Transformable 3D curved high-density liquid metal coils – an integrated unit for general soft actuation, sensing and communication | Nature Communications

Nature Communications volume 15, Article number: 7679 (2024) Cite this article

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Rigid solenoid coils have long been indispensable in modern intelligent devices. However, their sparse structure and challenging preparation of flexible coils for soft robots impose limitations. Here, a transformable 3D curved high-density liquid metal coil (HD-LMC) is introduced that surpasses the structural density level of enameled wire. The fabrication technique employed for high-density channels in elastomers is universally applicable. Such HD-LMCs demonstrated excellent performance in pressure, temperature, non-contact distance sensors, and near-field communication. Soft electromagnetic actuators thus achieved significantly improved the electromagnetic force and power density. Moreover, precise control of swinging tail motion enables a bionic pufferfish to swim. Finally, HD-LMC is further utilized to successfully implement a soft rotary robot with integrated sensing and actuation capabilities. This groundbreaking research provides a theoretical and experimental basis for expanding the applications of liquid metal-based multi-dimensional complex flexible electronics and is expected to be widely used in liquid metal-integrated robotic systems.

The past few decades have witnessed the remarkable potential of soft robots in diverse application scenarios, owing to their exceptional safety features and adaptability to environmental conditions1,2,3,4. Systems resembling living organisms, capable of environmental sensing, self-awareness, and controlled motion, have long been a sought-after goal5,6,7. In general, advanced soft robots require high precision, a large working range, multi-physics sensing capabilities8,9,10,11, high response speeds, large power densities, and strong driving force actuation capabilities12,13,14. Moreover, it is challenging to find a single unit that can integrate both sensing and actuation functions; typically, multiple units need to work in tandem for such capabilities. For instance, flexible pressure and temperature sensors usually lack motion capabilities15,16,17, while soft actuators like dielectric elastomers, pneumatic or hydraulic muscles do not typically incorporate sensing functions18,19,20,21,22,23. This inevitably leads to an excessively bulky robot. Fortunately, among the various types of sensors and actuators, soft actuators utilizing electromagnetic force-driven mechanisms hold greater potential for integration.

This soft actuator comprises a soft coil that generates a force in the presence of an external magnetic field, thus triggering the motion of the robot. Thanks to the recent advancements in liquid metal technology, this electromagnetic actuator can seamlessly transition from copper coils to liquid metal coils24,25,26,27,28. The high-power electromagnetic actuator exhibits not only exceptional flexibility but also possesses a splendid sensing capability. For instance, the application of pressure induces a change in its resistance, thereby facilitating the detection of external forces29,30. Compared to actuators such as dielectric elastomers, ionic electroactive actuators, hydraulic muscles, and liquid crystal elastomers, robots equipped with soft electromagnetic actuators typically exhibit a better combination of response speed, motion displacement, and force output capabilities12,14. Consequently, they can be effectively employed for the development of soft grippers, land-running robots, and water-swimming robots26,27,28. Furthermore, precise motion control can be accomplished by adjusting the input electrical signal, enabling programmed operation25. The lower operating voltage of the actuator facilitates seamless integration with smaller batteries26. However, unlike rigid coils wound with copper wire, the fabrication of liquid metal soft coils poses significant challenges. The similar formation of liquid metal wires is unattainable due to the material’s fluidity and high surface tension. Instead, it can be infused into soft silicone tubes featuring a helical structure to generate coils31. The liquid state of soft silicone materials such as polydimethylsiloxane (PDMS), Ecoflex, and human silicone prior to curing poses challenges in the formation of channels. Consequently, most current research on liquid metal coils focuses on single-layer two-dimensional planar coils. However, these coils not only face difficulties in achieving curved surfaces but also exhibit a significant width for the insulating layer between the channels, which significantly impacts the utilization of soft electromagnetic elastomers in soft robots.

In recent years, the development of soft robotics has necessitated the integration of multifunctional components capable of performing sensing, communication, and actuation. The 3D curved high-density liquid metal coil (HD-LMC) introduced in this study offers a solution to these requirements through its unique structural and material properties. Additionally, we present a universal method for creating intricate channels within flexible silicone to produce high-density, three-dimensional multilayer, curved liquid metal flexible coils without the risk of short-circuiting. The 3D curved HD-LMC, constructed using liquid metal (EGaIn) and an elastic PDMS substrate, ensures exceptional flexibility. The minimum insulation thickness of 0.1 mm can be achieved for three wire diameters (D = 0.68, 1.2, 1.7 mm), resulting in wire diameter to corresponding insulation ratios (defined as parameter k) of 7, 12, and 17 respectively. These densities are consistent with those of enameled wires (approximately 10) and surpass the densities previously reported for liquid metal coils (highest being 1.25) or wires (highest being 5.75). A range of environmental sensing capabilities with HD-LCM unit, i.e., encompassing pressure, temperature, distance sensing and signal interaction are implemented. Moreover, we have successfully showcased a puffer fish robot capable of swimming in water and a wheel-shaped robot that can traverse land. Interestingly, even robots composed solely of HD-LMC units can achieve sensing and motion capabilities, showcasing an impressive level of integration between sensing and actuation.

Figure 1a illustrates the design concept of an integrated unit of 3D curved HD-LMCs. This unit features a stacked structure consisting of three layers of curved HD-LMCs, all enveloped by PDMS for insulation and isolation to achieve a highly resilient performance. The coil channels are filled with liquid metal (EGaIn) for the conductive core. The design of coils with three distinct wire diameters (D = 0.68, 1.2, and 1.7 mm be tagged as HD-LMC0.68, LMC1.2, and LMC1.7, respectively) was accomplished within a confined volume (20 mm in length and a sector with a 60° radius of r = 11 mm in cross-section), as shown in Supplementary Fig. 1. All of these HD-LMCs have achieved the maximum density of triple stacking.

a. Structural design and composition of HD-LMC. The EGaIn is encapsulated with PDMS, resulting in an overall softness. The Ball represents the magnetic field generated by its energization. b. HD-LMC real cross-section. There are three configurations for wire diameter D = 0.68, 1.2, and 1.7 mm. c. SEM images of two neighboring liquid metal channels in three structures. The thickness of the insulation layer between the channels reaches 0.1 mm for all three wire diameters. d. Optical image showing the mechanical flexibility of the HD-LMC being stretched, compressed, twisted, and bent. e. Factors influencing the performance of coils. The findings indicate a positive correlation between Ball and both D and k. The significance of this change is more pronounced when k is small. When the insulation thickness δ = 0.1 mm, an increase in D leads to a corresponding increase in Ball. f. The present work demonstrates higher values of D and k compared to the reported research, surpassing even the structural density of enameled wires. Source data are provided as a Source Data file.

