Ultrafast Untethered Levitation Device Utilized Squeeze Film for Omni‐Directional Transport

Abstract

The demand for ultrafast omnidirectional transport capable of moving small components, such as electronic parts, soft materials, and droplets, continues to grow. However, their operational speeds are often constrained by surface friction. To address this limitation, an untethered levitation device with dimensions 95 × 72 × 45 mm³ and a weight of 106 g is developed, using a piezoelectric actuator to generate a squeeze film. Lightweight driving electronics, including a function generator, amplifier, and battery, with a combined weight of 77 g, are developed to eliminate wires and achieve ultra‐high speed. A body speed of 15 s⁻¹ is achieved, which is significantly higher than that of conventional carriers, ensuring both flexibility and efficiency. Based on experimental evaluation, the device maintains frictionless movement on flat surfaces made of various materials, including those commonly found on desks and whiteboards. On a whiteboard, it moves horizontally at speeds over 1.4 ms⁻¹ and maintained frictionless sliding at over 3.0 ms⁻¹ on an inclined surface. With a payload capacity exceeding 0.4 times its weight, the device is suitable for ultrafast surface transport. Transporting a dish filled with tiny parts demonstrates its feasibility for electronics, machinery assembly, and biomedical and chemical applications.

Introduction

In recent years, the miniaturization of electronic products has led to a growing demand for technologies that can rapidly transport small components such as electronic and machinery parts, biomedical cells, chemicals, and test tubes. To meet this demand, various transport systems have been developed, including conveyor-based systems,^[1–5] magnetic transport systems,^[6–9] and systems utilizing small autonomous mobile robots. As the system size increases, the payload-to-self-weight ratio decreases. The use of small autonomous mobile robots (AMRs)^[10–12] offers a space-saving alternative to linear conveyor systems. While magnetic transport systems are limited to surfaces with magnetic properties or embedded magnetic actuators, small mobile robots can operate over a wide range of flat surfaces, including desktops, due to their internally housed actuators. Various actuators, such as motors, air cylinders, electromagnets, liquid metal engines,^[13,14] and piezoelectric actuators, have been employed to drive these small robots. Piezoelectric actuators are particularly suited for the precise movement of small robots due to their compactness, lightweight, high displacement resolution, and rapid responsiveness. Examples of piezoelectric-based robots include walking robots utilizing the expansion and contraction of piezoelectric actuators,^[15–18] vibration-driven robots,^[19–22] and robots combining piezoelectric effects with magnetic effects.^[23–25] However, many of these robots face difficulties in achieving higher speeds due to the effect of solid friction between the robot and the surface. To overcome this limitation, we investigated a method to reduce the effects of solid friction by developing a “levitation device” using a multilayer piezoelectric actuator. Methods to generate the levitation force include diamagnetic levitation,^[26–28] pneumatic levitation,^[29–31] and acoustic levitation using piezoelectric actuators.^[32,33] For driving autonomous mobile robots, diamagnetic levitation is restricted to magnetic surfaces; pneumatic levitation is unsuitable for transporting small components owing to the risk of them being blown away and difficulty in maintaining constant flying height above the surface. Thus, we opted for acoustic levitation using multilayer piezoelectric actuators and proceeded with the design and prototyping. Levitation devices utilizing acoustic levitation, where piezoelectric actuators are sandwiched between an inertial body and a plate, have been developed.^[34,35] Figure S1 and Movie S1, Supporting Information, illustrate the levitation device in the initial and the levitation states. In the levitation state, the laser spot appears bigger, indicating that the plate is levitating. In the levitation device, the piezoelectric actuators are connected to external driving circuits via cables, and solid friction with the floor is eliminated due to levitation. However, as shown in Figure S2, Supporting Information, even a slight tension in the cable can easily move the device, making precise positioning challenging. To address this issue, we developed an untethered drive circuit for the levitation device. Figure 1A shows the principle of levitation of the tethered levitation device on a squeeze film (ULS). Figure 1B presents the fabricated prototype of the untethered levitation device on a squeeze film (ULS), which consists mainly of an inertial body, a plate, and a multilayer piezoelectric actuator with a drive circuit mounted on top. Figure 1C illustrates an enlarged view of the ULS structure. By removing the tether, the tension caused by wiring is eliminated, enabling more unrestricted movement. For instance, as shown in Figure 1D, the untethered levitation device can transport electronic, machinery, chemical, and biomedical components by frictionless ultrafast omnidirectional movement or rotate a test tube using ultrafast frictionless spin to achieve mixing, although this device requires adequate outer pushers such as servo motors with levers. The primary objective of this study was to develop an untethered levitation device utilizing squeeze film and evaluate its utility and potential applications. The objectives of this study were largely achieved through system design, performance evaluation, and demonstrations. Because the device is enabled by untethered levitation, it possesses diverse application potential. Measurements made on the prototype device are discussed. Additionally, we present the results of the demonstrations, discussing the utility, potential applications, and challenges.

