Sarcomere‐Inspired Multilayer Artificial Muscle Units for Hyperconfigurable Robotic Applications

Soft pneumatic biomimetic robotic systems excel at the specific application they are designed for, often to interact or navigate unstructured environments safely. However, redeployment to new purposes requires substantial resources, from redesign to revalidation. Despite most pneumatic artificial muscles surpassing the power and contraction performance of natural muscles, natural muscles largely remain unmatched in terms of their versatility and complex performance. This is likely due to artificial muscle's low effective strain and high radial expansion, limiting parallel operating efficiencies. To address these challenges, a class of compact versatile pneumatic actuators, called multilayer artificial muscle (MAM), that are capable of deployment to different applications through configurable modularity, is presented. The MAMs are biomimetically inspired by the sarcomere, the building block for natural muscle architecture. Similarly, MAM can extend and contract as well as be rearranged to mimic muscle‐like actions and functions, such as a caterpillar locomotion robot and an entire robotic arm. The MAMs are fabricated through multilayer, multimaterial, low‐cost additive manufacturing, which offers certain advantages such as higher extension, contraction force, and durability. MAMs have the potential to provide a crucial fundamental building block toward future versatile reconfigurable architecture.


Introduction
The sarcomere is the fundamental contractile unit in all muscles to produce versatile, powerful, and efficient movement.The sarcomere is classified as linear actuators that produce force by contraction.Despite consisting of identical sarcomere units, all muscles are different in terms of their architecture due to the hierarchical structure resulting in various shapes, sizes, and functions.Complex muscle arrangements within the body enable adaptable movements, dexterity, force, and speed.Overall, our natural muscle [1,2] is a soft biological actuator with unmatched versatility, durability, self-healing, and compliance.This have inspired soft robotic actuators capable of muscle-like contraction, [3][4][5][6][7][8][9][10][11][12] also known as artificial muscle.Unlike traditional mechanical actuators (electromagnetic motors and pneumatic pistons), soft robotic actuators provide safe human-machine interactions through compliant materials, smart morphologies, and unconventional power sources, enhancing compliance and safety features.Although most artificial muscles have surpassed natural muscles in terms of force output, actuation strain, and power, their overall performance, adaptability, and versatility remain primarily unmatched.
[5][6] Fluidic actuators are selected for this work, as they remain unchallenged regarding force, efficiency, inherent safety, power, and durability compared to the other activation means.However, it can be bulky and noisy when considering the power system as a whole, especially for pneumatic actuation.Nonetheless, SPAs' advantages outweigh the drawbacks, particularly in scenarios that require safety, high force, and durability.
SPAs' simple working principle of expansion/contraction with positive and negative pressure requires mechanically preprogramming the SPAs to achieve diverse motions.][38] However, these methods are often designed for a specific application, which lacks versatility and requires substantial resources when applied to new applications.
To alleviate such issues, researchers have sought to make SPAs more reconfigurable and modular.][41][42][43] However, these SPAs often have significant radial changes, resulting in inefficient high-density parallel operations as actuators rub against each other causing frictional force or make user wearability difficult.Furthermore, many claimed to have a high extension, but their effective strain remains low.In addition, contraction often requires passive extension designs.All these factors contribute to generally bulky SPAs.45][46][47] However, these often lack the ability to return to their initial state rapidly without external factors.
Here, we introduce the concept of a new artificial muscle unit that combines other SPA advantages and solves the aforementioned drawbacks by having high strain, low radial expansion, passive compactness, rapid self-retractability, reconfigurability, modularity, and high contraction forces.Drawing inspiration from a sarcomere unit in our striated muscles, we developed an actuator that similarly contracts, extends, and regulates force output through a modular arrangement of series and parallel units.We named this actuator the multilayer artificial muscle (MAM).Figure 1 shows a brief overview of the MAM, showcasing its likeness of a sarcomere muscle unit, its ability to be scalable and tunable, fabricated using low-cost additive manufacturing, and its capability to output different motions and applications through configurable modularity (Movie S1, Supporting Information).

