ultrasonic\nexcitation at 25 V (exceeding the minimum actuation voltage for complete deformation of the\nASM), the operational duration of the microbubble decreased to 8 minutes, as shown in Figure\nS13(A). Using PBS buffer as the liquid medium can increase the lifetime of the microbubble.\nWithout ultrasonic excitation, the microbubble maintained a constant volume for 64 minutes,\nrepresenting a 156% increase compared to its lifetime in deionized water. Under 25 V ultrasonic\nexcitation, the working time reached 29 minutes, a 263% increase over that in deionized water,\nas presented in Figure S13(B). Thus, through experimental configuration, sufficient operational\ntime for the ASM can be secured, during which the microbubble volume remains constant.\nUnder our experimental conditions, this ensures that the ASMs maintain in-phase vibrations\nand ultimately undergo mutual attraction under ultrasonic excitation.”\n(Supporting information) Page S23\nwater with and without ultrasonic excitation. (b) Lifetime of microbubbles in PBS buffer with\nand without ultrasonic excitation.\nComment 2: Related to the above, in cases where the bubble volume is sufficiently small,\ntransient shifts in its resonance frequency could undermine the reproducibility or fidelity of the\nintended deformation response. Further clarification is requested on the protocols employed\nfor precise generation of such small-volume bubbles, and on the temporal stability of their\nvolume during operation. In addition, previous investigations have shown that both the\noscillation amplitude of microbubbles and the magnitude of the resultant acoustic streaming\nand secondary radiation forces vary with the spatial offset from the piezoelectric transducer\n(PZT). It would be of interest to determine whether similar spatially dependent phenomena\nwere observed in the present experiments, and if so, how they were accounted for in the design\nand analysis.\nResponse: We sincerely thank the reviewer for these valuable suggestions. We recognized that\nmicrobubble lifetime and stability are critical to the deformation of the ASM. Therefore, we\nevaluated the stable operational duration of microbubbles in different solutions. As addressed\nin response to Comment 1, it was concluded that in PBS buffer, the microbubble maintains\nstable operation for 29 minutes. During this period, the microbubble responds to ultrasonic\nexcitation without exhibiting volumetric changes, as demonstrated in Figure S13.\nFigure S13. Temporal stability of microbubbles. (A) Lifetime of microbubbles in deionized\nwater with and without ultrasonic excitation. (b) Lifetime of microbubbles in PBS buffer with\nand without ultrasonic excitation.\nAdditionally, plasma treatment of the structure prior to experiments (e.g., using\ntetrafluoromethane gas) can increase the hydrophobicity of the structure, which also contributes\n8\nto prolonging microbubble lifetime. Therefore, both environmental configuration and pre-\nexperimental treatments can effectively extend the microbubble operational time to half an hour\nor longer without volumetric change, thereby ensuring stable operation of the ASM.\nAlthough microbubble lifetime is inherently limited by gas diffusion, our experimental\ntreatments provide sufficient operational duration for the ASM. In other words, the\nmicrobubbles remain stable and responsive well within the time window required for effective\nmanipulation and actuation.\nWe acknowledge that the number and spatial offset of piezoelectric transducers influence\nthe distribution of acoustic waves propagating into the liquid medium, thereby modulating the\noscillation amplitude of microbubbles as well as the magnitude of the resulting acoustic\nstreaming and secondary acoustic radiation forces. As indicated by Minas' study, the quantity\nand spatial offset of transducers determine the morphology and number of vortical structures\nwithin the acoustic streaming field[R1].\nHowever, in our experiments, this factor was meticulously controlled. The transducer and\nacoustic chamber were securely mounted on a glass slide, with their position and orientation\nrelative to the work area remaining unchanged throughout the experimental process. The design\nand calibration of the integrated acoustic chamber–transducer assembly were aimed at ensuring\na reproducible and Uniform acoustic field. Furthermore, the experimental setup remained\nunaltered between trials, thereby maintaining a spatially homogeneous acoustic field. The\nspecific positional relationship is illustrated in the Figure S14(A) (Supporting information).\nAcoustic field simulations under this configuration were also performed, as shown in the Figure\nS14(B) (Supporting information). It can be observed that when the printed structure is\npositioned at the center of the acoustic chamber—a condition readily achievable in two-photon\ndirect laser writing fabrication—it is subjected to a uniform acoustic field under 103 kHz\nultrasound excitation.