Braiding Polythene Lay‐Flat Tube into Cotton Threads for Artificial Muscle Actuation

In wearable robotics, soft actuation principles have been increasingly explored and tested due to their safety and comfort in human–robot interactions. Herein, a braided flat‐tube artificial muscle (BFAM) is presented. BFAMs are fabricated by braiding cotton threads together with an inexpensive lay‐flat tube (LFT) in a specific conform‐to‐LFT weaving method. They generate uniaxial contractions when powered by compressed fluids. The basic structure and working mechanism of the proposed BFAM are explained, and a quasistatic model is also developed. A comparison with other fluidic driven soft actuators is made and tabulated. Based on experimental studies, the proposed BFAM can contract close to 30% and yield force outputs more than 150 times their weight at an air pressure of 0.12 MPa. BFAM can be braided with multiple layers of flat tube without large increase of size. Experimental studies have shown that more layers of flat tube give a larger strain and output force up to four layers, beyond which layer increase does not yield visible improvement in strain and output force. Finally, potential applications of BFAM to arm joint actuations are illustrated to show its easy fitting to wearable robotics.


Introduction
Conventional actuators exhibit high efficiency and reliability in many tasks, yet their rigid structures and demands for accurate sensing are always concerning when they are required to interact with humans.Thus, for applications with human-robot interactions (HRIs), soft actuators have quickly attracted the attention of researchers due to their inherent environmental compatibility. [1,2]In pursuit of relatively safe HRIs, the activating method of soft actuators also needs to be considered carefully.Though thermally driven actuators demonstrate a relative safe actuating temperature range (25-42 °C), [3,4] fluidic actuators are generally less risky than electrically and thermally driven actuators, and at the same time with a larger cycle time. [5]rtificial muscles, [6,7] and wearables, [8][9][10] are typical applications in HRIs.Many fluidic soft actuators have been developed and adopted for these applications.
To better appreciate the performance of these fluidically driven soft actuators and clarify their suitability for HRIs, the human skeletal muscles [11,12] were also referenced, based on which Table 1 was produced.The major metrics employed for soft actuator evaluation in Table 1 are stress, strain, specific work, and radial/axial expansion.The radial/axial expansion intends to describe the inflation perpendicular to the direction in which the actuators contract upon excitation.The large radial or axial change of actuators may hinder the motions of users and make parallel placement of actuators difficult when pursuing high payload.Additionally, though some actuators demonstrate prominent performance at maximum pressurization, their maximum actuation pressure is too bursting to be possibly available and safe for applications with HRIs.In fluidic systems, a larger actuation magnitude commonly indicates a bulkier energy source system.Thus, to seek an efficient and meaningful comparison, Table 1 also refers to the performance of actuators at a typical pressurized state (0.1 MPa), which can be easily reached by a compact energy source.
[15] The muscle is made of a thin-walled rubber wrapped in a braided sheath with a crossed double-helix pattern.Upon pressurizing the inner rubber (bladder), the muscle contracts in length and expands radially due to the constraint of the sheath.Pleated pneumatic artificial muscles (PPAMs) [16,17] are a brilliant improvement of conventional McKibben muscles.By applying a folded membrane with an origami-like structure as the bladder, PPAMs spend much less energy in expanding the bladder and overcoming friction.They can generate stress of 0.67 MPa, contractions of 38%, and specific work of 1.1 kJ kg À1 at a maximum activation state of 0.4 MPa.However, for McKibben actuators (PAMs and PPAMs), their large radial expansions may obstruct their interactions with humans.These radial expansions demonstrate a convex shape, which occupies more design space than homogeneous (flat) expansions.[20][21][22] Because of the tiny dimension of the TPAMs and the planar shape of the entire composite structure, this type of actuator exhibits small and uniform radial expansions after pressurization.However, its composite structure and large surface area always lead to high internal friction, and some of its energy input must be used for the elastic expansion of the long TPAMs.Therefore, the TPAMs-type actuator is somewhat deficient in mechanical performance.It produces stress of 0.08 MPa, contractions of 2% at a typical pressurization of 0.1 MPa and stress of 0.33 MPa, contractions of 22%, and specific work of 0.023 kJ kg À1 at a maximum magnitude of 0.6 MPa.Though the conformable structure and textile-like appearance of the TPAMs-type actuator are attractive for applications with HRIs, better performance in an easily available actuation range may make it more practicable.