Additionally, the real cross sections of three HD-LMCs with different conductive path diameters are shown in Fig. 1b. The Scanning Electron Microscope (SEM) images and Energy Dispersive Spectrometer (EDS) based element mapping provide a clear visual representation of the PDMS elastomer and liquid metal channels, demonstrating its universality in fabricating HD-LMC with a consistent minimum insulation layer thickness of 0.1 mm, irrespective of the channel diameter (Fig. 1c and Supplementary Fig. 2). Additionally, Fig. 1d showcases the exceptional mechanical compliance of the transformable soft HD-LMC, which allows for stretching, compression, twisting, and bending without incurring any damage.

It is widely acknowledged that coils exhibiting superior performance should have a greater number of turns within a constant volume, and finer wire diameters are commonly employed to achieve this objective. However, contrary to conventional belief, as elucidated in Supplementary Note 1, employing a finer wire diameter for a given volume and heating power leads to increased resistance (Supplementary Eq. 5) and decreased excitation current (Supplementary Eq. 9). This clearly presents a highly disadvantageous impact on it.

The performance of the electromagnetic elastomer is significantly influenced by both the insulation thickness δ and the coil channel diameter D. Therefore, a structural evaluation parameter k = D/δ is defined to more effectively reflect the coil density. The magnetic field B excited by the solenoid coil increases with a larger value of k, as depicted in Fig. 1e and Supplementary Eq. 15. Additionally, when the thickness of the insulation layer δ (the intersection of the black arrow with the curve in the figure indicates the case of δ = 0.1 mm) or the value of k remains constant, there is a positive correlation effect between the diameter D and the magnetic field B. Therefore, when selecting a solenoid coil with a constant volume and a large k, it is advisable to opt for the largest possible diameter within the limits of the required inductance value (L) and maximum current (Isupply) that can be supplied (refer to Supplementary Note 1, Supplementary Fig. 3 and Supplementary Fig. 4 for more details).

The flexible coil compositions with large cross-sections of conductive pathways can be broadly classified into two types. One type involves the fabrication of flexible wires that are subsequently wound to form coils27,32. The k of the coils formed by this method is dependent on the wire insulation. Furthermore, elastic wires are generally incapable of achieving coil fabrication with significant curvature. This limitation can lead to the collapse of the runners, causing a sudden spike in resistance or even circuit breakage (Supplementary Fig. 5). The second approach involves the construction of the coil channel within the elastomer, followed by filling it with liquid metal to create the coil24,25,28. This methodology is also employed here. A comparison was made with previously reported work in Fig. 1f using k-D plots that incorporated coils24,25,26,28,33,34,35,36, flexible wires27,32,37,38,39,40,41,42,43,44,45, and enameled wires (refer to Supplementary Table 1 for further details). The HD-LMC in this study exhibits higher D and k values, surpassing even the structural density of enameled wires (refer to Supplementary Fig. 6).

The utilization of water-soluble materials, such as poly vinyl acetate (PVA), poly acrylic acid (PAA), poly acryla mide (PAM), and poly ethylene oxide (PEO)46, along with high-temperature sacrificial materials like paraffin wax and low-melting-point metals47, is deemed more appropriate for the fabrication of intricate internal cavities. The cavities required in this work, however, are more intricate. They encompass not only curved surfaces but also multilayer structures. Furthermore, the diameter of the channels is small and the spacing between them is a mere 0.1 mm. These factors pose challenges for various sacrificial materials to effectively fulfill their task. For instance, paraffin wax is prone to breakage. And utilizing PVA materials for 3D printing lacks the required precision, often leading to PVA flocculation issues (Supplementary Fig. 7). A solution to this problem can still be found in the low melting point metal Bi32In51Sn17, which has a melting point of approximately 60.5 °C and exhibits high toughness and stiffness in its solid state (Supplementary Fig. 8 and Supplementary Table 2).

The liquid alloy of Bi32In51Sn17 was poured into the silicone tube and subsequently peeled off after cooling and solidification to obtain the metal wires utilized for fabricating HD-LMC channels (Supplementary Fig. 9 and Supplementary Table 3). Subsequently, the metal wire was enveloped with a PDMS film obtained through spin-coating and curing, and pressed into a coil using a mold. Next, it was placed in a 3D printing mold to introduce PDMS before undergoing curing. Finally, by rinsing off the Bi32In51Sn17 alloy in a water bath and infusing it with EGaIn, the HD-LMC could be successfully produced (Supplementary Fig. 10). The Supplementary Fig. 11 presents photographs of the physical HD-LMC featuring three distinct runner diameters, both with and without liquid metal infusion. Therefore, this approach enables precise control of the channel diameter through manipulating the BiInSn wire diameter and accurate regulation of the insulating layer thickness via modulation of the PDMS film thickness.

The SEM images of the channel diameter and insulating layer were captured at multiple locations for various samples of the three coils, respectively. It can be inferred that employing the methodology outlined in this study results in a high level of structural uniformity for 3D curved HD-LMC (Supplementary Fig. 12). Additionally, based on the non-uniformity data obtained from SEM analysis, HD-LMC0.68 was employed to generate 100 random structures for 1× non-uniformity and 5× non-uniformity, respectively. By calculating the magnetic field excited at a current of 2 A, it has been determined that there is a maximum error of 0.82% in the 1× non-uniformity and 3.35% in the 5× non-uniformity (Supplementary Fig. 13). Finally, Supplementary Fig. 14 showcases the exceptional reproducibility of the BiInSn coil structures, which is pivotal for ensuring consistent formation of the channel structure in the HD-LMC.