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Results

Demonstration of ULS

Demonstration using a Servo Motor

To evaluate the transport capacity of the untethered levitation device, we conducted an experiment in which the levitation device was driven horizontally. To move the ULS horizontally, just as an air hockey mallet pushes a disk, we used a servo motor (MG996R, TOWER PRO). The experimental results are shown in Figure 2A. The ULS exhibited both linear and rotational movements on a whiteboard surface, depending on the launch angle of the servo motor. Without load, the device achieved a maximum translational speed of 1.4 ms⁻¹ and a rotational speed of 90 rpm, demonstrating the ability to move across the whiteboard without erasing the marker ink.

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This maximum translational speed is constrained by the performance of the MG996R servo motor, particularly the speed at the lever tip. A detailed discussion of the velocity estimation is provided in the Supporting Information (Figure S3 and Figure S4, Supporting Information, and Table 1). In principle, translational speeds of at least 3 m s⁻¹ are achievable, as demonstrated in the slope experiment. Even higher speeds could be achieved by increasing the lever actuation speed. By using a servo motor, as shown in Figure 1D, the ULS can transport objects along various trajectories. Furthermore, the device combines rotational and translational motions, enabling high-speed transport with flexible posture adjustments. For more details, please refer to Movie S2, Supporting Information.

Table 1 Mass of each component in the driving circuit developed for the levitation device.

Component	Model number, manufacturer	Mass [g]
Amplifier module	IFJM-001, Marutsu	13
Microcontroller unit	Arduino Nano Every, Arduino Foundation	5
LiPo battery	633 010 345 382, Fytoo	12
Signal generator module	AD9851, Analog Devices	24
Universal board	–	15
Others	–	8
Total weight	–	77

Demonstration on Various Floor Surfaces

While the ULS has a limitation in that it can move only over smooth surfaces, such as an aluminum plate, glass surfaces, and office desks, we tested its ability to traverse a small height difference on an office desk. As shown in Figure 2B, the ULS successfully maneuvered a step of ≈50 μm, equivalent to the thickness of a cellophane tape. Next, its transport capability was evaluated on an office desk. As shown in Figure 2C, when the ULS was pushed horizontally at an acceleration of less than ≈3.3 m s⁻² to reach a speed of up to 1 m s⁻¹, it successfully transported a container filled with screws or ≈70% water without spilling. This result demonstrates the system's feasibility for transporting machinery parts, chemicals, and biomedical components. For more details, please refer to Movie S3, Supporting Information.

Slope Sliding Demonstration

To verify that the ULS achieves levitation and operates without friction, a demonstration was conducted where the device was released from rest (initial velocity is 0 ms⁻¹) and allowed to slide along a commonly used whiteboard marker tray (length 1.8 m), as shown in Figure 3A. The velocity v as a function of position l along the rail was plotted as shown in Figure 3B for two cases: with levitation turned ON and OFF, at an angle of inclination of 20°. In each case, the velocities were obtained from a single measurement. When levitation was OFF, the plate remained in contact with the marker tray and slid down the slope. Let the coefficient of kinetic friction be μ. The equation of motion is expressed as1$m\frac{{\mathrm{d}}^{2}l}{\mathrm{d}{t}^2}=mg\sin \theta -\mu mg\cos \theta$where m is the mass of the ULS and g is the gravitational acceleration. Integrating Equation (1) with respect to time t yields the velocity v, and further integration gives the position l2$\frac{\mathrm{d}l}{\mathrm{d}t}=v=(g\sin \theta -\mu g\cos \theta )\times t$3$l=\frac{1}{2}(g\sin \theta -\mu g\cos \theta )\times t^2$