To further pursue a better performance than McKibben actuators, researchers proposed various designs, such as fluid-driven origami-inspired artificial muscles (FOAMs), origami-based vacuum pneumatic artificial muscle (OV-PAM), Cavatappi, and fabric artificial muscles.Both FOAMs and OV-PAMs are origami-based vacuum-activated actuators and are composed of skeletons and sealing films.The FOAM uses a skeleton with a zigzag origami structure and a thermoplastic-polyurethane (TPU)-coated nylon fabric as the sealing film.Upon vacuuming, external air pressurizes the film, and the actuator contracts driven by the tension force of the film.FOAM stands out for its strain of 90%, yet this great contraction decreases significantly with small payload increments. [23]The OV-PAM consists of a sealed polyvinyl chloride (PVC) film chamber connecting a top and a bottom plate and several unconnected, evenly spaced transversal reinforcements.Compared to the FOAM, it can still produce great strains even under large payloads.The OV-PAM generates stress of 0.6 MPa, a strain of >90%, and specific work of 0.19 kJ kg À1 at a maximum activation of À80 kPa. [24,25]Though FOAM and OV-PAM show superior operating properties, their space occupancy and adaptability are in doubt when interplaying with humans because of their relatively rigid skeletons and taut membranes (especially for large forces and contractions).In recent years, some researchers proposed the use of coiled-polymerfiber-based artificial muscles because of their remarkable performance, including fast actuation rate, high actuation load, etc. [26][27][28][29] However, it is a challenge to achieve high actuation load and high actuation stroke simultaneously.Cavatappi artificial muscle exploits the anisotropic microstructure of drawn polymer tubes to develop linear contractions.It can be fabricated to dimensions of less than 1 mm and allows for parallel configurations in principle.At the maximum actuation state near 2 MPa, Cavatappi demonstrates stress of 0.7 MPa, contractions of 50%, and specific work range 0.11-0.38kJ kg À1 .However, its performance degrades substantially under a typical activation (0.1 MPa).Stress of 0.24 MPa and slight contractions are shown at this state. [30]n general, the energy sources used by applications of HRIs are difficult to compress the air to the MPa level.The fabric artificial muscles are composed of multiple thin-walled fabric bladders connected in series.When pressurized, the bladders are inflated and contract axially.Because of the minimum energy used for expansion (no elastic deformation), the fabric artificial muscles require less energy input to achieve appreciable performance.26][27][28][29][30][31][32][33][34][35][36] In this study, we propose a new type of artificial muscle named braided flat-tube artificial muscles (BFAM) because of its braided-craft-like appearance (Figure 1).Lay-flat tubes (LFTs) are braided together with cotton threads in a specific conform-to-LFT weaving method to make the proposed BFAM.It is possible to braid a single layer of LFT into the cotton threads for smaller contraction or multiple layers of LFT for larger contraction as shown in Figure 1A.BFAM exploits the inflation (unfolding) of LFT-induced curling of cotton threads to develop axial contractions.Compared with the thin McKibben muscles, LFTs remain a sheet-like shape rather than rounded shape when uninflated.Furthermore, as the material of LFT is nearly inextensible, the proposed BFAM is more energy efficient as it does not rely on strain for actuation.Unlike the uniform radial expansion (from a small radius to a larger radius) of thin McKibben muscles, the LFTs bugle unevenly (from a flat layer to a circular shape) when pressurized.LFTs expand along the axis of the initial minimum diameters and contract along the axis of the initial maximum diameters.The latitude expansion of the thin McKibben muscles is unnecessary for the curling of the cotton threads and even may hinder the contraction of actuators, while the uneven deformation of LFTs avoids this problem incurring a more effective actuation (better performance with the same Table 1.Metrics of various fluid-driven soft actuators.