The proposed method in this study has demonstrated its universal applicability for fabricating 3D curved HD-LMCs. It enables the creation of coil structures with any desired number of turns on various surfaces. As shown in Supplementary Fig. 15, two complex supercoils have been successfully fabricated to illustrate this point. Firstly, a multi-layer tapered coil has been successfully fabricated on the surface of a cone using PDMS, while maintaining its central hollow structure. Secondly, it has demonstrated the fabrication of a multi-layer planar coil consisting of approximately 30 turns per layer and achieving a minimum wire spacing of 0.1 mm.

To further demonstrate the universality of our method, we also fabricated HD-LMCs using epoxy resin (hard), human silicone (soft), and Ecoflex 00-30 (soft) as the matrix materials (Supplementary Fig. 16). The process involved the same steps of creating intricate channels and filling them with liquid metal (EGaIn). This confirms that our fabrication technique is versatile and applicable to a wide range of elastomers.

The performance of the transformable HD-LMC as a fundamental integrated unit for flexible actuation and sensors is directly linked to its mechanical, electrical, magnetic, and thermal characteristics. The mechanical properties reflect the softness of the HD-LMC and its susceptibility to mechanical damage. The electrical properties dictate its impact on the circuit when connected. Magnetic characteristics reveal the strengths and limitations of the HD-LMC on performance. Furthermore, thermal characteristics determine the potential for overpowering during operation and the overall stability of the HD-LMC during use.

The conceptual diagram of the HD-LMC undergoing compression testing is illustrated in Fig. 2a. Due to the small modulus and soft behavior (HD-LMC0.68), the compression rate has minimal impact on the test results (Supplementary Fig. 17a). Their successive multiple compressions at a compression rate of 5 mm/min demonstrated favorable agreement (Supplementary Fig. 17b). Moreover, HD-LMC1.7 with a larger wire diameter displays a higher modulus for pressures up to 63 kPa, with a reversal in behavior for pressures exceeding 63 kPa (Supplementary Fig. 17d). The simulation analysis reveals that the stresses are primarily concentrated in the central region during compression (Fig. 2b and Supplementary Fig. 17e). The mesh-independence verification (Supplementary Table 4) and its consistency with the experimental findings (Fig. 2c) ensure the reliability for these results. Furthermore, the HD-LMC can endure an ultimate pressure exceeding 357 kPa and an ultimate compression of 2.4 mm, underscoring its exceptional mechanical reliability. Simultaneously, the performance of the HD-LMC was unaffected when dropped from a height equivalent to 233.28 times its body height, as evidenced by the undamaged internal coil and normal conductivity observed in the test (Fig. 2d).

a. Conceptual diagram of the HD-LMC compression process. b. Stress distribution of HD-LMC at a compression of 2 mm. c. The pressure-compression curve of the HD-LMC0.68 demonstrates excellent agreement between experimental results and theoretical calculations. d. The HD-LMC undamaged after dropping from a height equivalent to 233.28 times its own height. e. Potential distribution of HD-LMC0.68 with 1 A current applied. f. Impedance characteristics, including impedance and impedance angle, exhibited by the three HD-LMCs at different frequencies. g. The inductance values of the three HD-LMCs exhibit good agreement between theoretical and experimental results. h. Resistance values of HD-LMC, theoretical and experimental (measured by the four-wire method) are in good agreement. i. Magnetic field distribution at the center cross-section of HD-LMC0.68 at 2 A. j. The magnetic field strengths excited at the centers of the three HD-LMCs, with a current of 2 A, exhibit exponential decay with distance. k. Transmission of energy by electromagnetic radio. l. A LED board with a driving voltage of 3 V is successfully lit. m. Thermograms of the three HD-LMCs with current incrementing every 5 minutes. n. Temperature evolution curves for the three HD-LMCs upon energizing the current, with gradual current increments every 5 minutes. o. The HD-LMC0.68 was tested for the cyclic stability of its Joule heating performance by alternately switching the current between 0 and 1.5 A. All error bars are the standard deviation of three independent samples. Source data are provided as a Source Data file.

The potential distribution of the HD-LMC0.68 is depicted in Fig. 2e after a current of 1 A has passed through it, which can also be interpreted as the variation of resistance with length (refer to Supplementary Fig. 18 for other HD-LMCs). Figure 2f illustrates that the impedance characteristics of the three distinct HD-LMCs at varying frequencies show low-frequency impedance dominance and high-frequency inductive impedance dominance. The inductance at different frequencies can be determined by fitting the impedance characteristics with a series equivalent model, which demonstrates consistent values for frequencies exceeding 1000 Hz (Supplementary note 2 and Supplementary Fig. 18). Furthermore, the HD-LMC0.68 showcases an inductance value of 1.37 μH, highlighting its elevated coil turn density (Fig. 2g). The measured inductance is consistent with the theoretical calculations, which have also been validated for grid-independence (Supplementary Table 5). The obtained results further elucidate the more pronounced augmentation in impedance and phase angle observed in HD-LMCs with higher inductance at elevated frequencies. While the other two HD-LMCs exhibit lower inductance, they can handle higher currents due to their thicker wire diameters with reduced resistance. The resistance of HD-LMC0.68 is significantly high, reaching 391 mΩ, as depicted in Fig. 2h. In contrast, the resistance of HD-LMC1.7 is merely 22 mΩ.

The magnetic field distribution in Fig. 2i exhibits the highest magnetic field strength at the center of the HD-LMC, while experiencing significant attenuation as distance increases due to the low permeability of air and PDMS (Fig. 2j). Moreover, as depicted in Fig. 2j, the HD-LMC0.68 with more turns generates a stronger magnetic field at the same current (2 A). The current input needs to be increased in order to achieve the same magnitude of magnetic field for HD-LMCs with thicker wire diameters (Supplementary Fig. 19). The theoretical results also passed the network irrelevance analysis (Supplementary Table 6).

