FDM‐Printed CMOS Logic Gates from Flexing Beam Mechanisms for the Control of Soft Robotic Systems

Abstract

Fluidic control systems target unique applications where conventional electronics fail. However, current fluidic control systems face challenges in accessible fabrication, reproducibility, and modifiable characteristics such as operating pressure and instability count. Herein, fused deposition‐modeled compliant mechanisms with flexing beams and soft linear actuators for fluid switching and the control of soft robotic systems are introduced. A linear actuator switches a compliant mechanism to cut off airflow through off‐the‐shelf tubing. The modular compliant logic devices can be configured as normally open or normally closed switches, as NOT, AND, and OR gates, and as nonvolatile memory elements. Their use is demonstrated in controlling a fluidic stepper motor, a worm‐like robot, and a fluidic display. These fluidic switches are printable using inexpensive desktop 3D printers, can be reliably reproduced in large quantities, and offer a wide range of modifiable parameters, including scalability, adaptability in operating pressure, and the tunability of instability counts for computational and memory functions.

Introduction

Over the past decade, robotics has experienced significant advancements due to developments in the semiconductor and automation sectors, leading to reduced costs and an increased presence of robots in daily life.^[1] Most robots rely on modern electronics; however, electronic systems face unique challenges in specialized environments. In radioactive settings, electron–hole pairs quickly impair functionality, necessitating radiation-hardened electronics.^[2] In explosive settings, such as oil rigs, devices must be spark-free to avoid ignition.^[3] Areas with strong magnetic fields, such as magnetic resonance imaging machines, pose risks where magnetic materials can become hazardous projectiles.^[4,5] To address these challenges, recent research has shifted toward nonelectronic control systems for robots, spotlighting fluidic logic circuits as a viable alternative.^[6,7]

Microfluidic control elements, typically characterized by micrometer-scale channels, have been used to construct complex circuits.^[8,9] However, their utility to create new types of soft robots is hindered by low flow rates^[10] (ranging from 0.01 to 10 mL min${}^{-1}$) and constrained reconfigurability;^[11] once microfluidic devices are fabricated, their structures are fixed. Recent developments in macrofluidic control systems have enabled higher flow rates, faster response times, and greater flexibility for reconfiguration.^[12] These increased flow rates allow fluidic soft actuators to be directly controlled, enabling autonomous, electronics-free interaction with their environment.^[13] Research in macrofluidic control systems has emphasized the development of fluidic transistors as fundamental building blocks.^[14] Analogous to electronic systems, CMOS (complementary metal–oxide–semiconductor) transistors are favored over PMOS (p-channel metal–oxide–semiconductor) or NMOS (n-channel metal–oxide–semiconductor) transistors due to their lower power consumption.^[15] The existing literature can be mainly divided into two major categories: 1) manually fabricated and 2) digitally fabricated MOS- and CMOS-equivalent fluidic transistors (Figure 1).

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Manually fabricated fluidic transistors are typically made via soft lithography.^[16] The soft bistable valve, a CMOS-equivalent fluidic transistor, addresses many limitations found in microfluidic devices; it can control macroscale actuators and can be (re)configured as NOT, AND, and OR logic gates, set–reset (S–R) latches, or a system clock (e.g., ring oscillator).^{[12,14,17–19]} Unlike soft lithography, which often uses expensive materials and processes, recent research has focused on using readily available, low-cost materials such as tubes and balloons,^[20–22] acetate sheets,^[23] acrylic sheets,^[6,7] and textiles.^[24] However, manually fabricated fluidic devices are inherently prone to fabrication imperfections, leading to increased performance tolerances.

Digitally fabricated robots with fluidic control systems made from soft and flexible materials have seen an upward trend.^[25,26] Hubbard et al. used PolyJet printing to create fluidic diodes, normally closed and normally open transistors, demonstrating soft robots with integrated fluidic circuitry.^[27] Wang et al. introduced a tunable soft CMOS-equivalent bistable valve and investigated the effects of different support removal techniques on the behavior and durability of the valve using PolyJet printing.^[28] However, the high cost of PolyJet printing, along with its maintenance requirements, intensive postprocessing, and health hazards of the print materials, has limited its adoption.