Results
The MAM was fabricated solely using thermoplastic polyurethane (TPU) filaments printed using a modified low-cost fused deposition modeling (FDM) 3D Printer.Three TPU types, which differ in their Young's modulus and shore hardness, were used to fabricate the MAM.In this article, the materials used will be denoted by their shore hardness, from softest to hardest, 60A (Â60, Diabase Engineering, USA), 85A (Ninjaflex, NinjaTek, PA), and 75D (Armadillo, NinjaTek, PA).The rationale for using different materials ranging in shore hardness enables increased durability and performance.
Figure 2 shows how the cross section of the MAM closely resembles the sarcomere unit by evaluating the key components in their extended and contracted state.The sarcomere working principle is due to a chemical reaction called adenosine triphosphate hydrolysis, sliding the actin (thin filament) and myosin The MAM is fabricated using low-cost FDM printing which can be scalable or tunable to allow for a wide range of applications.Furthermore, the MAM can be utilized standalone or in hybrid designs enabling modular and reconfigurable applications such as a continuum robot or as an artificial muscle powered arm.
(thick filament) past each other, shortening the sarcomere length.In a similar mechanical fashion, the MAM is an actuator with a collapsible internal air chamber that contracts when pressurized air is removed.In our design, the MAM inner chamber has a "myosin" head that slides forward and back comparable to the sarcomere's working theory.
The MAM has a simple fabrication of utilizing a singlenozzle FDM printer to print different TPU layers on top of each other.The main portion of the MAM was fabricated using alternating layers of high-(85A) and low (60A)-Young's-modulus elastomer.The lower-Young's-modulus elastomer provides increased extension, while the higher-Young's-modulus elastomer acts as an antagonistic layer to restrict radial expansion and increase actuator durability.When pressurized air is introduced, the mirrored square-wave-like structure (MAM cross section) unfolds, causing the MAM to extend.In contrast, the material's tensile properties and design allow the MAM to collapse and contract back to its original compact state upon depressurization.Contraction decreases depending on the applied load, but vacuum pressure can be used to increase the generated contraction force.The sarcomere's Z-disk separates adjacent sarcomere, anchors actin filament, maintains structural integrity, and assists in the force transfer.The MAM's Z-disk works in a similar manner, by anchoring the "actin," separating and jointing multiple MAM units together, and upholding its structure and aiding in the force transfer.The MAM's Z-disk were made from "rigid" TPU (75D), providing an airtight seal and allowing for modularity through assembly.The M-line is in the center of the sarcomere and helps stabilize the myosin filaments.Similarly, the MAM's M-line (made from 85A) helps in stabilization and prevents buckling when vacuum pressure is used to increase the contraction force at high loads.The MAM also resembles other components of the sarcomere, such as the A-band (a region of myosin and actin filament that does not change in length) and I-band (a region of only actin filament that changes in length during extension and contraction).
In addition, the MAM can be easily scalable by changing specific parameters (Table S1, Supporting Information).In this article, we showcase a small MAM that can be printed at milliscale, with an alternating material layer of 1 mm with a width of 0.6 mm.The medium and large MAMs were scaled two and four times bigger than the small MAM.Alternatively, we can also redesign the MAM.We then illustrate how versatile and modular the MAM is for an array of applications when assembled together, similar to how a sarcomere is the fundamental building block of our various muscle architectured and functions.