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Eliminating t between Equation (2) and (3) gives4$v=\sqrt{2g(\sin \theta -\mu \cos \theta )}\times \sqrt{l}$

This shows that v is a function of $\sqrt{l}$. From the plot in Figure 3B, when levitation was turned OFF, the value of μ = 0.28. On the other hand, when levitation was ON, the ULS did not come in contact with the marker tray. Substituting μ = 0 into Equation (4) results in5$v=\sqrt{2g\sin \theta }\times \sqrt{l}=2.6\sqrt{l}$

The experimental results align closely with the theoretical values, confirming that the ULS slides over the marker tray without friction while levitating. It maintained frictionless sliding movement over 3.0 ms⁻¹ on an inclined surface. For the same position, l, the velocity in the OFF case was approximately half that in the ON case. Next, the inclination angle was set to 10°, and the levitation state of the ULS was alternated every second. In the ON state, the ULS slid freely without friction, while in the OFF state, it stopped on the slope. However, during these experiments, rotational motion not accounted for in Equation (1) was observed. This rotation is believed to result from two main factors: contact between the ULS and the side wall of the slider and rotational moments caused by surface roughness between the contact legs and the ground. Additionally, the ULS consistently rotated in the same direction, which is likely due to the slider being slightly tilted not only along the direction of motion but also vertically. For more details, please refer to Movie S4, Supporting Information.

Basic Performance

Figure S5, Supporting Information shows the tethered levitation device on squeeze film (TLS). Unlike the ULS, the TLS lacks an integrated circuit and features a frame that encloses the piezoelectric elements. To investigate the basic performance of TLS and ULS, we conducted three experiments. In all the experiments, the circuit was not mounted on the ULS, ensuring that the measurements were not influenced by the circuit's mass. It should be noted that the results for the TLS are presented in the Supporting Information. In addition, details of the experimental setup and the measured point on the plate are provided in Figure S6 and S7, Supporting Information.

Frequency Dependence

The applied voltage was fixed at 20 V_pp. The frequency f was varied from 0 to 14 kHz, and the sampling frequency for the measurements was set at 125 kHz. Based on the measurements, h_m for the ULS reached 24.8 μm at f = 12.6 kHz, which corresponds to the resonant frequency of the combined system, including the inertial body, plate, and piezoelectric actuator.

Dependence of ULS on Mass

We conducted an experiment in which the voltage is 20 V_pp, and f_r = 12.6 kHz while varying the mass of the weights M from 10 to 150 g. The weight was mounted on the inertial mass via a shock absorber (Crystal Gel, CRG-T150220, TANAC). The shock absorber, made of a soft material capable of absorbing high-frequency vibrations, serves two purposes in this system:^[36–38] 1) increasing the resonant frequency of the levitating mechanism by reducing the inertia mass of the upper part m₁ and 2) suppressing the vibration z_w of the added objects on the device.

For more details, please refer to Figure S8, Supporting Information.

The change in levitation height with mass is shown in Figure 3C as a plot of M vs h_m. However, when M reached 150 g, the device could no longer levitate, and the plate displacement z_p reached its minimum value of zero (h = 0 μm). Figure 3C also illustrates the time response of the plate displacement z_p for M = 150 g. With M = 120 g, h_m of 6.6 μm was observed. From Table 1, it is observed that the total mass of the circuit is 77 g, allowing for an additional weight of 43 g to be mounted on top of the ULS along with the circuit.

Discussion

Comparison

Figure 4 compares the ULS and TLS with conventional transport devices.^[39] The vertical axis represents the payload-to-self-weight ratio, while the horizontal axis shows the body-speed-to-self-length ratio. Devices capable of levitation, such as drones and magnetic levitation systems, typically exhibit relatively high payload capacities and maximum achievable body speeds. The TLS achieves a higher payload capacity, whereas the ULS exhibits a 1/10 payload ratio. This discrepancy arises because the wired device receives power from an external driver circuit, while the untethered device levitates, carrying its circuit onboard. As demonstrated in Section 2.1.1, the ULS can travel in a straight line at a speed of 1.4 ms⁻¹ without having to deal with external wires. Additionally, it can rotate at a speed of over 90 rpm and operate on various flat surfaces, such as commonly used whiteboards and desks. This capability enables high-speed transportation of objects under versatile conditions on various flat surfaces. To expand the potential applications of the ULS as a transport solution, its payload capacity should be increased, and self-propulsion functionality should be incorporated. In the future, we plan to develop a robot by integrating multiple levitation devices and equipping them with propulsion mechanisms.