As demonstrated in Supplementary Note 1 and Supplementary Fig. 4, for coils with the same channel diameter, the k value results in a greater number of turns (n) within a limited volume, thereby enhancing the magnetic field generated under the same current. This finding is further validated by the model using the 3D curved HD-LMC0.68, which also demonstrates that a higher k value leads to increased inductance due to the higher number of turns (Supplementary Fig. 20). Additionally, under the same conditions, it is also imperative to consider the performance of coil structures ranging from 1-layer to 4-layer. The findings, as illustrated in Supplementary Fig. 21, demonstrate that augmenting the number of layers significantly amplifies the magnetic field generated by the coils and yields higher values of inductance. This enhancement is particularly useful when a single-layer structure has reached its maximum potential, yet further performance improvements are needed.

Additionally, a demonstration of wireless energy transfer utilizing an HD-LMC is employed to explore another magnetic characteristic of the integrated unit. The complete energy transfer device is illustrated in Fig. 2k. More specific circuit components and the wire connections between them are depicted in Supplementary Fig. 22. After the HD-LMC is energized with sinusoidal AC power, the LED board can be easily illuminated through wireless energy transfer (Fig. 2l and Supplementary Movie 1). The maximum induced voltage amplitude in the secondary coil reaches 10.6 V when the HD-LMC’s current is approximately 1 A, with the voltage amplitude at its terminals also approaching 1 V (Supplementary Fig. 23a-c). The mutual inductance coefficient of the HD-LMC0.68 can be determined by measuring the voltages across the primary and secondary coils, which exhibit a nearly linear decay as the distance between the two coils increases. This trend is also reflected in the amplitude of induced voltage (Supplementary Note 3 and Supplementary Fig. 23d-f). Furthermore, the HD-LMC0.68 shows a peak mutual inductance of 17.95 μH, outperforming the HD-LMC1.2 and HD-LMC1.7, which have maximum mutual inductances of 9.78 μH and 6.01 μH, respectively.

Joule heating behavior plays a crucial role in determining the maximum operating power of the HD-LMC. To prevent damage to the coil, the operational temperature should generally be kept below 150 °C (with PDMS being capable of withstanding high temperatures up to 200 °C). The HD-LMC0.68, depicted in Fig. 2m, achieves a temperature of 142.2 °C when subjected to a current of 2 A, whereas the other two variants (1.2 and 1.7 mm HD-LMCs) exhibit higher tolerance for current inputs (4 and 8 A respectively). The temperature evolution of the HD-LMC over time is depicted in Fig. 2n, with the current incrementing every 5 minutes. Supplementary Movie 2 showcases the infrared thermography of three HD-LMCs during both the warming and cooling processes. The HD-LMC0.68 underwent repeated cycles of warming (105 ± 1 s) and cooling (160 ± 1 s) by applying a current of 1.5 A, fluctuating between 40-60 °C.

The versatile properties of the HD-LMC make it an ideal candidate for various sensing applications. The capabilities of pressure sensing, temperature sensing, non-contact distance sensing, and near-field communication (NFC) are investigated. The flexibility of the HD-LMC enables it to enhance versatility compared to conventional rigid copper wire coils. Unless otherwise specified, the applications discussed in this section and beyond will primarily focus on HD-LMC0.68 with higher inductance and lower operating currents.

The spatial position of the channel inside the HD-LMC undergoes changes during the pressure application process, which can be accurately reflected in the alteration of the inductance signal. Figure 3a demonstrates its potential application in designing pressure sensors, a task that cannot be achieved with other single-layer flexible coils. The corresponding signal feedback can be obtained as long as the pressure applied to the HD-LMC does not result in physical damage. As shown in Supplementary Table 7, the proposed sensor exhibits a wider sensing range and superior signal linearity response compared to other previously reported pressure sensors17,29,30,39,48,49,50,51,52,53,54,55,56. The linear signal change over a wide pressure range (35.71-357.14 kPa, equivalent to 5-50 N) is depicted in Fig. 3b (refer to Supplementary Note 4 for detailed information on the rate of change and signal error). Additionally, linearly varying signals can be generated within the medium range of 7.14-71.43 kPa (1-10 N) and the ultra-small range of 0.714-7.14 kPa (0.1-1 N). A resolution as small as 0.357 kPa (0.05 N) is attainable. Moreover, the inductance values align with the theoretical calculations (Supplementary Fig. 24a-d).

a. Conceptual design of pressure sensors. b. The value of the inductance change of the HD-LMC is linear over a wide range of applied pressure (35.71-357.14 kPa, corresponding to 5-50 N). c. 100 cycle tests were conducted at higher pressures (214.29 kPa, corresponding to 30 N) and stable inductive signal changes were observed. d. The inductive signal changes during a pressure cycle, with the signal increasing and decreasing relatively quickly. e. Conceptual design of temperature sensors. f. The inductance signal of HD-LMC from room temperature 27 °C to 100 °C also has a strong linear relationship. g. The inductance signal of HD-LMC exhibits a stable step-like shape with relatively consistent changes when the temperature is raised by 5 °C every 30 minutes. h. HD-LMC exhibited good cycling stability when heated and cooled in a water bath for 3 min between room temperature 27 °C and 80 °C. i. HD-LMC is used for non-contact sensing of distance to metal surfaces. j. HD-LMC is used to sense the distance of metal plates with high magnetic permeability. k. HD-LMC is employed to sense the distance of lower permeability metal plates. l. Conceptual diagram of the principle of non-contact eddy current detection. m. HD-LMC is used for Near Field Communication (NFC) for information exchange. n. Return loss S11 for different quality factors Q. o. Impedance characteristics exhibited by NFC with different Q. p. Utilize the HD-LMC integrated unit for a variety of functions such as receiving text messages, sending text messages, creating new contacts, making phone calls, opening emails, obtaining location information, accessing WiFi, and browsing websites. All error bars are the standard deviation of three independent samples. Source data are provided as a Source Data file.