Metric
BFAM PPAM [14,15] TPAM [16] FOAM [21] OV-PAM [22,23] CAVATAPPI [24] FBA [25] Muscle [9,10] Stress  energy input).However, a single LFT has a limited amount of expansion regardless of the pressure input due to its nonstretchability, and the force output and contraction of BFAMs highly depend on the expansion amount.To overcome this limitation, multilayer LFT can be used.By braiding in the LFTs repeatedly to form a multilayer LFT structure, a larger contraction can be realized.Owing to the capability of stacking multiple layers of LFTs, the performance of BFAMs can be enhanced significantly, which will be introduced in detail in the modeling section.Eventually, BFAMs have the conformability and textile-like sheet appearance (Figure 1B,D) and demonstrate efficient actuation that matches and even surpasses other fabric-based actuators.As shown in Table 1, BFAMs can generate stress of 0.35 MPa, contraction of nearly 30%, and specific work of 0.026 kJ kg À1 at a maximum pressurization of 0.12 MPa.The BFAM employed for Table 1 is a quadruple-layer BFAM with a length of 160 mm, a width of 120 mm, and a weight of 70 g.The properties of the BFAM that have been exhibited, including considerable output, easily accessible energy input, conformable structure, and planar textile-like appearance are attractive for many applications with HRIs.Some potential applications of BFAMs include elbow flexion/ extension, wrist movement, and forearm supination/pronation as shown in Figure 1C.A mobile robot demonstrating the flexibility and versatility of BFAMs is also demonstrated in the figure.

The Braiding Patterns
The composition of BFAMs is very simple.Several cotton threads and a long LFT make up the BFAM. Figure 2A shows a prototype BFAM and its braiding pattern schematic illustration.The long LFT is braided into a textile sheet composed of cotton threads in a specific geometric configuration to realize a uniaxial contraction.The total braiding process is divided into two periods: the positive direction braiding from the start to the end and the negative from the end back to the start, as shown in Figure 2A.During the braiding process, three key points need to be followed, including the method for fixing the LFT in the textile sheet, the weaving path of LFT, and the LFT folding direction at the corners.The LFT can be braided into and fixed in the textile sheet through a basic warp-and-weft weaving method.The weaving path in the positive direction is a zigzag and is a reverse zigzag in the negative.These two opposing zigzag geometric configurations can cancel out the mutual motions except for the uniaxial contraction of the BFAM.At the corners, the LFT needs to be folded to create a zigzag geometry.The direction in which the corners are folded also influences the movement of the BFAM.To achieve a uniaxial contraction, the folding direction must be continuously reversed during the braiding process (folding up and then down, or in reverse).By braiding in the fashion mentioned above, the warp threads are jacked up in longitude by the weft LFT and contract in latitude when the LFT is pressurized by fluids.Furthermore, the BFAM with a multilayer structure can be fabricated by repeatedly stacking the LFT along the previous braiding path after completing the first braiding process.To characterize the specific structure of a BFAM, some parameters need to be defined, including the length and width of the BFAM, the diameter and number of warp threads, the circumference of LFT cross section, the number of weft sections, and the number of stacking LFT layers.These parameters play important roles in the performance of BFAMs and will be analyzed in the modeling section.