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Definition and Property of Levitation Height

The definitions of the coordinate axes are shown in Figure S9, Supporting Information, and the mechanical parameters are listed in Table 2. Figure S10, Supporting Information, illustrates the vertical displacements of the plate along the z-axis (z_p) from its initial state. An expanded view of the interval between t = 0.400 and t = 0.401 s is also provided in Figure S10, Supporting Information. A sinusoidal voltage, with f = 5.6 kHz and V_pp = 28 V_pp, was applied beginning at t = 0.05 s and continued until t = 0.55 s. During this time interval, the plate is said to be in the “levitation state.” The measurement sampling frequency was 42 kHz, and h_m was averaged over every 1,000 points (referred to as “1,000-point averaging”) and superimposed on the graph. During the transient state, the displacements z_p increased significantly and exhibited oscillatory behavior. Subsequently, the amplitudes of the oscillations gradually decreased and stabilized. In the steady state, the displacement of the plate is denoted by d, while the average obtained from “1,000-point averaging” is defined as the levitation height h. If h = d, meaning the levitation device is in contact with the floor surface while vibrating, h cannot be defined. (For clarity, the levitation height under this condition is plotted as h = 0 in Figure 3C.) In Figure S10, Supporting Information, d = 4.8 μm and h = 23.9 μm.

Table 2 Mechanical parameters.

	Parameter/equation	Value	Unit
t	Time		[s]
l	Position along the marker tray of whiteboard	0–1.8	[m]
V(l)	Velocity of the ULS at position l	0–3.0	[M s−1]
θ	Angle of the whiteboard marker tray with the floor	5–20	degree
V(t)	Voltage applied to the piezoelectric actuator (applied voltage)	0–150	[V]
V pp	Peak-to-peak voltage	0–150	[Vpp]
f	Voltage frequency (=frequency of zp)	0–14	[kHz]
f r	Resonant frequency of levitation device	–	[kHz]
f rm	Measured resonant frequency of levitation device	5.5	[kHz]
h	Levitation height	0–100	[μm]
h m	Measured levitation height	–	[μm]
h t	Theoretical levitation height	–	[μm]
d	Displacement amplitude of the plate	0–50	[μm]
K ta	Theoretical proportional constant of ht = Ktad	12.7	–
K 2	Correction factor for error caused by the device geometry	0.85	–
K 3	Correction factor for error caused by plate deformation	0.82	–
K ma	Measured proportional constant of hm = Kmad4	–	–
C	Capacitance of a piezoelectric actuator	0.50	[μF]
z i –(t)	z-axis displacement of an inertial body's center of gravity from the initial state		[m]
z p(t)	z-axis displacement of a plate's center of gravity from the initial state		[m]
Z w (t)	z-axis displacement of a weight's center of gravity from the initial state		[m]
m i	Mass of upper part	23.0	[g]
m p	Mass of lower part	8.2	[g]
M	Mass of the added weight	20–150	[g]
m	Mass of levitation device of mi + mp	31.2	[g]
m red	Reduced mass of $\frac{m_i{m}_p}{m_i+m_p}$	6.0	[g]
k	Spring constant of a piezoelectric actuator	18	[N μm−1]
ζ	Damping ratio	0.046	–
c	Damping coefficient	–	[Kg s−1]
F(t)	Blocked force		[N]
c 0	Speed of sound	340	[m s−1]
ρ 0	Air density	1.2	[Km m−3]
S	Area of plate	0.000707	[m2]

Frequency Dependence of Levitation Height

Figure S11, Supporting Information, shows plots of h and f. Based on the measurements, we identified the measured resonant frequency of TLS as f_rm = 5.5 kHz. In the Ansys frequency analysis, a generative force equivalent to a V of 28 V (61.6 N) was applied to the piezoelectric actuator while constraining all movements except that in the direction of the z-axis. The simulation results showed that the displacement amplitude was maximum at f = 7.7 kHz, identifying the analytically derived resonant frequency of TLS as f_ra = 7.7 kHz = 1.4 f_rm.