Bimaterial Bonding and Finite-Element Analysis
Before performing finite-element analysis (FEA) on commercial FEA software ABAQUS (Dassault Systèmes), uniaxial tensile characterization of each material was conducted to determine the material properties and analyzed to select the best hyperelastic model for FEA (Figure 3; Table S3, Supporting Information).Both crosswise and longitudinally printed TPU samples demonstrated similar results.As such, crosswise data was selected for FEA and bimaterial bonding.To determine the bond strength, a bimaterial dogbone was fabricated by printing one material over another, as shown in Figure 3B, at a 45°angle (scarf joint) and subjected to uniaxial tensile testing.Three variations of the bimaterial dogbone were printed, that is, the 75D-85A bond, 75D-60A bond, and 85A-60A bond.The 75D-60A bond was the weakest with an ultimate tensile strength (UTS) of 5.54 MPa, followed by the 75D-85A bond at 7.43 MPa and the 85A-60A bond at 12.1 MPa.
FEA was performed using the "best-fit" hyperelastic model.Three FEA characterization tests were conducted on the various-sized MAM, that is, 1) MAM's extension up to 300 kPa, 2) blocked force generated up to 200 kPa, and 3) pull force generated at 100% stroke at vacuum pressure increments of À20 kPa from no vacuum pressure to À60 kPa.These data were compared with the experimental data below.In addition, FEA can also be used to analyze the von Mises stress, which is crucial during expansion.The FEA data shows that the highest stress concentration during the 300 kPa extension was located on the inner layer between 85A and 60A bond at under 9 MPa, lower than the bimaterial bond UTS.

MAM Performance
The MAM was subject to different characterization tests, as shown in Figure 4 and 5, mainly extension, blocked force, and contraction force to validate the FEA results, as well as cyclic durability and dynamic response to explore the MAM viscoelastic effects and speed.To better understand why the alternating material approach is beneficial, we compared the MAM with its pure material counterpart in Supporting Information (Figure S3-S5).Ultimately, the MAM with alternating layers of 85A and 60A materials had better durability, extension, and pulling force output than the pure 60A actuator.
We first characterized the MAMs extension (Figure 4B) by pressuring the MAM at 10 kPa increments up to 300 kPa.Due to the material tensile properties and the MAM wave-like design, the MAM exhibited a telescoping effect, whereby a certain pressure was required to unfold the wave.The maximum extension for the small, medium, and large MAM was 9.40, 22.9, and 53.5 mm, respectively.The blocked force (Figure 4C) at 200 kPa for the small, medium, and larger MAM was 18.5 N, 76.2 N, and 342 N, respectively.The experimental extension and blocked force data followed the FEA closely with slight variations, likely due to the 3D printer's printing accuracy to print narrow widths.For the small MAM, this could result in a slightly stiffer MAM (overextrusion), resulting in less extension and blocked force.The medium MAM, on the other hand, showed slightly delayed telescope effects.As for the large MAM, slight deformation on its end caps was observed during pressurization, resulting in higher extension during data collection and lower blocked force than the FEA simulation.
Next, we investigated the MAM's contraction force with no vacuum pressure (0 kPa) and at negative pressure intervals from À20 kPa up to À60 kPa.The MAM was subjected to a tensile pull at a constant rate of 0.5 mm per second at %100% of its stroke.Our area of focus was the contraction force of the MAM when it is close to its initial compact state at 2 and 5 mm extension for the small and medium.Without vacuum pressure, the MAM can exhibit high contraction force depending on the extension, and the contraction force can be further increased when subjected to negative pressure.For the small MAM (Figure 5B), the contraction force at the 2 and 5 mm extension without vacuum pressure was 7.5 N and 13.8 N, respectively, which can be increased with vacuum pressure (À60 kPa) to 13 N and 19.3 N, respectively.Likewise, the medium MAM (Figure 5C) had 18 N and 39 N, respectively, without vacuum at the 2 and 5 mm extension, and 32 N and 55 N, respectively, when À60 kPa vacuum pressure was applied.The larger MAM (Figure 5D), due to its thicker width, resulted in an increase in stiffness and contraction force.At the 5 mm extension point, the contraction force without and with À60 kPa vacuum pressure was 51.8 N and 120 N, respectively.Hence, the contraction force performance depended on the load pulled, the size of the MAM, and the vacuum pressure used.Overall, compared to PAMs capable of returning to their initial state and our natural muscles, the MAM exhibits better strain with higher contraction force depending on the size and pressure used.FEA simulation trends with the experimental data; however, at the initial point (0% stroke), FEA contraction starts off stronger, likely due to damping.
We then tested the medium MAM cyclic durability at 150 kPa pressure.The MAM had an average durability above 24 k cycles.However, it also had a considerable standard deviation of 11 k cycles, depicting that plastic deformation likely changes the MAM properties over time.In addition, this resulted in slight permanent changes during the return phase (depressurization).From Figure 5E, the initial state of the MAM was not recovered, likely due to the material's viscoelasticity.After stopping the test after 20 K cycles, the MAM recovered to an average of 27% stroke slowly.However, we showed in Figure 5F vacuum pressure could eliminate the viscoelastic effects and reduce the permanent damage to the MAM during cyclic loading, returning to an average of 15% stroke almost immediately upon depressurization after 20 K cycles.We also tested the contraction force before and after cyclic loading to failure to observe how the plastic deformation with failure changes the performance (see Figure S6 and S7, Supporting Information).Overall, depending on the failure size and location, there is an observed small decrease in the contraction force performance, although this could be negligible if vacuum pressure is increased.In addition, we tested the dynamic response of the medium MAM (Figure S8, Supporting Information), with ten actuation cycles with input frequency spanning from 0.5 to 3 Hz at 200 kPa pressure without vacuum pressure, to showcase how fast the MAM can actuate and return its initial position.At 3 Hz, the MAM could return to its original state; however, it requires more time to extend, although this strongly depends on the system flow rate.