Quasistatic Modeling of BFAMs
To clarify the working principle of the LFT-based BFAMs, a quasistatic model analyzing the force output and contraction of the BFAM is established in this section.According to this model, parameters affecting the performance of BFAMs can be determined and optimized in further design.The parameters of BFAM employed and their abbreviations are illustrated in Figure 2B,C, including the initial length of BFAM L 0 , the final length L 1 , the width of BFAM h, the total number of the warp threads m, the diameter of the warp threads d w , the circumference of LFT cross section c, the number of weft sections N, the First, the resistance force f, including the major friction force and the minor obstruction originating from the mass of warp threads, remains the same during contraction and is proportional to the air pressure input P and LFT stacking number t.Second, the LFT and warp threads are nonstretchable.It indicates that the warp length and the LFT cross-sectional circumference always maintain the same.Third, the mass of LFT is neglected.That means the LFT without any load will be inflated completely under infinitely low pneumatic pressure input.Finally, as demonstrated in Figure 2C, the cross section of LFT is assumed as the splicing of two identical arcs with a radius of r, and it approximates a full circle of diameter d p when expanded completely.
To braid the LFT into the sheet made up of warp threads, the condition 2S/N > c þ (2tÀ1)d s must be satisfied, where S is the length of a single thread and 2S/N is the total length of warp in a weft section.As shown in Figure 2Bii,C, the supporting force F s of LFT to a single warp thread is Here, d le is the effective length of LFT section wrapped by the warp yarn when pressurized and θ 1 is the angle of zigzag braiding pattern.d le can be expressed as ∅ 1 and ∅ 2 are the angle at which the warp thread of the front and back end is jacked up by pressurized LFT.As demonstrated in Figure 2Bii,iii, ∅ 1 is equal to ∅ 2 only where the LFT completely overlaps (A-A section) and not elsewhere (B-B section).They can be approximated by Here, n describes the number of warp threads and nd w indicates the distance away from the overlapping (A-A section).Then, as shown in Figure 2Biii, the contraction forces of a single warp thread in two conditions F c1 and F c2 can be expressed as The total contraction force of F c of the BFAM depends on the total number of warp threads m.If m is the multiples of four, the BFAM can be considered as completely symmetrical.Then, the two conditions F c1 and F c2 emerge at the same times in the BFAM.By combining Equation (1-4), F c is the summation of F c1 and F c2 : Evaluating BFAM's motion needs to consider two scenarios that determine whether LFT can be fully expanded.The two scenes are detailed in the supplemental material.It is assumed that the LFT can expand completely over the pressure input range here.The BFAM will start to contract when F c ≥ ( f þ F load ) and terminate the contraction until F c = ( f þ F load ).Furthermore, to predict the force output and contraction of BFAMs, some geometric relationships are referred, including the constant circumference and the shape (the splicing of two identical arcs) of LFT cross section, and they are introduced thoroughly in the supplemental material.

Multilayer Structure of BFAMs
Because of the nonstretchability of LFT, the maximum expansion of a single LFT exists regardless of pressure input.The multilayer structure can increase the maximum expansion by accumulating the expansion of each LFT layer.Generally, a larger expansion amount of the LFT results in a greater contraction of the BFAM.The main factors that affect the maximum contraction of multilayer BFAMs are friction and the dimension of the LFT (the circumference of LFT cross section).The internal friction of multilayer BFAMs increases with the stacking number t of LFT due to a larger contact surface area.Though LFTs expand unevenly, multilayer LFT structure has a larger long diameter d l1 than the single-layer LFT structure and may hinder the tightening of warp yarns, as shown in Figure 2D.Therefore, with the same braiding pattern, smallsize LFTs are more unlikely to resist the movement of the warp threads, inducing a larger strain of multilayer BFAMs.Compared to single-layer BFAMs, besides greater strain, multilayer BFAMs also provide large contraction forces.As shown in Figure 2D, in the condition of the same total amount of expansion, the LFT segments wrapped by the warp yarn (or the effective length d le ) of multilayer BFAMs are greater than that of single-layer BFAMs.According to Equation (1, 4, and 5), the contraction forces of BFAMs F c are proportional to the effective length d le .In general, multilayer BFAMs exhibit better performance in contraction and force output.Experimental results in the subsequent sections also prove this proposition.Moreover, compared to single-layer BFAMs, the axial expansion or the ratio between the short diameter d s1 before and after pressurization of multilayer BFAMs is smaller due to the less individual inflation amount of each LFT layer.

Characterization of BFAM Actuation
With the working mechanisms of BFAMs analyzed, BFAM actuation performance characteristics can be estimated.
To present the practical actuation response of BFAMs, we have conducted several tests, including isotonic actuation test, isometric actuation test, hysteresis test, response time test, and fatigue resistance test.The strain, stress, and specific work demonstrated are characterized by these tests.The dimensions and materials of test actuators as well as the experimental setup will be clarified in the Experimental Section.