A low-cost alternative to PolyJet printing is fused deposition modeling (FDM). Zhai et al. demonstrated the potential of low-cost FDM printers by creating an airtight pneumatic valve, analogous to a MOS transistor.^[29] Another work employs a flueric approach, using jet interaction to deflect airflow and create fully FDM-printed interactive objects with embedded digital logic, such as NOT, OR, AND, and XOR gates.^[30] The recent introduction of an FDM-printed CMOS-equivalent pneumatic logic gate (PLG), based on kinking tubes, represents a significant step forward in nonelectronic fluidic switching for soft robots.^[31] Two tubes are initially fabricated in an open state; applying supply pressure results in a kink in one tube, while a control pressure simultaneously induces kinking in one tube and unkinking in the other. The PLG serves as an OR, AND, or NOT gate, and a central pattern generator, forming an integrated circuit to generate oscillatory signals for a soft fluidic robotic walker.

The current FDM-printed logic gates show great promise, yet they face limitations. These include energy dissipation from airflow loss with MOS transistor designs; limited reproducibility due to filament elasticity causing buckling and clogging; lack of geometric parametric studies to adjust control pressure ranges and achieve bistable states; lack of modularity requiring full redesign and refabrication for changes in device functionality; and inability to configure as nonvolatile memory elements. While existing FDM-printed logic gates possess some of these advantages, none integrate all these benefits into a single device.

Our work is motivated by the advantages of 3D-printed compliant mechanisms from flexing beams (i.e., flexure mechanisms), including their power efficiency, low cost, ease of fabrication, friction-free motion, being electronics-free, wide design space, scaling laws, modularity, and programmability.^[32–35] Compliant mechanisms with flexing beams have been adopted to replace traditional rigid parts that are connected with hinges or joints in space applications as nonexplosive release mechanisms, mechanical switches, latches, and relays.^[36,37] Micromechanical logic devices with curved-beam-based structures are preferred for complex logic operations due to their immunity to electromagnetic interference and resilience against radiation-induced damage.^[38–41] While compliant mechanisms with flexing beams are predominantly used in mechanical structures or for mechanical computation, their potential for fluidic switching and the control of soft robotic systems remains unexplored.

We present an FDM-printed compliant logic device that employs a flexing beam mechanism to switch fluidic signals. Our logic device, analogous to a CMOS transistor, consists of a flexing beam mechanism, a soft linear actuator, and off-the-shelf soft tubing. This work explores the feasibility of using compliant mechanisms with geometric nonlinearities in flexing beams to control fluid flow in soft robotic systems. By 3D printing the compliant mechanism from rigid materials like polylactic acid (PLA), we emphasize ease of fabrication and accessibility while combining the benefits of previously published work (Section S1 and Figure S1, Supporting Information). The compliant logic device can be configured into logic gates, memory elements, and stacked into ring oscillators with programmable geometrical parameters. We demonstrate the utility of the flexing beam-based fluidic switching strategy by controlling a 3D-printed fluidic stepper motor for rotary motion, a worm-like soft robot for linear motion, and a fluidic display. Employing a compliant mechanism with flexing beams for fluidic switching provides a novel, simple, and accessible method of nonelectronic control for soft robotic systems.

Results

Compliant Logic Device

The compliant logic device comprises an FDM-printed compliant mechanism with flexing beams from PLA and a soft linear actuator from thermoplastic polyurethane (TPU) with integrated off-the-shelf silicone tubing (Figure 2A,B). The compliant mechanism houses a soft linear actuator on its upper section, with soft silicone tubing inserted through channels at the top and bottom. When configured as a normally open switch, actuation pressure ($P_{\text{act}}$) is directed to the soft linear actuator; top and bottom tubing merge into a single pressure output, with supply pressure ($P_{\mathrm{s}}$) applied to the bottom tubing and atmospheric pressure ($P_{\text{atm}}$) to the top tubing. In the unactuated state ($P_{\text{act}}$ = 0 kPa), the bottom tube permits airflow while the top tube is pinched and obstructs airflow, resulting in an overall output pressure equal to the supply pressure ($P_{\text{out}}=P_{\mathrm{s}}$) (Figure 2A and Movie S1, Supporting Information). In the actuated state ($P_{\text{act}}$ = 90 kPa), the soft linear actuator expands and flexes the beams downward. The tube pincher radially compresses the bottom tube, obstructing airflow, while releasing the complementary upper tube, resulting in an overall output pressure equal to atmospheric pressure ($P_{\text{out}}$ = $P_{\text{atm}}$) (Figure 2B).