MAM-Based Continuum Robot
The MAM end caps can be redesigned to allow for modularity.Using the medium-sized MAM, each end cap was designed with a threaded hole to enable the MAMs to connect to each other in series.We created a continuum robot with three parallel rows of three MAMs in series (Figure 6).A 3D-printed 1 mm rubber grommet was designed to hold the MAMs at each intersection, constricting the rows of MAMs together to prevent unwanted buckling and increase bending.We briefly demonstrated the continuum robot's ability to be used as a parallel manipulator that generates multiple degrees of freedom (multi-DOF) and caterpillar crawling locomotion.The parallel manipulator multi-DOF motion is produced by activating one or more MAM in series to produce a bending effect toward the unactivated MAM row acting as an antagonistic layer (Figure 6A).
As for the caterpillar locomotion robot, we feature a continuum robot similar to Figure 6A but with individual MAM control.This was achieved by connecting each MAM to a 12 mm spacer, which only directs airflow to a single MAM unit and blocks airflow from the connecting unit, increasing the system length to 120 mm.The caterpillar robot has motion somewhat akin to a caterpillar, whereby it starts extended, followed by a wave-like action swinging its hind legs forward to inch itself. [48]s shown in Figure 6B, the caterpillar robot was placed on the ground, with two parallel rows of MAMs on the ground.To initiate crawling, all MAM units were fully extended.Crawling was then achieved by sequentially deactivating the bottom MAMs sequentially (0.15 s delay) from front to back and activating them back in reverse.The single toprow MAMs remain activated, which causes the robot to bend when deactivating the bottom rows.This bending motion inches the back legs forward upon deactivation and pushes the robot forward upon activation.Small TPU rubber legs lift the robot 2 mm above the ground and help to provide some friction to improve the crawling at 20.2 mm s À1 (Movie S3, Supporting Information).It is worth noting that the connecting tube to each individual MAM had to be supported over the robot to decrease the drag and friction caused by the tubes.