Next, the theoretical resonant frequency of TLS f_rt is derived using the parameters listed in Table 2. The dynamic model is shown in Figure S12, Supporting Information. The mass of the upper part, m_i (23.0 g), is defined as the sum of the mass of the inertial body (20.5 g) and half of the combined mass of the frame and the piezoelectric actuator (2.5 g). Note that added weight is excluded in m_i because the high-frequency vibrations are suppressed by the shock absorber of the gel sheet in the steady state, as shown in Figure S8, Supporting Information. Similarly, the mass of the lower part, m_p, is defined as the sum of the mass of the plate and half of the combined mass of the frame and the piezoelectric actuator. The damping ratio ζ was determined to be 0.046 using the half-power bandwidth method^[40,41] based on the frequency dependence data. The equations of motion for the inertial body and the plate are given as6$m_i\frac{{\mathrm{d}}^2{z}_i}{\mathrm{d}{t}^2}+c\frac{d}{\mathrm{d}t}(z_i-z_{\mathrm{p}})+k(z_i-z_{\mathrm{p}})=F(t)$7$m_{\mathrm{p}}\frac{{\mathrm{d}}^2{z}_{\mathrm{p}}}{\mathrm{d}{t}^2}-c\frac{d}{\mathrm{d}t}(z_i-z_{\mathrm{p}})-k(z_i-z_{\mathrm{p}})=-F(t)$

From Equation (6) and (7), we derive8$\frac{{\mathrm{d}}^2{z}_i}{\mathrm{d}{t}^2}-\frac{{\mathrm{d}}^2{z}_{\mathrm{p}}}{\mathrm{d}{t}^2}=-\left(\frac{1}{m_i}+\frac{1}{m_{\mathrm{p}}}\right)\{k(z_i-z_{\mathrm{p}})-F(t)\}-c\left(\frac{1}{m_i}+\frac{1}{m_{\mathrm{p}}}\right)\frac{d}{dt}(z_i-z_{\mathrm{p}})$

Introducing the reduced mass m_red, defined as9$m_{\text{red}}=\frac{m_i{m}_{\mathrm{p}}}{m_i+m_{\mathrm{p}}}$

Equation (8) is rewritten as10$m_{\text{red}}\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}(z_i-z_{\mathrm{p}})+c\frac{d}{\mathrm{d}t}(z_i-z_{\mathrm{p}})+k(z_i-z_{\mathrm{p}})=F(t)$

Equation (10) corresponds to the equation of motion for a forced single-degree-of-freedom vibration system. Therefore, the theoretical resonant frequency f_rt is given by11$f_{\text{rt}}=\frac{1}{2\pi }\sqrt{\frac{k}{m_{\text{red}}}(1-{\zeta }^2)}=8.7[\text{kHz}]=1.6f_{\text{rm}}$

Here, the values of m_red, k, and ζ have been substituted into (Equation 11).

The theoretical value f_rt was 1.6 times higher than the measured value f_rm, while the analytical value of f_ra was 1.4 times higher. These discrepancies are believed to stem from the spring constant (stiffness) of the system. In the theoretical calculation, the spring constant in the mechanical model was assumed to be equal to the spring constant of the multilayer piezoelectric actuator (SA030318, Piezo Drive) at 18 N μm⁻¹. However, the actual spring constant of the levitation device is most likely lesser than that of the piezoelectric actuator. Additionally, the connection methods differ between the simulation model and the actual device. In the simulation, the frame and the inertial body, as well as the frame and the plate, are connected via plane-to-plane contacts (surface connection). In contrast, the actual device uses screw fastening, which results in point-to-point connections. This discrepancy in connection methodology reduces the overall spring constant of the actual levitation device compared to that in the simulation, leading to a lower resonant frequency in practice.