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We can configure the compliant logic device as normally open and normally closed switches (Figure 2C,D), exhibiting hysteresis equivalent to a Schmitt trigger. We define the cutoff pressure ($P_1$) as the threshold at which a tube is completely pinched off and the release pressure ($P_{\mathrm{R}}$) as the pressure required to fully release the tube. When the actuation pressure equals the release pressure ($P_{\text{act}}\le P_{\mathrm{R}}$), the bottom tube is released, allowing airflow. The hysteresis allows the device to withstand variations in actuator pressure, ensuring stability even if the actuator pressure fluctuates within a range ($P_{\mathrm{H}}$ = $P_1-P_{\mathrm{R}}$). When configured as a normally open switch (at P_s = 100 kPa), the device blocks airflow through the bottom tube when the actuator pressure exceeds the cutoff pressure ($P_{\text{act}}\ge P_1=88\hspace{0.17em}\text{kPa}$) (Figure 2E and Movie S2, Supporting Information). As the actuator pressure decreases ($P_{\text{act}}\le P_1=88\hspace{0.17em}\text{kPa}$), the pincher starts retracting to its original state, allowing complete airflow at the release pressure ($P_{\text{act}}\le P_{\mathrm{R}}=36\hspace{0.17em}\text{kPa}$). Our compliant logic device exhibits a hysteresis (P_H = 52 kPa), providing immunity to noise and withstanding actuator and supply pressures ($P_{\text{act}}=P_{\mathrm{s}}=395\hspace{0.17em}\text{kPa}$), corresponding to the maximum pressure our test setup could provide.

To analyze the effect of increased supply pressure and fabrication repeatability using FDM printing, we studied identical compliant logic devices (N = 10) configured as normally open switches (Figure 2F,G). All devices were printed with the same print settings, printer type, filaments, tube material, and geometric parameters. For low supply pressures (P_s = 100 kPa), the devices require low cutoff (P₁ = 81 $\pm$ 9 kPa) and release pressures (P_R = 32 $\pm$ 16 kPa). As the supply pressure increases (P_s = 300 kPa), the cutoff (P₁ = 110 $\pm$ 10 kPa) and release pressures (P_R = 55 $\pm$ 23 kPa) also increase (Figure 2F). The $\pm$ sign denotes a standard error. The variability in both cutoff and release pressures is attributed to the manufacturing tolerances associated with FDM printing (Figure 2G).

Design and Characterization

The design space for compliant mechanisms with flexing beams allows for extensive exploration of optimal geometric parameters, significantly affecting the operating pressure range and the stability of the device (mono- vs bistable). A monostable device requires sustained control pressure for actuation (to cut off airflow through the bottom tubing), while a bistable device maintains its current state even after the actuation pressure is discontinued ($P_{\text{act}}=0\hspace{0.17em}\text{kPa}$).^[42,43] A bistable device requires a cutback pressure ($P_2$) to transition back to the other stable state (Figure 3A). Monostable devices are typically used as logic gates, whereas bistable designs are used as nonvolatile memory elements.^[19] We modified the design of the compliant mechanism to accommodate a second linear actuator for bistable devices. We assessed the impact of beam thickness (t), beam angle (θ), beam length ($b_{\mathrm{L}}$), beam separation distance ($b_{\mathrm{s}}$), and beam-to-frame width (w) on actuator pressure and mono- and bistability (Figure 3B).