MAM-Powered Robotic Arm
Apart from the scalability of the MAM, it can also be tuned by redesigning (see Supporting Information).Here, we reshape the MAM to a more curved form to create a more compact MAM to conform to the human body curves for wearables such as an elbow flexion and/or extension assistive device.To validate this claim, we tested the MAM on a robotic arm (Figure 7).Additionally, we developed the robotic arm to be modular to demonstrate the MAM versatility by adding different modules to output basic motions, that is, extension (Figure 7A) and contraction (Figure 7B) from the biceps and triceps module, bending from the finger modules (Figure 7D), and rotation/twisting from the wrist module (Figure 7D).We would further like to emphasize that the same MAM was used throughout the entire robotic arm.
For biceps and triceps extension and contraction, we designed and printed an upper arm connected to the forearm via a hinge joint, allowing it to pivot at 130°.In addition, we attached the bicep and tricep modules akin to our arm, at 20 mm away from the pivot point for the bicep tendon and just under the pivot point for the tricep.Due to the placement of the tendons, the bicep module required six MAMs in series to provide the extension needed to fully extend the arm, whereas the tricep module required four MAMs in series.The top of the MAM modules was then anchored to the upper arm, and the bottom MAM modules were connected to 6 mm-wide nylon cloths acting as tendons, which were attached to the forearm.The bicep and tricep modules work antagonistically to provide flexion and extension.We tested the dynamic and static loading force that the bicep modules can achieve (see Figure S4, Supporting Information), with various input vacuum pressures (0-60 kPa) and increasing the number of parallel bicep modules.Weights of 100 g increment were loaded onto the forearm until the arm flexion angle reached lower than 90°(Figure 7E).The weight was placed 150 mm away from the pivot.We showcase that increasing the "muscle density" or having muscle bicep modules in parallel increases the dynamic force output.Three bicep modules were able to dynamically lift 2.7 Kg to 90°flexion.Combined with the forearm weight of 0.35 Kg, that is %4.5 Nm of torque generated, which is more than enough to support an average person (<4.45 Nm, [49] ), the tricep force was more challenging to test, but we showcased the max tricep extension blocked force with three tricep modules at À60 kPa pressure by having the arm pull down on a force gauge (Figure S11, Supporting Information).The tricep achieved an average of 14 N, which is %4.2 Nm of torque.In Figure 7C, we show the arm's position when power was cut off, illustrating the safety of the MAM during a power failure, providing passive assistance.
A simple hand was designed to allow the MAMs to be directly used as an end effector.The finger modules were assembled by weaving a 10 mm nylon cloth along each MAM, anchoring the cloth between each connecting MAM with a 3D-printed 2 mm plate.Upon pressurization, the cloth acts as a strain-limiting layer, causing each MAM module to bend at an angle of %32°a t 200 kPa, closing the hand.In addition, a MAM can be placed within the palm to abduct the fingers (Figure 7G) when activated.
The wrist module consisted of two modular components, one to provide rotation and the other for various deviations.The rotational module was designed to provide pronation upon pressurization and supination upon depressurization, although the reverse is also possible if we mirror the design.The rotation was achieved by anchoring down five MAMs in series, 30 mm away from the pivot point, around a ball bearing.The first and last MAMs were constrained to the inner and outer ball bearings, allowing the ability to friction lock the first MAM down to the robotic arm and provide smooth rotation when pressurized.Five MAMs provide %62.5°of rotation at 200 kPa.The rotating performance is not ideal, considering five MAMs leave only %110°of free rotation.Nevertheless, this provides an insight into how adaptable and modular the MAMs are.As for the other component, four MAMs were placed antagonistically to each other to provide flexion and extension (AE8.6°) or radial and ulnar deviation (AE8.5°),depending on which was activated.
Overall, we showcased the redesign MAM's configurable modularity to different applications.The MAM was designed such that all modules can be connected in a hybrid approach or standalone.We showcased more applications in Movie S3, Supporting Information, demonstrating a simple endoscopic demo with a continuum robot for potential teleoperation assistance (Figure 6C) using the redesigned MAM for a slimmer profile.In Movie S5, Supporting Information, we demonstrated various applications of the robotic hand and arm, such as holding various objects (Figure 7N-Q), holding and pouring water (Figure 7R), attaching the entire robotic arm onto a UR5 (Universal Robots, Odense, Denmark) to show a punching motion(Figure 7S), attaching the hand on an UR5 to pitch and grab a tissue to pass to a person, and playing on a xylophone for a Christmas greeting.