Isometric Actuation Response
To illustrate the isometrical response of BFAMs, four BFAMs made with different number of layers ranging from single-layer structure to quadruple-layer structure were fixed at their initial lengths and activated under increasing air pressure input.The test BFAMs were prestretched with a 5 N load to keep them from bending due to gravity, and the force and length at this condition were defined as the initial state.These tests measure the relationship between contraction force and compressed air pressure under isometric actuation.The results of the multilayer BFAMs are shown in Figure 3A.It shows that the force outputs of multilayer BFAMs are significantly enhanced by increasing the stacking number of LFT layers.However, as the number of LFT stacks increases, the enhancement effects diminish because of the increasing friction among layers.In supporting this observation, we also discuss the ideal maximum contraction of BFAMs when friction is neglected.For a specific braiding pattern (the number of weft sections N is known), because the LFTs may hinder the tightening of warp yarns, the limit of a BFAM's maximum contraction exists, as shown in Figure S5, Supporting Information.Therefore, when the stacking LFT layer number is high, the performance of BFAM approximates the limit and shows no visible improvement.It is also observed from Figure 3A that the contraction forces are linearly proportional to the input pressure in general except for the single-layer BFAM.As demonstrated in Figure 3D, the individual LFTs expansion of multilayer BFAMs is small (small increase in d s1 ) while that of the single-layer BFAM is comparably larger, inducing a nonlinear force versus pressure relationship, which also conforms to the mathematic model established.The quadruple-layer BFAM demonstrates a maximum contraction force reaching 111.7 N under a 0.12 MPa input air pressure.

Isotonic Actuation Response
The isotonic actuation test provides insights into how the contraction ratio of BFAMs depended on the air pressure.Besides, it also shows the relationship between the force generated and the contraction ratio of BFAMs.A 5 N load is attached to the four test actuators distinct in layer structures.According to Figure 3B, the contraction ratios of both multilayer BFAMs and single-layer BFAMs increase nonlinearly as the pressure input increases, and the slope of plot or the contract ratio degrades continually in general.Compared to the single-layer BFAM, the multilayer BFAMs display a clear improvement in contraction ratios, as shown in Figure 3B; yet the degree of improvement also reduces as the stacking LFT layer number increases, just like the isometric response mentioned before.Under the 0.12 MPa input pressure, the quadruple-layer BFAM deforms the most achieving a nearly 30% contraction ratio.Figure 3C depicts how the BFAM force output correlates with its contraction ratio.It is found that the contraction force is inversely proportional to the contraction ratio.Furthermore, the slope or the drop rate of contraction force for each type of BFAM also decreases.This is in line with the general property of soft pneumatic actuators.

Hysteresis Test
Soft mechanisms often exhibit a large hysteresis due to the flexibility of materials and structures.We concentrate on the hysteresis of BFAMs under both isometric and isotonic actuation in Figure 3E,F, respectively.No obvious hysteresis is shown by BFAMs under isometric actuation as shown in Figure 3E, while distinct hysteresis is exhibited by BFAMs under isotonic actuation as shown in Figure 3F.For the mechanism of BFAMs, as the LFTs and warp threads are inelastic, friction is the main factor contributing to hysteresis.Under isometric actuation, as the movement of BFAMs is constrained, causing limited friction, thus only slight hysteresis is observed.However, under isotonic activation, the BFAMs contract and produce non-negligible friction (mainly from the sliding between warp threads), therefore obvious hysteresis exists in this case.

Response Time Test
We focus on the response time of BFAMs in Figure S2, Supporting Information.Under the 0.1 MPa air pressure input, it takes nearly 1.4 s for the BFAM to reach a full maximum contraction.This time is highly dependent on the energy rate provided by the energy source.The BFAM extends back to the near initial position in 4 s.The extension time is mainly determined by the load and the internal friction in BFAM.Furthermore, because of the inelasticity of the BFAM structure, no obvious damping phenomenon is observed during its contraction and extension process.