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Due to the interdependence of geometrical parameters, we introduce the ratio of the beam angle to beam-to-frame width (r, °mm⁻¹). We chose initial values for beam-to-frame width and beam angle (w = 2.5 mm, θ = 8°), resulting in a ratio of 3.2. We plotted cutoff ($P_1$) and cutback pressures ($P_2$) for selected parameters (t, b_L, and b_s) at varying ratios (r, w = 2.5–5.5 mm in 1 mm steps and θ = 8°–20° in 4° increments).1$\text{ratio} (r)=\frac{\text{beam\hspace{0.17em}angle} (\theta )}{\text{beam-to-frame} \text{width} (\mathrm{w})}$

Thicker beams necessitate higher actuation pressure; compliant logic devices exhibit bistability at higher ratios with thinner beam thicknesses (Figure 3C). The plot shows the mean values of five measurements (N = 5), with error bars indicating the standard deviation scaled up by a factor of five for enhanced visibility (Section S4, Supporting Information). As the beam length increases, the actuation pressure decreases (Figure 3D), validating the analytical pseudo-rigid-body model of the compliant mechanism (Section S2 and Figure S2, Supporting Information). The influence of beam separation distance ($b_{\mathrm{s}}$) on actuator pressure was not as significant as other parameters (Figure 3E). An increase in θ results in a decrease in actuation pressure (Figure 3F). Smaller beam angles yield straighter beams, limiting travel distance. Conversely, larger angles generate greater stresses in curved beams due to increased bending moments, suggesting an optimal range lies in intermediate angles. For bistable configurations, high beam ratios are important, characterized by thin and short beams. Design parameters need to be ultimately informed by fabrication constraints; for 3D printing, layer thickness and maximum feature size are considered.

For complex circuits with multiple control elements, accommodating a large number of devices in a small space is crucial (Figure 3G). We miniaturized compliant mechanisms and linear actuators to their smallest feasible scale, informed by 3D printer specifications, and evaluated two printing methods: FDM and stereolithography (SLA). Reducing the size of the linear actuator presented challenges, including excessive layer overlap and pressure leaks when scaled to 70% of its initial size (Figure 3H). Decreasing the size of the linear actuator to 50% of its original dimensions ensured a minimum of three print layers using a 0.1 mm nozzle. As the actuator is reduced in scale, its elongation decreases, illustrating an approximately linear correlation with minor deviations.

The compliant mechanism exhibits monostability (Figure 3I) with the following parameters: t = 1.2 mm, θ = 8°, w = 2.5 mm, b_L = 30 mm, b_s = 7 mm, and T_d (tube diameter) = 3.2 mm. These parameters are informed by fabrication constraints from our FDM printers. When scaled down to 70% of its original size, the beams lacked sufficient spring force to cut off airflow through the top tubing. By increasing the beam thickness to t = 2.1 mm, we successfully scaled the device down to 50%. Further downscaling raised durability concerns, resulting in single print layers for beam thickness. At 70% scale, the channel size decreased from 4 to 2.8 mm, necessitating the use of off-the-shelf tubing with a smaller outer diameter (T_d = 1.6 mm).

We used SLA for printing the compliant mechanism because of its high resolution. Despite successful prints down to 20% scale, mechanical failure ensued upon actuation, revealing the brittleness of the PLA resin at this feature size. Even at the original 100% scale, the mechanism failed after approximately ten actuation cycles, highlighting the unsuitability of tough resin for this application.

To select specific design parameters and study the stress distribution and displacement under a given pressure, we conducted finite element analysis of compliant mechanisms and linear actuators (Section S3, S4 and Figure S3 and S4, Supporting Information). Due to the bending moments of the beams, the mechanism experiences high stresses at the joints, resulting in plastic deformation under cyclic loading. Three FDM-printed compliant logic devices were tested with cycling actuation (0.5 Hz, $P_{\text{act}}=P_{\mathrm{s}}=81\hspace{0.17em}\text{kPa}$) (Section S5 and Figure S5, Supporting Information); after an average of 49,800 actuation cycles, we observed air bubbles leaking from the top tube. Fatigue tests showed that the performance of the device declined due to plastic deformation of the beams. As the restoring force in the beam became insufficient to kink the top tube, we glued the linear actuator to the platform using adhesive, causing it to pull the pincher upward. We increased the actuator pressure ($P_{\text{act}}=102\hspace{0.17em}\text{kPa}$) and conducted fatigue tests for up to 100,000 actuation cycles.