Discussion
We present a sarcomere-inspired novel fully 3D-printed compact multilayer multi-material actuator with a wave-like design whilst showcasing the materials' bonding strength, the MAM's characterization and the MAM's versatility in a hybrid approach.The MAMs have performance comparable to state-of-the-art PAMs (Table S4, Supporting Information), while showing better versatility.In addition, the MAM has better max strain, which when compared to other SPA bicep muscle-like demonstrations [3,4,6] allows for full arrangement of motion (>120 flexion/extension) depending on the applied load.The demonstrated bicep/tricep modules were able to generate high torque for potential assistive or rehabilitative application.The MAM has specific power (0.289 kW kg À1 ) close to our natural muscle but exhibited the lowest specific power among other SPA artificial muscle, because the MAM utilizes vacuum pressure for contraction instead of positive pressure.The vacuum pressure used in this work was À60 kPa with a vacuum flow rate of 11.9 L min À1 , providing an actuator efficiency of 23.1% when subjected to a 4 kg load.Overall, the MAM provides a few key advantages: 1) increased extension when the wave structure unfolds with positive pressure, 2) increased contraction force when vacuum (negative) pressure is applied, 3) increased durability, 4) high initial tension (self-retractability) which also aids in the contraction force output since vacuum pressure is limited to À100 kPa, 5) versatility through reconfigurable modular assembly, and 6) limited radial expansion for efficient parallel operation.This work takes a design-centric approach to adaptably utilize the MAM with various hybrid applications.Essentially, we can think of the MAM as a versatile artificial motor unit that can translate its linear motion into functional applications, to animate devices or be used directly as an end effector.Furthermore, the MAM presented moderate cyclic durability of 10 5 cycles when subjected to positive pressure, and even when a failure occurred (rupture between the layers), it showed negligible effects on the MAM contraction performance.
Although multilayer printing of material for the MAM provides certain advantages (see Supporting Information), its main limitation lies in its multistep fabrication.Even though we can sequentially print multiple actuators simultaneously, each layer still requires manually exchanging the filament and applying tape to prevent unwanted layer adhesion at certain layers.While other 3D printers with multiple tool heads can automatically switch material, these are costly alternatives and might not be able to print flexible filament effectively.Each actuator, if printed alone, takes %100 mins, not including loading times.Another drawback of the MAM depends on its applications, such as for antagonistic effect (as shown in the arm), which requires one set of MAMs to be activated.This could potentially reduce durability depending on input pressure.In addition, increasing the contracting force requires vacuum pressure, which is limited to a maximum of À100 kPa; therefore, increasing the contract force output further requires further tuning the stiffness or design of the MAM.The MAMs were also subjected to a common problem in SPA, called hysteresis (Figure S14, Supporting Information).This is due to the high initial tension of the MAM, requiring higher pressure to overcome but lower pressure to maintain during the return phase.However, the MAM extension was more stable at high pressure and during the return phase.In general, this issue makes future control implementation more complicated.In additional, applications that require multiple MAM units, especially if individual control is required, have complex tubing that adds to the weight and bulk of the system.In general, these issues make future control implementation more complicated.
As multimaterial printing for soft materials matures, MAMs can potentially provide a crucial fundamental building block for versatile soft robotic applications.Future work will explore a comprehensive material selection and characterization to provide a more accurate FEA.An analytical model will be explored to easily retune the MAM, although this is potentially challenging when reshaping the MAM.The low-cost fabrication and modularity show how accessible the MAM is to anyone, and assistance or strength augmentation wearable applications will be explored.