Peak-to-Peak Voltage Dependence

Theoretically, h_t is proportional to the displacement amplitude of the plate d, which is approximately proportional to V_pp. Here, Figure S13, Supporting Information, represents h_m of the TLS at f_rm = 5.5 kHz and voltage range of 2–28 V_pp. In Figure S13, Supporting Information, no levitation is observed up to 18 V_pp; however, beyond this threshold, V_pp and h_m of the TLS exhibit a proportional relationship. A discussion of this nonlinear behavior is provided in Figure S14, Supporting Information. Similar proportional relationship, as shown in Equation (12), is also considered to hold for the ULS.12$h_{\mathrm{t}}=K_{\text{ta}}d=K_{\text{tb}}{V}_{\text{pp}}$

Next, the theoretical proportionality coefficient K_ta is derived from the conditions of acoustic levitation and compared with the measured value K_ma. When the plate levitates at h_t with d, the average pressure p between the ground surface and the plate is given by^[40]13$p=\frac{1}{2}{c}_0^2{\rho }_0\frac{{\mathrm{d}}^2}{h_t^2}$where c₀ represents the speed of sound, and ρ₀ is the density of air.

By substituting d in Equation (13) with the measured point plate displacement amplitude d₄ and assuming that p is equal to the pressure exerted (mg s⁻¹), Equation (13) can be rewritten as14$h_{\mathrm{t}}=K_{\mathrm{ta}}{\mathit{K}}_2{\mathit{K}}_3{\mathit{d}}_4=\sqrt{\frac{{\mathit{c}}_0^2{\mathit{\rho }}_0\mathit{S}}{2\mathit{mg}}}{\mathit{K}}_2{\mathit{K}}_3{\mathit{d}}_4=8.2{\mathit{d}}_4$

Here, K₂ and K₃ represent the correction factors derived from the differences between the experimental conditions in references^[41,42] and the present study. The derivation of these factors and further details regarding the differences can be found in the Supporting Information (Figure S15 and S16 and Table S2, Supporting Information). Figure S17, Supporting Information, shows plots of the theoretical levitation height of TLS h_t and the measured height h_m against the plate displacement amplitude d₄. Overall, the relationship h_m = K_mad₄ holds, but the graph's intercept falls below the origin. Despite this, the proportional constant was K_ma = 5.5, which is 67% of the theoretically derived proportional constant K_taK₂K₃ = 8.2. This discrepancy likely stems from the surface characteristics of the plate and the floor. The theoretical model assumes an ideal plane surface. However, if the surface roughness of the plate or floor is significant, the squeeze film may escape more easily, reducing pressure and causing the levitation height to be less than h_t.

This study successfully developed and evaluated a newly developed untethered levitation device (ULS) utilizing a squeeze film. The ULS achieved almost ideal frictionless motion with a velocity of 3.0 ms⁻¹. The ULS also achieved frictionless transport of various small objects, including electronic components and liquids, with a payload of 0.4 times self-weight. Key results include quantitative evaluations of achievable speed, resonance frequency, levitation height, and payload. The significance of this research lies in its potential applications in fields requiring contactless and rapid handling, such as chemical transportation and biomedical centrifugation. By eliminating tethering cables, the ULS provides greater speed and stable levitation height on commonly used flat surfaces compared to traditional levitation systems.

Experimental Section

Principle and Setup

Figure S5, Supporting Information, shows the principle of levitation of the TLS. The TLS is structured with a multilayer piezoelectric actuator sandwiched between an inertial body and a plate. The multilayer piezoelectric actuator is an electronic component that expands and contracts nearly proportionally to the applied voltage V(t), which is supplied through two wires connected to the actuator. When a high-frequency sinusoidal voltage, defined by its peak-to-peak value V_pp and frequency f, as shown in Figure S18, Supporting Information, is applied to the actuator, the actuator vibrates vertically at frequency f. This vibration generates a thin air layer, known as a squeeze film, between the plate and the floor, enabling the levitation of the device.^[43–45] The levitation height h depends on f and V_pp of the applied sinusoidal voltage. Generally, h is proportional to the amplitude of oscillation of the plate d.^[46,47] Furthermore, when f matches the resonant frequency of the entire levitation structure f_r, which includes the actuator and its mechanical components, oscillations in the plate become more prominent, resulting in an increased h. A sinusoidal voltage was applied to the piezoelectric actuator (SA030318, Piezo Drive, resonant frequency: 138 kHz) in the levitation device, and the displacement of the inertial mass along the z-axis was measured using a laser Doppler vibrometer (VibroOne, Polytec). The displacement of the edge of the plate was measured. The measured displacement was assumed to be equal to the z-axis displacement of the plate's center of gravity, z_p.