Modes of Operation

Analogous to electronics, our compliant logic device can be configured into normally closed and normally open switches, as well as NOT, AND, and OR gates, and nonvolatile memory devices (Figure 4). For a normally closed switch (Figure 4A), the supply pressure is connected to the top tube ($P_{\mathrm{s}}$), while the bottom tube is exposed to atmospheric pressure ($P_{\text{atm}}$). When the input is high ($P_{\text{act}}=A=1$), the output is high (Q = 1), and vice versa. In this configuration, the device serves as the electronic equivalent of a buffer but adds a time delay to the system.

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The compliant logic device can operate as a normally open switch, equivalent to a NOT gate (Figure 4B). The supply pressure is connected to the bottom tube ($P_{\mathrm{s}}$), and the top tube is exposed to atmospheric pressure ($P_{\text{atm}}$). When the input is high (A = 1), the output is low (Q = 0). AND and OR gates have two inputs and one output. For an AND gate, it only outputs high (Q = 1) if both inputs are high (A = B = 1) (Figure 4C). For the OR gate, it outputs low (Q = 0) only if both inputs are low (A = B = 0); for all other combinations, the output remains high (Q = 1) (Figure 4D). These three gates are Boolean operators and functionally complete, capable of being assembled into arbitrary logic circuits. Fluidic logic gates can be stacked to create memory devices, but developing a memory element from monostable devices is cumbersome and only allows for volatile information storage (Figure 4E).^[19] With our bistable design, a single compliant logic gate can be used as a non-volatile memory device to store binary information. When the set signal is high (S = 1), the output is high (Q = 1); only a reset signal switches the output to low (R = 1, Q = 0). Our bistable design enables permanent storage of information, promoting the development of sequential logic for executing complex operations in fluidic systems; the device maintains its state after power discontinuation.

Demonstrations

Pneumatic Stepper Motor

Oscillatory fluidic signals can be generated from a constant supply pressure.^[18] An odd number of NOT gates connected in series forms a ring configuration, where the output pressure of one inverter serves as the input pressure of another. We configured three compliant logic devices into NOT gates and interconnected them in series, obtaining an oscillatory fluidic signal of 20 Hz at a constant supply pressure (P_s = 180 kPa).

As electric motors are the predominant mode of actuation in robotics, we introduce a 3D-printed fluidic stepper motor capable of generating rotary motion from a constant pneumatic signal using a ring oscillator (Figure 5A and Movie S3, Supporting Information). Our stepper motor comprises three main components: a stator, a rotor, and a controller (i.e., a ring oscillator). The stator consists of a stationary housing with six linear actuators placed at 60° phase shifts; each actuator has a disc magnet integrated at its end. The rotor consists of a bearing and housing with four disc magnets positioned at 90${}^{\circ }$ phase shifts (Section S6 and Figure S6, Supporting Information). We connect the three outputs of the ring oscillator to three pairs of linear actuators. The fluidic stepper motor operates similarly to an electric stepper motor; when the soft actuators on the stator are pressurized, their embedded magnets rotate the rotor block, generating rotary motion (Figure 5B,C).

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To modify the rotary behavior of our pneumatic motor, we adjusted the tubing connected to atmospheric pressure (i.e., pull-down resistors). CMOS-equivalent devices still deplete pressure against atmosphere; by modifying the tube dimensions of the pull-down resistors, we were able to alter the frequency of oscillations, and consequently, the angular speed of the motor. We empirically tested and selected pull-down resistors based on changes in fluidic resistance and their effect on oscillation frequency, which we have previously studied.^[18] Large pull-down resistors indicate high power efficiencies for ring oscillators but also reduced oscillation frequencies. Short pull-down resistors deplete larger volumes of air over time, resulting in lower power efficiencies. Pull-down resistors of 15 cm in length and an inner diameter of 0.79 mm reduced the frequency of oscillation to 4.2 Hz and resulted in an angular speed of 98 RPM, using only a constant supply pressure. We also studied the impact of different tube lengths of pull-down resistors on the frequency and power efficiency (Section S7 and Figure S7 and S8, Supporting Information).