Experimental Section
MAM Fabrication and Application Assembly: The MAMs were modeled in Autodesk Fusion 360.Each layer was converted to stereolithography (STL) files to be imported to a slicing software (Simplify3D L.L.C., OH) into g-code format to print.To fabricate the MAM, we modified an Ender 3 Pro (Creality 3D Technology Co., Ltd., Shenzhen) with a direct drive extruder (Diabase Engineering, USA) with a 0.40 mm-diameter nozzle.Before printing the MAM, the print parameters were tuned to print each material to ensure each layer was printed without over-extrusion and with no internal gaps at a 100% infill.Since we used a single-extruder 3D printer, the MAM was printed layer by layer, manually switching out filament when completed.The rational for using a single-nozzle low-cost FDM printer, despite many advancements in this field, [50][51][52][53][54][55] was the fact that it can be easily modified and tuned to reliably print highly flexible 60A filament with high durability.More details on the fabrication steps, printer modification, and printing parameters (Table S2) are present in Supporting Information.
The modular continuum robot and the robotic arm were also modeled on Autodesk Fusion 360, and printed on a 3D printer using polylactic acid (PLA) material.To assemble the MAM to the various applications or connect the MAM together, a threaded insert (Mubux-M, Kerb-Konus, Germany) was used.This inset had both outer and inner thread, allowing for assembly and airflow.The inset was also used as an input source, as we can thread a polyurethane tube through or attach a fitting.
Material Characterization: A uniaxial tensile test on an Instron Universal Tester 3345 (Instron, MA) was used to investigate the various TPU material properties and the bonding strength between different TPUs.Following ASTM 412 (Standard Test Methods For Vulcanized Rubber And Thermoplastic Elastomers) guidelines, we prepared dogbone samples following the type C die.Each TPU sample was printed in two infill directions, crosswise and longitudinal, to determine if the properties were isotropic.Five samples from each TPU were stretched till failure at a 500 mm min À1 rate.The uniaxial tensile test results were processed using Matlab to determine the material Young's modulus and the average stress-strain data.The collected stress-strain data was evaluated using Abaqus to generate the coefficients of various hyperelastic models such as Yeoh, neo-Hookean, and Ogden.The bimaterial samples were printed one material over the other, by printing the second material over the first, connecting both pieces via a 45°scarf joint in the middle.This is not a fully accurate representation of how the bond is in the MAM, as we cannot print a flexible dogbone in a vertical orientation.Nevertheless, it gives us some insight into how strong the bond is.
Finite-Element Analysis: Before performing nonlinear FEA on the MAM, we had to determine the best hyperelastic model coefficients.The various hyperelastic models were compared against the average uniaxial tensile data, whereby the smallest sample standard deviation was used to determine which model fit best.For FEA, the MAMs were also modeled in Autodesk Fusion 360.Layers with the same materials were grouped and exported as a single.stepfile.This was then imported into ABAQUS, creating individual parts.The material behavior properties were input based on the obtained hyperelastic model (85A and 60A) and elastic model (75D) completely from uniaxial tensile test data (Table S3, Supporting Information).Sections were created based on each material and assigned to each part.Parts were then assembled and merged into a single part for meshing.A reference point was coupled to the top MAM end cap, allowing us to extract the extension and force output data.ENCASTRE boundary condition was applied to the bottom of the MAM.Next, individual steps were created to apply a load, such as gravity; pressure/vacuum or tensile pull, was applied depending on the test.As previously mentioned, extension, blocked force, and contraction force were simulated in FEA.Finally, the part was meshed using quadratic tetrahedral solid hybrid elements (C3D10H), chosen to account for the large deformations generated from hyperelastic materials.It is worth nothing that for blocked force and contraction force, the step requiring pressurization had automatic stabilization (damping factor of 0.0002) turned on, to solve nonconvergence due to the instabilities of nonlinear hyperelastic models.
MAM Characterization: Five characterization tests were performed on each MAM, that is, 1) extension, 2) blocked force, 3) contract force, 4) cyclic durability, 5) dynamic response.Extension tests for all MAMs were conducted three times at positive pressure of 10 kPa increments up to 300 kPa or until failure.A camera (Cannon EOS M50; Cannon) was used to record the extension data and extracted using an open-source image analysis software (Tracker, http://physlets.org/tracker).The extension test doubled as a durability test to determine if the actuators could withstand high pressure.However, for all other characterization data, we applied a safe working pneumatic pressure limit (<200 kPa, recommended by Occupational Safety and Health Standards 1910.242(b)).
For the blocked force and contraction force tests, data was extracted using an automatic vertical pull test machine (ALGOL Instrument Co., Ltd., Taiwan) that recorded force output with a 1000 N load cell and distance.Simple mounts were designed and printed to hold the MAM samples in place onto the machine's base and the load cell's tip.The blocked force was conducted with the load cell fixed in place (isometric), and the force was recorded at pressure increments of 10 kPa, up to 200 kPa.For the contraction force test, the MAM was subject to a tensile pull rate of 30 mm min À1 .Vacuum pressure was supplied at À20 kPa increments up to À60 kPa.The stroke pulled distance depended on the MAM variation at approximately 100% stroke length.
Cyclic durability was performed at 150 kPa at a 1 Hz square wave cycle on the medium MAM after contraction force testing.A test setup was designed to hold the MAM below a laser displacement sensor (BL-030NMZ, Boyi Jingke, Shenzhen).The test was performed without vacuum pressure and with À60 kPa vacuum pressure to see the viscoelastic effects over time.Cyclic durability time, extension, and pressure were captured and extracted from an Arduino Uno.The dynamic response test was conducted similar to the cyclic test with a distance sensor, but we used an electropneumatic regulator to output pressure.We applied a sinusoidal wave input at frequencies ranging from 0.5 to 3 Hz at ten cycles each (Figure S7, Supporting Information).