Fatigue Resistance Test
A fatigue resistance test is conducted to investigate whether the non-negligible internal friction would severely shorten the life of BFAMs.The triple-layer BFAM is actuated 3000-cycle under 0.1 MPa air pressure and 2 N load.The cycle frequency in this test is 0.25 Hz.After the 3000-cycle fatigue test, no obvious performance degradation of the sample BFAM is observed, as shown in Figure S3, Supporting Information.In principle, the internal friction may lead to irreversible damage to cotton threads and LFTs, thus obvious fatigue of BFAMs may be found after a much larger cycle time.

Potential Application of BFAMs
To illustrate the operability, practicality, scalability, versatility, and compliance of BFAMs, we developed several potential applications of the proposed BFAMs, as shown in Figure 4. We mainly focus on showing their performance in applications related to human robot interactions.A video file Movie S1, Supporting Information, is supplemented to provide a clearer observation of the sample applications.

Scalability
BFAMs have composite structures and utilize materials that are easily available as well as scalable.The circumference c of commercially available LFT cross sections varies from a few millimeters to several hundred millimeters.Therefore, BFAMs are characterized by superior scalability and can be used to realize devices of different sizes from millimeter to meter scale.The fundamental dimensions of BFAMs are length and width.The maximum contraction displacement of the BFAM is proportional to its length.The BFAM width is directly related to the contact surface between warp threads and LFTs and determines the force output of the BFAM.Several prototypes have been fabricated to explore the scaling of BFAM for different applications.Figure 4A demonstrates two BFAM prototypes of different dimensions.The larger BFAM is more than 4 times the size of the smaller one.

Potential Applications to Wearable Robots
Normally, wearable robots should always resemble commonly worn fabric or garment-made clothes.It indicates that users prefer wearable robots to possess the lowest possible bulk, profile, weight, and opacity in the precondition of the capability of sufficient force and displacement.BFAMs appear to be able to meet the above requirements.We provide potential applications of BFAMs to wearable robotics through a mannequin.As shown in Figure 4B-D, a mannequin wearing various size BFAMs accomplishes several humanoid motions, including elbow flexion/extension, wrist movement, and forearm supination/ pronation.The range of elbow and wrist flexion/extension reaches 130°and 90°, respectively, and the supination/pronation of forearm also achieves 90°.By wearing the BFAMs, the movement of the mannequin wrist and forearm reaches almost the maximum range of motion of the average person.A longer BFAM can provide more elbow flexion/extension for the mannequin in principle.The parallel placement of BFAMs may fulfill the high force requirement of some applications, such as function augmentation.Furthermore, the input air pressure for the sample applications shown in the demonstrations is less than 0.12 MPa.This suggests that the energy source demand is readily available and could be made compact and lightweight.To realize the forearm supination/pronation, the BFAM is bent and twisted to a specific configuration around the forearm.This does not affect the normal operation of the BFAM.It indicates that BFAMs are flexible and compliant even pressurized.BFAMs also have cloth-like appearance, acceptable opacity, and small axial expansion when activated as in Figure 4. Overall, BFAMs are applicable and promising for wearable robots.

Mobile Robots
To display the flexibility and versatility of BFAMs, we also used it to fabricate a mobile robot, as shown in Figure 4F.By attaching a constraint layer to one facet, the BFAM realizes an out-of-plane bending.The prototype can crawl forward through appending an adhesive film and a film with less adhesive to the upper face and lower face of the BFAM, respectively.The planar shape of BFAMs results in less air resistance, making them potentially appropriate to be employed in mobile robots.