3D-Printed Fluidic Linear Robot

We developed a linear robot capable of forward movement by repeatedly contracting and expanding (Figure 6A,B and Movie S4, Supporting Information). Our fluidic linear robot draws inspiration from earthworms, which feature segmented bodies with flexion and extension motions, enabling peristaltic locomotion.^[44,45] To achieve this, a ring oscillator is configured, and its output is directed toward the actuator of a normally closed relay. By using two distinct supply pressures, we operate the linear robot independently of the supply pressure of the ring oscillator, thereby separating the load from the oscillator circuit (using a fluidic relay). The ring oscillator operates at 180 kPa, while the linear robot operates at 200 kPa. Without pull-down resistors, the robot is actuated at a frequency of 20 Hz, resulting in rapid expansion and relaxation, causing vibrations only. To increase the delay between signals and transition from high-frequency vibration to forward locomotion, we added pull-down resistors (30 mm in length and 0.4 mm in diameter) to the top tube of each NOT gate in the three-ring oscillator, reducing the actuation frequency to 1 Hz. To expedite the release of the relay, we added an additional pull-down resistor (10 mm in length and 0.79 mm in inner diameter) to the input actuator of the normally closed relay ($P_{\mathrm{B}}$). The linear robot achieved a maximum velocity of $4.5 \text{mm} {\mathrm{s}}^{-1}$ (Figure 6C). Though the cost of transport, the energy required to move a system of a specific weight over a given distance, of our worm-like robot is high,^[46–48] it can be reduced by printing with lower Shore hardness filaments (Section S8, Supporting Information).

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3D-Printed Fluidic Digital Display

In addition to using compliant logic devices to achieve linear and rotary motion, in a third demonstration, we control a fluidic display to depict the letters “W,” “P,” and “I,” corresponding to Worcester Polytechnic Institute (Figure 7A and Movie S5, Supporting Information). The digital display comprises a 5 by 3 array totaling 15 pixels. A pixel consists of a closed monostable membrane within a cylindrical chamber, accompanied by a slit resembling a Phillips screw head.^[19] Each pixel, referred to as a dot, is FDM-printed and incorporates two different colored materials: red for the membrane and chamber, and white for the slit. This display visualizes binary states: “ON” in the color red and “OFF” in the color white. Connecting the pressure chamber to atmospheric pressure results in a white pixel, while a positive pressure (P = 140 kPa) flips the membrane, indicating a red pixel.

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Two bits allow for four different combinations; we use two inputs to switch between three letters (W, P, I) and a blank state on the display. With both inputs off (A = 0, B = 0), we observe a blank display. Activating input B (B = 1) triggers the depiction of the letter “W”. Activation of input A (A = 1) illustrates the letter “P”. Activating both inputs A and B (A = B = 1) yields the letter “I”. We map the inputs to the outputs via a logic circuit made from combinations of compliant logic elements. First, we assign numbers 1–15 to the pixels (Figure 7B). Second, we determine pixel combinations that represent specific letters. For example, to display the letter “W” on the 3D-printed display, we activate pixels P1, P3, P4, P5, P6, P7, P9, P10, P11, P12, and P15. We identify similar outputs for other letters. Third, we search for logic expressions that control multiple pixels at once using the truth table. For example, P1, P3, and P9 need to be actuated for all three letters, so they are connected to a compliant logic device configured as an OR gate (Figure 7C). With optimization, a total of five compliant logic gates are required to achieve the desired fluidic circuit (Figure 7D) (Section S9 and Figure S9, Supporting Information). By connecting the fluidic digital circuit to inputs A and B, we demonstrated the fluidic digital display (Figure 7E).

Discussion

This article introduces compliant mechanisms with flexing beams for fluidic switching. It demonstrates the configuration of various logic gates and how parameterizing these mechanisms leads to different device characteristics, such as mono- versus bistable states and varied operating pressures. Our approach leverages standard desktop FDM printers with the most commonly used printing filament (PLA), making the fabrication process accessible and cost-effective.