Figure 1 .
Figure 1.MAM overview and concept.(Center) MAM mimics a sarcomere unit when contracted and extended.(Overview)The MAM is fabricated using low-cost FDM printing which can be scalable or tunable to allow for a wide range of applications.Furthermore, the MAM can be utilized standalone or in hybrid designs enabling modular and reconfigurable applications such as a continuum robot or as an artificial muscle powered arm.

Figure 2 .
Figure 2. Comparing the MAM and sarcomere similarities in their extended and contracted states.The sarcomere's key components are actin filaments, myosin filaments, Z-disks, A-band, I-band, and M-line.MAM closely mimics the sarcomere design and functions, despite having a different working principle of a pressurized air chamber to illicit extension and contraction.

Figure 3 .
Figure 3. Various TPU material characterization tests.A) Dogbone-printed infill direction.B) Printed dogbone samples as well as the bimaterial dogbone samples.Bimaterial dogbone was printed with a scarf joint bonding (magnified side view).C) Stress-strain data for all dogbone samples and bimaterial dogbone samples.

Figure 4 .
Figure 4. MAM scalable size upon pressurization.A) Actual MAMs of various sizes in their unpressurized and pressurized states, and the FEA of pressurizing MAM with its Von Mises stress.B,C) Experiment and simulated results of the various MAM extension and block forces, respectively, when pressurized.

Figure 5 .
Figure 5. MAM contraction force and cyclic durability.A) Medium-and large-sized MAM holding and lifting a load of 4 and 10 kg, respectively.Holding the load when unpressurized (0 kPa), the medium and large MAM had some elongation.Both MAMs were capable of holding the load when pressurized (200 kPa) with high extension.When subject to vacuum pressure (À60 kPa), the MAMs were able to pull up the load with significantly reduced strain.B-D) Small, medium, and large MAM contraction force data.E,F) Cyclic durability of the MAM without and with vacuum.

Figure 6 .
Figure 6.MAM-based continuity robot.A) Parallel manipulator using nine MAMs connected in series and parallel.MAMs in series were powered together.Inactive (unpressurized) MAMs in parallel provide antagonistic effects allowing for various positioning.B) Caterpillar robot similar to Figure 6A with each actuator individually controlled to provide a crawling forward locomotion akin to a caterpillar.C) Endoscopic demo with continuum robot reassembled using the redesigned MAM for a slimmer profile.

Figure 7 .
Figure 7. MAM-powered robotic arm mimicking several upper limb movements.Taken from Movie S5, Supporting Information.A) Arm extension, showcasing the robotic arm with biceps, triceps, wrist, and finger modules.B) Arm flexion.C) Arm position when biceps and triceps modules were unpressurized.This showcases the MAM's safety ability in the event of a power failure.D) Finger module bending and wrist module twisting upon pressurization.E) Loading test.Showcasing that three parallel MAM bicep modules can hold 3 kg of load at À60 kPa pressure.F) Detached wrist and hand module at rest.G) Finger abduction.H) Finger flexion.I) Wrist supination.J-M) Four MAM actuators in antagonistic configuration provide wrist abduction, adduction, extension, and flexion, respectively.N-Q) Robotic arm with a friction lock thumb joint holding/pinching various items.R) The robotic arm holding a cup of water and rotating its wrist to pour water into another cup.S) The robotic arm on a UR5 simulates a pouching motion.