Conclusion and Discussion
A new family of artificial muscle, referred to as BFAM is proposed in this article.A BFAM is fabricated by braiding LFTs together with warp threads in a specific conform-to-LFT weaving pattern.When the LFT is inflated, the warp threads are jacked up by it, and the BFAM produces a uniaxial contraction and force output.The braiding patterns and the structure of BFAMs are illustrated for a clear fabrication process characterization.The multilayer structure of BFAMs is developed to increase the maximum contraction by accumulating the expansion of each LFT layer.Moreover, a quasistatic model is also established to clarify relationship between motion or force of BFAMs and air input pressure.In accordance with the mathematical model, major parameters relevant to the performance of BFAMs are determined, which can provide guidelines for BFAM design.Several tests, containing isometric actuation, isotonic actuation, hysteresis, and response time test were conducted to characterize the activation response of both single-layer BFAMs and multilayer BFAMs.It is proved that the multilayer BFAMs have significantly improved performance.From the results, the BFAM can yield strains of nearly 30%, and contraction forces exceeding 110 N, more than 150 times their weights.Sample wearable robot prototypes have been developed to demonstrate the remarkable advantages of BFAMs in applications with HRIs, such as planar shape, garment-like appearance, good scalability, high conformability, and comparable low requirement for energy input.A mobile robot prototype is also demonstrated to illustrate other potential uses for BFAMs.
Though the presented BFAMs exhibit promising performance and application prospects, some challenges still exist that need further investigation.To be practically wearable, BFAM's breathability needs to be considered in addition to its opacity.BFAMs may lack breathability due to densely packed cotton threads.Some fabric artificial muscles have humidity-adaptive breathability, which can provide a good reference for further development of BFAM. [37]The analytical model we established can predict the force and motion of actuator in general, yet the model is only for the quasistatic state.A dynamic model for achieving precise realtime control should be developed in future work.The braiding patterns inducing other motion of BFAMs except for contraction will be investigated as well.If BFAMs enable multiple motions, such as twisting and elongating, their potential application scenarios will be more extensive.Furthermore, human testing using the developed BFAM wearable prototypes will be conducted in the near future to assess the real applicability.The application of BFAM in mobile robots is still in a very preliminary stage.More possibilities for braided mobile robots can be explored in the future.We expect our studies can stimulate more research interests on BFAMs and explore their applications in various fields.