The inductive signal changes remained stable during the testing of the HD-LMC for 100 cycles at pressures of 214.29 kPa and 71.43 kPa at a rate of 20 mm/min (Fig. 3c and Supplementary Fig. 24a-d). The signal rise and fall in Fig. 3d and Supplementary Fig. 24e is observed to be rapid, but constrained by the compression rate. Specifically, compressing the HD-LMC at pressures of 214.29 and 71.43 kPa resulted in displacements of 1.8 and 1.05 mm respectively, corresponding to compression times of 5.4 and 3.15 s respectively. Consequently, the hysteresis during compression was found to be 0.35 and 0.6 s, while during relaxation it was 0.75 and 0.9 s for the respective pressure levels.

The PDMS thermal expansion effect renders the inductance of the flexible HD-LMC highly responsive to ambient temperature, thereby enabling its application as a temperature sensor, as depicted in Fig. 3e. Similarly, as demonstrated in Supplementary Table 8, a comparative analysis with other previously reported temperature sensors reveals that the proposed sensor in this study exhibits an expanded sensing range and superior signal linearity response16,49,57,58,59,60,61,62,63,64,65,66. The inductive signal exhibits a good linear variation across a wide temperature range interval of 27-100 °C (Fig. 3f). The ambient temperature is increased by 5 °C per 30 minutes to monitor the inductance signal, resulting in a distinct and consistent step signal change (Fig. 3g). The HD-LMC exhibits excellent stability, as demonstrated in Fig. 3h through repeated temperature cycling tests. Furthermore, it possesses a high sensitivity to ambient temperature changes, capable of detecting variations as small as 0.2 °C (Supplementary Fig. 25).

The HD-LMC integrated unit effortlessly achieves non-contact distance sensing, a type of flexible sensor that is relatively rare, as illustrated in Fig. 3i. A variety of metal sheets were utilized for the experiments, and non-contact distance sensing was successfully achieved in all cases. As depicted in Fig. 3j, there exists a positive correlation between the magnetic permeability of the metal and the signal change. For instance, 1J85 alloy can increase the inductance value of HD-LMC by 17.71%, while iron can increase it by 2.05%. However, compared to these two metals, nickel and cobalt possess much smaller magnetic permeability, resulting in a reversed change in HD-LMC inductance. Notably, other metals with magnetic permeability similar to that of air, such as 304 stainless steel, aluminum, and molybdenum, exhibit a reduction in the inductance value of the HD-LMC (Fig. 3k). However, it is worth noting that different metals can display significant variations in signal changes, thereby enabling the detection of substance conductivity. The sensing ability, as illustrated in Fig. 3l, is attributed to the eddy current effect between the HD-LMC and the metal plate, which is directly influenced by the mutual inductance coefficient M (including the impact of metal magnetic permeability) and the electrical conductivity of the metal plate (refer to Supplementary note 5 for detailed information).

The HD-LMC not only facilitates physical interaction with the environment but also enables the exchange of information. The HD-LMC, shown in Fig. 3m, functions as the central component akin to a brain, enabling non-contact transmission of commands to electromechanical devices and facilitating interaction with the external world. In order to achieve NFC, HD-LMC necessitates impedance matching, as detailed in Supplementary Note 6. The self-resonant frequency of the HD-LMC is located at 52.54 MHz. At the operational frequency f0 = 13.56 MHz, the impedance measures Z = 13.127 + 99.379j Ω, and an inductance value of 1.1664 μH is obtained (Supplementary Fig. 26). As illustrated in Fig. 3n, the matched NFC can achieve a minimum return loss S11 exceeding -50 dB with a broad bandwidth. The impedance at the operating frequency f0 should ideally have a real part of approximately 50 Ω and an imaginary part close to 0 Ω (Fig. 3o). As shown in Fig. 3p, the HD-LMC is capable of a wide array of functions, such as receiving text messages, sending text messages, creating new contacts, making phone calls, opening emails, obtaining location information, accessing WiFi, and browsing websites (Supplementary Movie 3).

Expanding upon the foundational understanding of the properties and sensing capabilities of HD-LMC, this study further investigates its potential application in soft actuation. The HD-LMC’s capacity to generate electromagnetic force renders it well-suited for the development of soft actuators. Additionally, The HD-LMC electromagnetic actuator features a fast response time and operates at a low drive voltage. It is highly programmable and offers precise control through current regulation. Unlike other soft actuators, this actuator is simpler and has fewer components.

Therefore, we presented a soft bionic pufferfish, fabricated using the HD-LMC electromagnetic actuator as depicted in Fig. 4a. The designed bionic pufferfish effectively achieves tail swing movement through the utilization of a simple lever principle, enabling it to attain the maximum swing angle of 22.8° (Fig. 4b).

a. Structural design of the flexible bionic pufferfish. b. The internal motion frame can be swung at an angle of 22.8°. c. Conceptual diagram of HD-LMC as an electromagnetic actuator. d. Electromagnetic force of the actuator under different currents. The maximum can be 58.67 mN, and the experimental and theoretical results are in high agreement. e. Under a square wave signal, the bionic pufferfish can execute a tail-swinging motion. f. Square wave drive current at three different frequencies. g. Kinematic behavior of bionic pufferfish in water at three current frequencies. h. Kinematic displacement of bionic pufferfish in water. All error bars are the standard deviation of three independent samples. Source data are provided as a Source Data file.

The motion of the pufferfish is powered by the Lorentz force on the HD-LMC, which is energized by an electric current and influenced by a magnetic field (Fig. 4c). The impact of excitation current and distance on the HD-LMC electromagnetic actuator is illustrated in Fig. 4d. Both the experimental and the theoretical evidences that it can generate the maximum force of approximately 60 mN when operating at a current of 2 A. Indeed, if the HD-LMC had a larger surface area and volume, it would be capable of producing an even greater force. Since the HD-LMC possesses a near-limit k value and a substantial D, the maximum force generated per unit volume reaches 5.0455 × 104 N/m3, and the power density reaches 8279.6 W/m3 (Supplementary Note 7 and Supplementary Table 9). Moreover, the HD-LMC utilized in this study features a fan-shaped cross-section with a considerable amount of ineffective volume near the center of the circle. Consequently, the actual power density exceeds that calculated.