Designing of the Device

Figure 1C illustrates an enlarged view of the ULS. The specifications of the ULS are summarized in Table 3, while those of the TLS are provided in Figure S19, Supporting Information. The ULS is an improved version of the TLS. Because the device is designed with a lower center of gravity, it is more stable and less prone to tipping, even when equipped with circuitry. The ULS eliminates the frame used in the TLS and incorporates thicker and shorter piezoelectric actuators compared to the TLS.

Table 3 Specification of developed levitation devices.

Name of device	TLS	ULS
Type	Tethered	Untethered
Levitation device	Dimensions [mm3]	30 × 30 × 42	95 × 72 × 45
Mass [g]	31.2 Inertial body: 20.5 Plate: 5.7	106 Drive circuit: 77.0 Inertial body: 20.5 Plate: 5.7
Continuous levitation time [min]		≈10
Piezoelectric actuator	Model number (maker)	SA030318 (Piezo Drive)	AE0505D08 (Tokin)
Maximum stroke (150 Vpp) [μm]	25	9.1
Capacitance [nF]	500	750
Stiffness [N μm−1]	18	93.4
Blocking force [N]	330	850
Resonant frequency [kHz]	83	138
Mass [g]	2.0	2.6
Length [mm]	18	10

Wireless Drive Circuit

Devices employing piezoelectric actuators are typically driven using large amplifiers such as the HSA4051 (NF Corp.). These amplifiers are particularly useful when high frequencies f and high peak-to-peak voltages V_pp are required, as they can output the current required for such operations. However, when using a large amplifier to drive a levitation device, the tension in the wires connected to the piezoelectric actuator causes the device to move in an unintended direction. This movement interferes with precise positioning, which is crucial for applications such as transportation robots. To address this issue, a wireless driver circuit was developed for the levitation device. Figure 5 shows an image and a simplified diagram of the wireless driver circuit wired on a universal board. In this circuit, a function generator (AD9851, Analog Devices) outputs a sinusoidal voltage having a peak-to-peak value of 1.0 V_pp. This voltage is then amplified by an amplifier module (IFJM-001, Marutsu) with a maximum amplification factor of 28. A 3.7 V LiPo battery serves as the power source. The circuit employs an appropriate boost converter and high-voltage converter to supply the required voltages to the MCU (Arduino Nano Every, Arduino) and the amplifier module. The amplifier module was selected based on considerations such as mass, output voltage, and frequency. The mass of each component is listed in Table 1, with the total mass of the circuit being 77 g. For more details, please refer to the Supporting Information (Figure S8 and Table S2, Supporting Information).

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This study focused on the development and testing of an untethered levitation device utilizing squeeze film. However, the device has several limitations. Its frictionless transport capabilities are restricted by surface conditions, and the levitation height is determined by the power supply and the structural design of the components. Future research should improve the levitation efficiency while optimizing the power and the stability of levitation height under various conditions, including irregular surfaces and dynamic loads. Investigating the scalability of the system for larger payloads, as well as its integration with other technologies, such as autonomous control and multidegree-of-freedom motion, will further broaden its applications in fields such as robotics, material handling, and precision manufacturing.

Acknowledgements

This work was supported by the Nakanishi Scholarship Foundation, the NSK Foundation for Advancement of Mechatronics, and the Takahashi Industrial and Economic Research Foundation.

Conflict of Interest

The authors declare no conflict of interest.

Author Contributions

Ohmi Fuchiwaki: funding acquisition (lead); project administration (lead); supervision (lead); validation (equal); and writing—review and editing (equal). Yuta Sunohara: conceptualization (lead); data curation (lead); formal analysis (lead); investigation (lead); methodology (lead); resources (lead); validation (lead); visualization (lead); writing – original draft (lead); and writing—review and editing (lead). Soushi Ueno: data curation (supporting); methodology (equal); validation (supporting); visualization (supporting); and writing—review and editing (lead). Rintaro Minegishi: resources (equal); visualization (equal); and writing—review and editing (lead). Yuta Kitamura: data curation (supporting) and writing—review and editing (supporting). Yuna Sugiyama: writing—review and editing (equal). Satoshi Ando: data curation (supporting) and writing—review and editing (supporting). Akihiro Torii: methodology (supporting); supervision (supporting); and validation (supporting). Chihiro Sekine: formal analysis (supporting) and writing—review and editing (supporting). Yuta Sunohara and Soushi Ueno contributed equally to this work.

Data Availability Statement

The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.

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