Experimental Section
Materials: Several BFAM prototypes based on the proposed method aforementioned were made to demonstrate both their appearance and functionality.The main materials of BFAMs need to be selected are LFTs and warp threads.The LFTs used are low-density polyethylene tubes of 12 mm pressed width and 1 mm thickness (cross-sectional circumference of 25 mm).The warp threads utilized are cotton threads of 2.5 mm diameter.Both the LFTs and warp threads are commercially available at low cost.Twenty-eight cotton threads of 175 mm length and a long LFT that is braided to 3 weft sections are applied in the BFAM prototypes used for tests.The triple-layer BFAM prototype is used in hysteresis test and response time test.The length, width, weft section numbers, and weight of the BFAM used for assisting wrist movement are 130, 80 mm, 3, and 30 g, respectively.The BFAM employed in the forearm supination/pronation device has a length of 140 mm, a width of 70 mm, weft sections of 5, and a weight of 35 g.To accord with the human elbow joint, the length, width, weft section numbers, and weight of the BFAM are designed as 200, 110 mm, 5, and 75 g respectively.For the mobile robot, it is characterized by a length of 124 mm, a width of 85 mm, weft sections of 5, and a weight of 36 g.
Metric Characterization: The metrics adopted for soft actuator evaluation are stress, strain, specific work, and radial/axial expansion, as shown in Table 1.Stress is defined as the generated force upon excitation normalized to the initial cross-sectional area of the actuators at rest.Because the BFAMs have composite structures, their initial cross-sectional area can be regarded as the initial volume divided by the initial length.The definition of strain here is the change in length upon excitation normalized to the initial length.The strains of BFAMs are just the contraction ratio that we have measured.Specific work refers to the output work generated by the actuators upon activation normalized to the mass of the actuators.The output work produced by BFAMs approximates to the calculated area under the force versus contraction displacement curve, as shown in Figure 3C (just change the contraction ratio to displacement).Radial/axial expansion can be considered as the evaluation of the inflation perpendicular to the direction in which the actuators contract when activated.The ratio between the radius or height (short diameter d s1 for BFAMs) before and after pressurization can give a reference for this metric.This ratio for the triple-layer BFAM prototype used in tests can be less than 2 under 0.1 MPa.
Experiment Setup: To characterize the actuation response of BFAMs, four tests in total have been accomplished, including isometric actuation test, isotonic actuation test, hysteresis test, and response time test.The previous three tests were conducted through the experimental platform, as shown in Figure S1, Supporting Information.One side of the BFAM is fixed and the other side is connected with a force sensor (DS2-200 N, Zhiqu, China) through wire ropes.The force sensor is installed on a stabilized linear guide with an encoder, whose displacement is recorded by a data terminal.The sampling frequency and resolution of the force sensor are 1000 Hz and 0.1 N, respectively.The input pressure's amplitude and frequency are controlled by a pressure regulator.For the isometric actuation test, by increasing the pressure in a constant interval (from 0 to 120 kPa in increments of 20 kPa), the corresponding contraction force can be measured by the force meter.For the isotonic test, to investigate how the pressure input influences the contraction ratio of BFAMs, the BFAM is pressurized at the initial state and is loosened gradually by moving forward the linear guide until the reading of force meter is zero.The recorded displacement of linear guide is regarded as the maximum contraction displacement under this pressure.To develop a contraction force versus contraction ratio relationship, a 0.1 MPa pressure is applied on the BFAM first.Then, the BFAM is loosened continually in a movement of 5 mm until a zero display of the force sensor emerges, and the corresponding contraction force is read at each movement.By recording both the depressurizing and pressurizing processes, the hysteresis of BFAMs can be evaluated.The response time test was completed on the experimental configuration, as shown in Figure S2, Supporting Information.The BFAM is suspended vertically, and its movement is detected and recorded by a laser displacement sensor (GC05-200PW, HEPU, China) and a data terminal.A 2 N load is attached to one end of the BFAM to ensure that the BFAM moves almost exclusively in the direction of contraction and extension.The magnitude of pressure input is 0.1 MPa.The maximum contraction of the BFAM remains constant at low-frequency input pressure.Then, the BFAM response time can be considered as the time that it takes to complete an entire maximum contraction.In addition, each test is repeated 3 times and the average is used for the plots in Figure 3 and S2, Supporting Information.

Figure 1 .
Figure 1.LFT inflation, BFAM schematic, application scenarios, and BFAM prototype.A) LFTs inflate unevenly, and the multilayer LFT structure with large increase of contraction.B) Schematic showing BFAM at both depressurized and pressurized states.C) Scenarios where BFAMs are applied, including elbow flexion/extension, forearm supination/pronation, and mobile robots.D) The BFAM exhibits a braided-craft-like appearance.

Figure 2 .
Figure 2. Braiding pattern, BFAM working mechanism, LFT geometry, comparison between single-layer structure and multilayer structure.A) BFAMs contract when pressurized.B) The geometric and force analysis at the different cross sections of BFAMs.C) LFTs are considered as the splicing of two identical arcs with a radius of r.D) The discrepancy between a single-layer structure and a multilayer structure.

Figure 3 .
Figure 3. Isometric actuation test, isotonic actuation test, and the effect of multilayer structure, hysteresis test.A) BFAM contraction force versus air pressure under isometric actuation.B) BFAM contraction ratio versus air pressure under isotonic actuation.C) The relation between contraction force and contraction ratio under isotonic actuation.D) BFAM contraction ratio with different layers.E) Small hysteresis is shown under isometric actuation.F) Obvious hysteresis is observed under isotonic actuation.

Figure 4 .
Figure 4. BFAM scalability, forearm supination/pronation, wrist movement, elbow flexion/extension, mobile (inchworm) robot.A) Two BFAM prototypes with different sizes.B) The BFAM assists the mannequin forearm supination/pronation. C) The mannequin wrist movement is actuated by the BFAM.D) A mannequin wearing the BFAM accomplishes its elbow flexion/extension.E) The elbow flexion angle versus air pressure input.F) The BFAM mobile robot crawls forward.