The bionic pufferfish demonstrates continuous tail swinging motion in response to a square wave current signal, as shown in Fig. 4e. Precise control over the tail swinging motion is achieved under an excitation current ranging from 0 to 5 Hz, with the frequency of the motion matching that of the driving current (Supplementary Movie 4). The square wave signal with a frequency range of 0-3 Hz is shown in Fig. 4f. Within this range, the pufferfish can achieve swimming motion in water; however, at frequencies of 4 and 5 Hz, only tail swinging motion can be realized in air. Beyond the frequency of 5 Hz, a perfect swinging motion cannot be achieved. Figure 4g illustrates that higher frequency drive currents enable faster swimming speeds (Supplementary Movies 5-7). We have employed the background difference technique for detecting moving objects, and accurately obtained the displacement time image of the bionic pufferfish in each frame, as depicted in Fig. 4h. The motion velocity was determined using the second-order difference format, as illustrated in Supplementary Fig. 27. For further details regarding the background difference method, please refer to Supplementary note 8.

The collaborative function of multiple HD-LMC units facilitates the execution of complex programmable motion with real-time feedback. This section employs a high-speed rotating robot as an illustrative example to demonstrate the integration of sensing and actuation functions within a single entity. The HD-LMC soft high-speed rotary robot shown in Fig. 5a can be controlled by employing programmed current along with position sensing and velocity feedback. The perfect wheel shape is formed by utilizing six HD-LMC units, with two coils in each diagonal forming a connected group through wires. This configuration allows for high-speed rotation under the excitation of three-phase alternating current (Supplementary Fig. 28). The mechanism is illustrated in Fig. 5b, where the energization of Coil group A with current results in the generation of torque that drives the robot to rotate until alignment between the excited magnetic field lines and the background magnetic field is achieved.

a. Schematic of the structure of the HD-LMC integrated high-speed rotary robot. b. HD-LMC actuation principle for high-speed rotating robots. c. The ideal current waveform of a high-speed rotating robot with a 120° phase difference between the three. d. Characterization of the magnetic field distribution of the HD-LMC high-speed rotating robot. e. The HD-LMC high-speed rotary robot performs in-situ high-speed rotation. f. The rotational speed and driving frequency show consistency during in-situ rotation, and the experiments and simulations are in good agreement. g. Theoretically calculated rotating moments at different drive currents. h-k. Kinematic pictures for excitation currents of 2, 3, 4 and 5 Hz, respectively, and their corresponding displacement-time relationships. l. HD-LMC high-speed rotary robot realizes RPM feedback. m. HD-LMC high-speed rotary robot realizes its own position sensing. All error bars are the standard deviation of three independent samples. Source data are provided as a Source Data file.

The HD-LMC designed in this study features a sector angle of 60°, which corresponds to three groups of coils. Therefore, a three-phase drive is employed, and the operating current waveform is depicted in Fig. 5c. It exhibits a sinusoidal waveform with a phase difference of 120° between each pair. The sinusoidal excitation currents captured experimentally, ranging from 0.5 to 5 Hz, are presented in Supplementary Fig. 29.

The spatial distribution of the robot’s magnetic field under the excitation current (2 A) is illustrated in Fig. 5d, wherein the black lines depict its excited flux lines while the red lines represent the flux lines of the background magnetic field. In order to mitigate the issue of wire entanglement during high-speed rotation, high-speed electric slip rings are integrated at the centers of the robotic circles (refer to Supplementary Fig. 30 for detailed information on rotational resistance moments). Figure 5e displays an optical photograph of the HD-LMC high-speed rotary robot rotating in suspension in situ, while Supplementary Movie 8 captures its kinematic behavior at current drive frequencies ranging from 0.5 to 5 Hz.

We developed a kinematic theoretical computational model (Supplementary Note 9) to investigate the underlying mechanism of its in situ rotation behavior, which have also been validated for grid-independence (Supplementary Table 10). The rotational speed of the robot is determined by the frequency of the excitation current, as demonstrated by both the experimental and the theoretical evidence. These two values are found to be essentially equal, which greatly facilitates precise control programming (Fig. 5f). Additionally, as shown in Fig. 5g, the maximum rotational torque of the HD-LMC high-speed rotary robot was theoretically calculated to be 1.3 mN·m under varying current intensities. Moreover, we observed that when the resistive moment is smaller than the maximum dynamic moment (Mr < Md), the robot can achieve smooth and stable rotation. The transient moments exhibit high-frequency sinusoidal waves determined by the resistive moments. When Md < Mr < 2Md, the robot oscillates during rotation, yet a consistent upward trend in the angle of rotation is still observable. The transient moment, influenced by the maximum kinetic moment, displays a lower frequency compared to the drive current. In cases where Mr > 2Md, the robot exhibits violent shock motions, slow increases in the angle of rotation, and can be characterized as oscillating in place. The amplitude of the transient moment is dictated by the maximum dynamic moment, while its frequency corresponds to that of the drive current (Supplementary movie 9 and Supplementary Fig. 31).

The HD-LMC high-speed rotating robot can easily navigate on the road, with its speed primarily determined by the excitation current frequency and the circumference diameter. Figure 5h-k displayed optical photographs of the robot on a magnet track, running a distance of 300 mm in 0.9 s at 5 Hz, achieving a speed exceeding 14 body lengths per second. Supplementary movie 10 illustrates the kinematic behaviors of the HD-LMC high-speed rotating robot at excitation currents ranging from 0.5 to 5 Hz. Target capture recognition was conducted on each frame to extract displacement and velocity information, as elaborated in Supplementary Fig. 32.

Importantly, the HD-LMC high-speed rotary robot facilitates position sensing and velocity feedback. The eddy current effect of HD-LMC with the conductive substance is observed to cause a change in its inductance, as shown in Fig. 3i-l. Furthermore, the non-contact sensing capability allows for the measurement of the distance between them. Supplementary Fig. 33 illustrates the variation in inductance signal generated by a group of HD-LMC coils at different rotational speeds. The rotary robot can accurately achieve rotational speed detection feedback by detecting the period of the inductive signal, as illustrated in Fig. 5l. Furthermore, the variation in the waveform of the inductive signal in each period is not random; it correlates with the positional information of the rotating robot. By utilizing this feature, the HD-LMC high-speed rotary robot can effortlessly achieve self-position sensing, as illustrated in Fig. 5m depicting a signal cycle corresponding to one full rotation.