While our compliant logic devices showcase the use of FDM printers, they are not entirely 3D-printed; the use of off-the-shelf tubing necessitates some manual assembly, although this is minimized, leading to a partially automated fabrication process. In our previous work,^[49] we discussed the challenges of FDM-printed tubing, as we obtained only one functional device out of five with limited life cycles (<10 000). The use of thermoplastic polyurethane or elastomer filaments makes it challenging to achieve reliable airtight prints for complex structures due to the inherent issues of soft filaments, such as filament buckling, filament slippage, and jamming of the extruder.^[50] The use of Eulerian path printing helps obtain airtight structures;^[29] however, it also constrains the design space. By using commonly available rigid filaments such as PLA to create compliant mechanisms, our devices can be printed without excessive tuning to the printer or constraint to the design space.

The size of our compliant logic devices may limit the creation of complex fluidic circuits. However, alternative printing techniques such as SLA and Inkjet printing can mitigate these issues by offering higher resolution and finer feature sizes. Although current materials for these printing techniques, such as tough resins and photopolymers, exhibit brittleness and often incur high fabrication costs, advancements in reducing costs and improving material properties could enhance the scalability and integration density of our fluidic circuits. This would further push the boundaries of what can be achieved with soft and rigid materials in compliant mechanisms with flexing beams in fluidic control systems.

By leveraging compliant mechanisms with flexing beams, we gain several benefits, including ease of fabrication and a parametric design space that allows for tuning device characteristics to meet specific requirements. Our work demonstrates that rigid compliant mechanisms used for fluidic switching, along with configurations such as n-stable devices, could be developed to create sophisticated yet accessible fluidic circuits in the future. The parameterized design approach allows for rapid prototyping and iterative testing, accelerating the development cycle for new fluidic devices. The introduction of bistable devices in our design will enable the creation of sequential logic and state machines, significantly expanding the potential applications of fluidic control systems. This opens low-cost, accessible, and automated fabrication avenues for nonelectronic control in environments, where traditional electronic systems may fail, such as in high-radiation areas, explosive atmospheres, or strong magnetic fields. Future work should focus on exploring alternative materials and fabrication techniques to overcome current limitations related to device size and manual assembly. Investigating the integration of rigid compliant mechanisms with other soft materials could lead to hybrid systems that combine the advantages of each material, enhancing overall performance and functionality.

Conclusion

Our work bridges the gap between the simplicity of flexing beam mechanisms and the complexity of fluidic logic circuits, introducing a novel, accessible method for nonelectronic control of soft robotic systems. By demonstrating the feasibility and potential of using compliant mechanisms with flexing beams for fluidic switching, this work paves the way for a wide range of innovative applications, from simple logic gates to complex state machines and sequential logic systems. This approach holds promise for simplifying the design and fabrication of fluidic circuits, thereby making advanced fluidic control systems more accessible and versatile.

Experimental Section

Fabrication of Compliant Mechanism with Flexing Beams

The compliant mechanism with flexing beams was entirely 3D-printed using a dual-head desktop FDM printer (UltiMaker S3, UltiMaker) (Section 10 and Figure S10, Supporting Information). We used PLA (Tough PLA, UltiMaker) as the primary printing material, along with the water-soluble support material (polyvinyl alcohol (PVA), UltiMaker). The mechanism designs were created in SolidWorks, and the STL (Standard Triangle Language) files were converted into G-code using a standard slicer (Cura 4.13.1, UltiMaker), with print settings recommended by the manufacturer. The PVA support material was dissolved in a water bath at room temperature for 15–20 h. The compliant mechanism requires 3 h and 22 min to print and can also be fabricated using any other desktop FDM printer.

For miniaturization, we printed the compliant mechanism with PLA resin (Tough Prusa Orange PLA, Prusa Research) on the SLA printer (SL1S SPEED, Prusa Research). We used default print settings with a layer height of 0.05 mm. After printing, the part was kept in an isopropyl alcohol bath for 3 min and cured for 2.5 min in the curing and washing units (CW1S, Prusa Research).