\nThe components and location distribution of the acoustic excitation device, including top and\nside views. (B) Simulated acoustic pressure distribution in the acoustic chamber and working\narea at 103 kHz.\nTherefore, although spatial variations could generally occur, in our present setup, the PZT\nposition and acoustic chamber geometry are fixed and calibrated to ensure that all\nmeasurements are conducted under identical and repeatable acoustic field conditions.\nConsequently, the observed acoustic streaming and secondary forces can be attributed to the\ncontrolled excitation conditions, rather than to variations in transducer placement.\n[R1] S. O. Catarino, J. M. Miranda, G. Minas, Effect of -PVDF Piezoelectric Transducers’\npositioning on the acoustic streaming flows. Micromachines 5 (3), 654–666 (2014).\n𝛽\nThe relevant parts have already been updated in the revision as follows:\nPage 6, Lines 140 to 142\n“The Materials and Methods section provides a detailed characterization of the acoustic\npressure distribution generated by our setup, as well as the operational lifetime of the\nmicrobubbles in the ASM.”\n“The transducer and acoustic chamber were securely mounted on a glass slide, with their\nposition and orientation relative to the work area remaining unchanged throughout the\nexperimental process. The design and calibration of the integrated acoustic chamber–transducer\nassembly were aimed at ensuring a reproducible and Uniform acoustic field. Furthermore, the\nexperimental setup remained unaltered between trials, thereby maintaining a spatially\nhomogeneous acoustic field. The specific positional relationship is illustrated in the Figure\nS14(A) (Supporting information). Acoustic field simulations under this configuration were also\nperformed, as shown in the Figure S14(B) (Supporting information). It can be observed that\nwhen the printed structure is positioned at the center of the acoustic chamber—a condition\nreadily achievable in two-photon direct laser writing fabrication—it is subjected to a uniform\nacoustic field under 103 kHz ultrasound excitation.”\n(Supporting information) Page S24\nFigure S14. Arrangement of acoustic excitation devices and acoustic pressure distribution. (A)\nThe components and location distribution of the acoustic excitation device, including top and\nside views. (B) Simulated acoustic pressure distribution in the acoustic chamber and working\narea at 103 kHz.\nTo facilitate a more rigorous and objective evaluation of the work’s novelty, it would be\nadvantageous for the authors to provide a concise synopsis of their prior related studies and to\ndelineate explicitly the principal advancements and distinctive contributions of the present\ninvestigation relative to those earlier efforts.\nResponse: We sincerely thank the reviewer for this thoughtful and encouraging comment\nregarding the originality and conceptual innovation of our work. We fully agree that providing\na concise summary of our prior related studies and clearly highlighting the key advancements\nof the present research will help clarify its novelty and contributions.\nWe note that various deformation mechanisms and soft robotics are currently widely\nemployed in medical devices and mechanical propulsion systems[R1]; however, most\ndeformable machines are confined to centimeter or millimeter scales, rendering them\ninadequate for performing tasks within highly confined spaces. For instance, Robert J. Wood\nand his team developed an insect-scale flapping-wing micro aerial vehicle, whose body forces\nand torques are governed by the deformation of piezoelectric materials[R2]. Additionally, these\ndevices often require tethered connections to external sources significantly limiting their\nmicroscale applicability. Therefore, the execution of delicate operations within confined spaces\nnecessitates a microscale deformation system capable of rapid response and precise control.\nAccordingly, we conducted a survey and summary of miniature deformable devices. It has\nbeen found that at the microscale, multi-physical field stimuli—such as chemical gradients,\noptical fields, thermal fields, electric fields, magnetic fields, and acoustic fields—are widely\nused for the actuation and control of shape-morphing micromachines. However, these strategies\nstill exhibit their respective limitations. A detailed analysis of each is provided below:\n(1) pH-Responsive Hydrogel Actuators: Miniature deformable devices capable of\nresponding to chemical gradients, such as hydrogels that react to variations in solution\nacidity/alkalinity, can achieve substantial volumetric changes and complex structural\ntransformations[R3]. However, their actuation mechanism is inherently constrained by the\nreconfiguration of the polymer network (water absorption and desorption), which typically\nresults in slow response times and a strong dependence on the local chemical environment.