The high-speed rotary robot offers versatile applications across various fields. In inspection and maintenance, the robot can navigate confined or hazardous environments like pipelines, ventilation ducts, and industrial machinery with precise speed and position. When combined with sensors and cameras, it enables real-time data collection and remote assessment, thereby reducing the necessity for human intervention and enhancing safety as well as operational efficiency.

In agriculture, the robot has the potential to automate crop monitoring, pest control, and precision spraying. It can quickly traverse large fields and gather detailed data on crop health, soil conditions, and pest infestations, optimizing irrigation, fertilization, and pesticide application, thus improving yields and resource efficiency. Its flexibility enables it to adapt to various terrains and crop types.

In the entertainment and education sectors, the robot can be used in interactive exhibits, theme parks, and educational demonstrations. Its programmable nature allows for intricate movements, making it ideal for robotics competitions, workshops, and education programs. By engagingly showcasing advanced robotics, it serves as a source of inspiration and knowledge for aspiring engineers and scientists.

In summary, the robot’s integration of sensing and actuation functions, coupled with its exceptional speed performance and precise control, establishes it as a pioneering tool capable of enhancing efficiency, safety, and innovation across multiple fields.

The utilization of soft liquid metal coils for integrated sensors and actuators is crucial in the development of soft robots, yet their implementation is hindered by the formidable challenge of designing high-density and intricate coil channels within elastomers. The present study demonstrates the successful design and fabrication of a HD-LMC that surpasses the structural density of enameled wires, thereby overcoming the limitations associated with planar single-layer structures and enabling the realization of curved multilayer three-dimensional structures. The structure comprises a helical conductive circuit, with a liquid metal (EGaIn) core, and an elastic shell made of PDMS material. Our approach to constructing HD-LMCs is universally applicable, resulting in coils with a consistent minimum insulation thickness of 0.1 mm for all three wire diameters (D = 0.68, 1.2, 1.7 mm). Those HD-LMCs are fundamental and versatile electromagnetic integrated components that possess excellent mechanical properties (able to withstand pressures up to 357 kPa and compression of 28.6%), exceptional electrical characteristics (including inductance values of 1.37, 0.41, and 0.14 μH, as well as resistances of 391, 75, and 22 mΩ respectively), impressive magnetic attributes (with an excited magnetic field strength of 2 mT), and the ability to withstand Joule heating at high currents (2, 4, and 8 A currents respectively).

As an integrated unit, the HD-LMC enables a diverse array of sensing and actuation functions. The initial design was focused on developing a pressure sensor capable of achieving a linear response of inductance across a wide range (0.714-357.14 kPa) with ultra-high resolution (0.357 kPa). As a temperature sensor, it can achieve a linear response of inductance within the range of 27-100 °C with an ultra-high resolution of 0.2 °C. The device is capable of non-contact distance sensing based on the eddy current effect and can accurately identify various conductive metal materials. Additionally, it can be utilized for NFC technology to enable non-contact information interaction and facilitate a wide range of communication functionalities. Furthermore, as a soft actuator, it can produce the maximum force of nearly 60 mN with a high-power density of 8279.6 W/m3. The bionic flexible pufferfish constructed using it can accurately control the swinging tail movement and swim through the water. Finally, we also present a programmable controlled HD-LMC high-speed rotary robot capable of traversing a distance of 300 mm in just 0.9 seconds while providing feedback for self-position recognition and rotational speed determination.

In summary, the HD-LMC demonstrates a remarkable ability to integrate multiple functionalities, including sensing, communication, and actuation, within a single unit. This versatility is also exemplified through various applications, from environmental sensing to complex robotic motion, highlighting the transformative potential of HD-LMCs in soft robotics. Moreover, its groundbreaking structural advancements are poised to revolutionize the realm of soft robotics.

PDMS (Dow Corning Sylgard 184 Silicone Elastomer was mixed at a 10:1 weight ratio) was first spin-coated onto the wafers in a homogenizer (EZ4-S, LEBO Science, China), and heated and cured to a 50 μm film. The Bi32In51Sn17 alloy (Bi: 32 wt%, In: 51 wt%, Sn: 17 wt%) was poured into the silicone tubes and subsequently cooled to form the metal wires. The metal wire wrapped with PDMS film is then pressed through a mold to form a coil, which is then placed into a 3D printing mold (printed by Shape 1 HD, RAYSHAPE, China) and added with PDMS to cure. HD-LMC was obtained by washing out the Bi32In51Sn17 alloy in a water bath and infusing it with EGaIn (Ga: 75.5 wt%, In: 24.5 wt%) (Supplementary Fig. 10). The performance of the soft coil system benefits from the liquid metal’s lower melting point (15.5 °C) and higher conductivity (3.4×106 S/m)67.

The HD-LMC cross-sectional morphology and corresponding elemental mapping images were measured using field emission environmental scanning electron microscopes (FESEM, QUANTA FEG 250, America) and their energy spectra (EDS), respectively.

Mechanical compression tests of HD-LMC, including pressure compression curves, multiple compression rate tests, and cyclic compression tests were performed on a universal stretching compressor (Shimadzu AGS-X Tester, SHIMADZU, Japan).

All inductance tests are measured at 1 V, 100 kHz with a precision inductance, capacitance, and resistance (LCR) meter (TH2832, Tonghui, China) unless otherwise noted. The inductance values were then obtained by fitting a series equivalent model. The resistance values were obtained using the four-wire method on a data acquisition system (Agilent 34420 A, Keysight, America). Current and voltage signals were acquired by a mixed signal oscilloscope (MSO2014, Tektronix, America).