Fabrication of the Linear Actuator and Assembly of the Compliant Logic Device

We fabricated the linear actuator from TPU (Filaflex 60 A, Recreus) using a single-head desktop FDM printer (Prusa i3 MK3S+, Prusa Research). To improve filament feeding and prevent slippage, the printer was equipped with a Bondtech extruder featuring a 0.4 mm diameter nozzle and a dual-drive system with an increased gear reduction ratio (Bondtech Mk3S + Upgrade IDGA, Bondtech). Without this extruder upgrade, achieving airtight results was still possible. We optimized print parameters such as temperature, flow rate, and speed to consistently yield airtight results (Section 11, 12, Figure S11 and S12, Supporting Information). We tested the airtightness of the linear actuators by pressurizing them underwater to a maximum pressure of 395 kPa. After 6 h and 11 min, we finished 3D printing the linear actuator and subsequently assembled the actuator with the compliant mechanism and off-the-shelf tubing (51135K11 Semi-Clear White, McMaster-Carr) with connectors (Masterflex Fitting Kit, Avantor Fluid Handling). The total assembly time was 2 min.

Fabrication of the Stepper Motor, Linear Robot, and Fluidic Digital Display

All components of the stepper motor, linear robot, and fluidic display were fabricated using a single-head desktop FDM printer (Prusa i3 MK3S+, Prusa Research). The housing for the fluidic stepper motor was constructed with Polymaker PLA (1.75 mm, Amazon), accommodating a ball bearing (Donepart 626-2Rd, 6 × 19 × 6 mm, Amazon). Each linear actuator featured a slot to hold a circular magnet (10 × 3 mm, Amazon).

The linear robot was an extension of a linear actuator with eight pneumatic chambers; its body was printed with TPU (Ninjaflex 85A, NinjaTek), while its legs were made from PLA (Prusa PLA, Prusa Research) and assembled postprinting. For the pixel, the slit and body with the membrane were printed using two filaments (Filaflex 60A for the slit and Filaflex 70A for the body and membrane) separately and glued afterward. These pixels were placed in the display holder (Prusa PLA, Prusa Research), facilitating tubing routing at the bottom.

Data Measurements

We measured pressure to analyze valve behavior under various supply and actuator pressures and to characterize valves for geometrical parameters. We used a digital pressure gauge (MGA-9 V, SSI Technologies) and a manual pressure regulator kit (AFR2000, TAILONZ pneumatic). We connected an array of digital pressure sensors (ADP5151, Panasonic) to a data acquisition (DAQ) board (NI-USB-6009, National Instruments) and recorded all measurements using custom LabVIEW code (LabVIEW 2021, National Instruments). For hysteresis analysis, we gradually increased pressure input using a pressure regulator (SMC ITV0010-2BL, SMC Pneumatics). We connected a flow meter (AWM5104VN, Honeywell) to the DAQ board to measure flow output.

To analyze the life cycle of our device, we used an electronic three-port solenoid valve (ZHV-0519, Zonhen) controlled by a microcontroller (Arduino UNO Rev3, Arduino). We actuated the compliant mechanism at a frequency of 0.5 Hz. We merged outputs from the top and bottom tubes of our compliant logic device in a water container to examine the presence of air bubbles.

Acknowledgements

This work was supported by the National Science Foundation under grant no. 2237506.

Conflict of Interest

The authors declare no conflict of interest.

Author Contributions

Savita Vitthalrao Kendre: Conceptualization: (lead); Data curation: (lead); Formal analysis: (lead); Methodology: (lead); Validation: (lead); Visualization: (lead); Writing—original draft: (lead); Writing—review & editing: (equal). Markus P. Nemitz: Conceptualization: (lead); Funding acquisition: (lead); Investigation: (equal); Project administration: (lead); Resources: (lead); Supervision: (lead); Writing—original draft: (equal); Writing—review & editing: (equal). Cem Aygül: Conceptualization: (supporting); Supervision: (supporting); Visualization: (supporting); Writing—review & editing: (supporting). Calvin S. Page: Conceptualization: (equal); Data curation: (equal); Methodology: (equal); Validation: (equal). Lehong Wang: Methodology: (supporting); Validation: (supporting).

Data Availability Statement

The data that support the findings of this study are available in the supplementary material of this article.

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