\nConsequently, the application of pH-responsive hydrogel deformation systems is limited for\nscenarios requiring rapid, repeatable, and frequency-programmable deformations.\n(2) Optically-driven Deformation Systems: Optical driving methods offer exceptional\nspatial resolution and enable extremely rapid localized responses within the range of light\ntransmission[R4]. However, in scattering media or biological tissues, both optical penetration\n12\ndepth and resolution deteriorate significantly. Consequently, optically-actuated deformation\nsystems are well-suited for environments with ample illumination, but are less applicable in\nscenarios that require actuation through opaque or highly scattering materials.\n(3) Thermally-driven Deformation Systems: Deformation systems based on\ntemperature variations are capable of reliably generating substantial forces and displacements\nwithin a compact volume[R5]. However, the cooling and heating processes for localized regions\nare often time-consuming. Furthermore, heating may be unsuitable or require stringent control\nin biological or temperature-sensitive environments.\n(4) Electrically-driven Deformation Systems: Deformation systems based on light-\npowered CMOS circuits exhibit a considerable deformation range and high actuation speed[R6].\nHowever, their energy supply is constrained by the efficiency of energy harvesting.\nConsequently, remote, untethered, and in vivo applications remain challenging for such\nelectrically-driven deformation systems.\n(5) Magnetically-driven Deformation Systems: Magnetic fields can effectively\npenetrate biological tissues and opaque media, enabling untethered control of magnetically-\ndriven deformation systems[R7]. However, the magnetic torque responsible for deformation is\nproportional to the degree of magnetization embedded within the deformable structure.\nGenerating strong magnetic field gradients at small scales requires complex coil array\nconfigurations. Consequently, magnetic deformation systems necessitate a trade-off between\nexcellent penetration capability and biocompatibility on one hand, and the complexity of\nexternal hardware on the other.\nUltrasonic fields have unique characteristics such as high penetration, flexibility, low cost\nand biocompatibility, and can generate strong power[R8]. Acoustically excited microbubbles can\ngenerate stable interaction forces, enabling structural actuation at the microscale. We design an\nacoustic shape-morphing micromachines (ASMs) that can alter their shape within 10 ms under\nacoustic-field stimulation and rapidly return to their initial state on acoustic-field removal. On\nacoustic field exposure, microbubble oscillation induces deformation within milliseconds; the\nforces and torques required for this deformation are provided by secondary acoustic radiation\nforces between the microbubbles and the flow induced by their oscillations. This can be\ncontinuously tuned by varying the exciting acoustic-field voltage. Therefore, ASM possess\nrapid deformation speed, simple control setups, remote actuation capability through opaque\nmedia, and programmable features, demonstrating superior environmental adaptability\ncompared to other deformation systems.\ncontextualization of our research contributions.\n[R1] K. Y. Ma, P. Chirarattananon, S. B. Fuller, R. J. Wood, Controlled flight of a biologically\ninspired, insect-scale robot. Science 340 (6132), 603–607 (2013).\n[R2] K. Y. Ma, S. M. Felton, R. J. Wood, Design, fabrication, and modeling of the split actuator\nmicrorobotic bee, in 2012 IEEE/RSJ International Conference on Intelligent Robots and\nSystems (IEEE) (2012), pp. 1133–1140.\n[R3] Y. Hu, et al., Botanical-inspired 4D printing of hydrogel at the microscale. Advanced\nFunctional Materials 30 (4), 1907377 (2020).\n[R4] Y.-C. Cheng, H.-C. Lu, X. Lee, H. Zeng, A. Priimagi, Kirigami-based light-induced shape-\nmorphing and locomotion. Advanced Materials 32 (7), 1906233 (2020).\n[R5] D. Hwang, E. J. Barron III, A. T. Haque, M. D. Bartlett, Shape morphing mechanical\nmetamaterials through reversible plasticity. Science robotics 7 (63), eabg2171 (2022).\n[R6] Q. Liu, et al., Micrometer-sized electrically programmable shape-memory actuators for\nlow-power microrobotics. Science Robotics 6 (52), eabe6663 (2021).\n[R7] X. Hu, et al., Magnetic soft micromachines made of linked microactuator networks.\nScience advances 7 (23), eabe8436 (2021).\n[R8] Z. Zhang, Z. Shi, D. Ahmed"}]

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