The magnetic flux density of the HD-LMC after energization was measured by a digital Tesla meter (KT-102, KeOuTe, China). The excitation current was regulated by an adjustable direct current-regulated power supply (eTM-12020C, eTOMMENS, China). To accurately quantify the impact of distance, 3D-printed brackets with varying heights were utilized to position both the magnetometer and HD-LMC. Moreover, a 100 kHz sinusoidal AC signal is employed to excite the HD-LMC. Through mutual inductance, the secondary coil connects to the rectifier filter circuit, resulting in the illumination of the customized LED board. The sinusoidal AC signal is generated by an arbitrary signal generator (DG1022, Rigol Technologies, China) and then passed through a power amplifier (KD 5702, Ti Kedong Electronic, China) to regulate the voltage.

The Joule thermal behavior was obtained by video recording using a thermal imager (testo 890, Testo Inc., Germany). In the airless confined space, the HD-LMC is subjected to four levels of heating, starting from low to high current. Each level of energized current lasts for five minutes, followed by natural cooling after the heating process is completed. The circulating Joule heat behavior was controlled by using 1.5 A heating and natural cooling to circulate it between 40 °C and 60 °C. The excitation current is regulated by an adjustable direct current-regulated power supply (eTM-12020C, eTOMMENS, China).

The pressure exerted on the HD-LMC is measured and recorded along with its corresponding inductance value for sensor calibration. Larger forces were realized on a platform with a 0-500 N pull-pressure sensor (DS2-500N, ZhiQu, China). For precise application of smaller force, a universal tensioning machine with a 0-500 mN tensile transducer (FS05-012, Mark-10, America) was used.

The temperature sensors were calibrated in a thermostat (DHG-9070A, BluePard, China). Each temperature was maintained for 30 minutes to ensure internal equilibrium was achieved, with a 5 °C increment each time up to 100 °C. Rapid temperature cycling was done using a water bath. The temperature statements involved in the experiments were monitored by commercial thermocouples.

A variety of 60 mm × 30 mm × 0.5 mm metal sheets (purchased from ShengShiDa, China) were used to realize the non-contact distance sensing test. To ensure distance accuracy, a series of highly 3D-printed brackets were taken for positional fixation.

The HD-LMC was impedance-matched via a circuit board and employed for wireless near-field communication. All parameters, including impedance characteristics at high frequencies and return loss S11, were measured using an ENA network analyzer (E5063A, Keysight, America).

The constructed bionic soft pufferfish comprises an internal 3D-printed frame and a hollow silicone pufferfish (purchased from MoZhiJing, China). The actuated structure is created using two HD-LMCs with a diameter of 0.68 mm and a magnet (40 mm×20 mm×10 mm with a central surface flux of 356 mT). The bionic pufferfish was suspended in the water by connecting it to an air bladder floating on the water’s surface using a fine copper wire. The square wave signal was produced by an arbitrary signal generator (DG1022, Rigol Technologies, China), and the voltage was subsequently adjusted using a power amplifier (KD 5702, Ti Kedong Electronic, China) to drive the movement of the pufferfish robot.

The high-speed rotary robot is composed of six HD-LMCs with D = 0.68 mm. A high-speed electric slip ring (purchased from SENRING, China) is used in the middle to solve the problem of wire winding. Frequency control is realized by using an inverter (380V-3kW, YINGSHIDA, China), and then connected to a three-phase voltage regulator (TSGC2-3KVA, ChengQiang, China) to realize the regulation of voltage. For safety, a 50 Ω 500 W high-power sliding varistor is connected for additional voltage division. The track for the high-speed rotating robot comprises multiple magnets (100 mm × 50 mm × 20 mm), with a central surface flux of 120 mT.

Numerical theory simulations were performed using the commercial software COMSOL Multiphysics (Version 6.1, COMSOL Inc., Sweden). The geometric model of the HD-LMC was designed by SolidWorks (Version 2021, Dassault Systemes, France) and imported into the software. All computational models have been analyzed for mesh independence, and a medium number of meshes has been used after comprehensive consideration. See Supplementary Note 10 for more information.

All optical photographs were taken by a digital SLR camera (EOS90D, Canon, Japan) with a resolution of 6960 ×4640 pixels unless otherwise noted. All video information was also captured by a digital SLR camera (EOS90D, Canon, Japan) at a frame rate of 50 fps with a resolution of 1920 × 1080 pixels.

The data generated in this study are provided in the Source Data file. Source data are provided with this paper.

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This work was partially supported by the NSFC Grant (No. 91748206) to J.L., the Frontier Project of the Chinese Academy of Sciences to J.L., and the Fundamental Research Funds for the Central Universities (BLX202343) to L.W.

State Key Laboratory of Cryogenic Science and Technology, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing, China

Nan Li, Yingxin Zhou, Yuqing Li, Chunwei Li, Wentao Xiang, Xueqing Chen, Qi Zhang, Jun Su, Bohao Jin, Huize Song, Cai Cheng, Minghui Guo & Jing Liu

School of Future Technology, University of Chinese Academy of Sciences, Beijing, China

Nan Li, Yingxin Zhou, Yuqing Li, Chunwei Li, Wentao Xiang, Xueqing Chen, Qi Zhang, Jun Su, Bohao Jin, Huize Song, Cai Cheng & Jing Liu

Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing, China

Pan Zhang & Jing Liu

Beijing Key Laboratory of Lignocellulosic Chemistry, Beijing Forestry University, Beijing, China

Lei Wang

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Conceptualization: N.L., L.W., J.L. Methodology: N.L., Y.L., C.L., Y.Z., L.W., J.L. Experiment: N.L., Y.L., Q.Z., J.S, B.J., H.S., C.C. Validation: N.L., Y.Z., C.L., W.X., X.C. Investigation: N.L., P.Z., Y.Z., C.L. Writing—original draft: N.L. Writing—review and editing: L.W., J.L. Visualization: N.L., M.G. Supervision: L.W., J.L. All the authors agreed on the final manuscript.

Correspondence to Lei Wang or Jing Liu.

The authors declare no competing interests.

Nature Communications thanks Xuechang Zhou, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

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Li, N., Zhou, Y., Li, Y. et al. Transformable 3D curved high-density liquid metal coils – an integrated unit for general soft actuation, sensing and communication. Nat Commun 15, 7679 (2024). https://doi.org/10.1038/s41467-024-51648-4

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DOI: https://doi.org/10.1038/s41467-024-51648-4

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