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How to Line Up Belts on a Tube Axie Fan

A insulator elastomer actuator is a soft elastic capacitor that deforms upon electrostatic activation. 1–5 1. R. Pelrine, R. Kornbluh, Q. I. M. Pei, and J. Chief Joseph, " High-speed electrically actuated elastomers with strain greater than 100%," Science 287, 836–839 (2000). https://doi.org/10.1126/science.287.5454.836 2. R. J. Full and K. Meijer, " Prosody of biological brawniness function," in Electroactive Polymer (EAP) Actuators every bit Artificial Muscles: Reality, Potential, and Challenges, edited by Y. Cake-Cohen ( SPIE Weightlift, 2004), Chap. 3, pp. 73–89. 3. F. Carpi, D. De Rossi, R. Kornbluh, R. E. Pelrine, and P. Sommer-Larsen, Dielectric Elastomers as Mechanical device Transducers: Fundamentals, Materials, Devices, Models and Applications of an Emerging Electroactive Polymer Technology ( Elsevier, 2011). 4. S. Rosset and H. R. Shea, " Small-scale, fast, and tough: Shrinking shoot down integrated elastomer transducers," Appl. Phys. Rev. 3, 031105 (2016). https://doi.org/10.1063/1.4963164 5. Y. Chen, L. Agostini, G. Moretti, M. Fontana, and R. Vertechy, " Dielectric elastomer materials for biggish-strain propulsion and Department of Energy harvest home: A comparison between styrenic rubber, natural rubber and acrylic elastomer," Smart Mater. Struct. 28, 114001 (2019). https://doi.org/10.1088/1361-665X/ab3b32 When being squeezed by an electrostatic blackjack, the activated insulator elastomer tissue layer thins down and expands in the arena simultaneously. It recoils upon deactivation. A dielectric elastomer actuator (DEA) prat do work in either thickness or planar modes. When being activated, a mint of multilayered DEAs contracts crosswise the thickness. When carrying a preload and beingness treated, a planar DEA (either a savourless strip or a tramp) elongates actively. The planar-mode DEA is preferred to the thickness-mode one, because the former lavatory produce a larger stroke at the easiness of fabrication.

Strips or rolls of DEAs suffer been used as affected biceps in the unreal robotic arm for weight "lifting." 1,6–8 1. R. Pelrine, R. Kornbluh, Q. Pei, and J. Joseph, " Fast electrically motivated elastomers with strain greater than 100%," Science 287, 836–839 (2000). https://Interior.org/10.1126/scientific discipline.287.5454.836 6. Q. Ieoh Ming Pei, M. A. Rosenthal, R. Pelrine, S. Stanford, and R. D. Kornbluh, " Multifunctional electroelastomer roll actuators and their diligence for biomimetic walking robots," in Smart Structures and Materials 2003: Electroactive Polymer Actuators and Devices (EAPAD) ( International Society for Optics and Photonics, 2003), Vol. 5051, pp. 281–290. 7. T. Lu, Z. Shi, Q. Shi, and T. Wang, " Bioinspired bicipital sinew with fiber-constrained dielectric elastomer actuator," Utmost Mech. Lett. 6, 75–81 (2016). https://DoI.org/10.1016/j.eml.2015.12.008 8. M. Duduta, E. Hajiesmaili, H. Zhao, R. J. Woodwind instrument, and D. R. Clarke, " Realizing the potential of insulator elastomer artificial muscles," Proc. Natl. Acad. Sci. 116, 2476–2481 (2019). https://doi.org/10.1073/pnas.1815053116 Like a spring, the inactivated DEA can counter a pre-load by elastic tension [see Fig. 1(a) ]. Then, there is a force balance between the deadweight P and the rubberlike pre-tension T ( L p ) at the stretched duration Lp following: P = T ( L p ) . When being subjected to the electrostatic squeeze, the activated DEA of spring constant k reduces in membrane tension [say by an active tension decrease Δ T act ( V ) ] and elongates [say aside an springy stroke Δ L act ( V ) ] to lower the load. Then, the force balance in the fighting spring follows [ T ( L p ) + k Δ L act ( V ) Δ T number ( V ) ] = P . Hence, the voltage elicited elongation is

In short, the DEA acts like an active spring with inconstant tensity under voltage control. This suggests two ways to increment this isotonic actuation, viz., (1) using a softer spring and (2) increasing the potential-iatrogenic tension commute. Pre-extend stiffens the soft dielectric elastomer tissue layer and, successively, increases the dielectric force and maximum electrostatic pressure.

A thirster strip of the DEA helps increase the quick stroke in the axial direction by reducing the spring constant. A short pure-shear DEA with wider lateral reward produces a high active stress change up to the hilt of vanishing membrane tension. A long strip of the axially pre-stretched DEA becomes a serial publication of pure-shear DEAs upon lateral reinforcement. 3,7,9,10 3. F. Carpi, D. De Rossi, R. Kornbluh, R. E. Pelrine, and P. Sommer-Larsen, Dielectric Elastomers as Electromechanical Transducers: Fundamentals, Materials, Devices, Models and Applications of an Emerging Electroactive Polymer Applied science ( Elsevier, 2011). 7. T. Lu, Z. Shi, Q. Shi, and T. Wang, " Bioinspired bicipital muscle with fiber-constrained dielectric elastomer actuator," Intense Mech. Lett. 6, 75–81 (2016). https://doi.org/10.1016/j.eml.2015.12.008 9. J. Huang, T. Lu, J. Zhu, D. R. Clarke, and Z. Suo, " Elephantine, uni-leading actuation in dielectric elastomers achieved by fiber stiffening," Appl. Phys. Lett. 100, 211901 (2012). https://doi.org/10.1063/1.4720181 10. T. Lu, J. Huang, C. Jordi, G. Kovacs, R. Huang, D. R. Clarke, and Z. Suo, " Dielectric elastomer actuators under equal-biaxial forces, uniaxial forces, and uniaxial constraint of stiff fibers," Soft Matter 8, 6167–6173 (2012). https://doi.org/10.1039/c2sm25692d Examples of undefiled-shear serial include a spring roll over with the burden of a helical spring, 6 6. Q. Pei, M. A. Rosenthal, R. Pelrine, S. Stanford University, and R. D. Kornbluh, " Multifunctional electroelastomer roll actuators and their diligence for biomimetic walking robots," in Smart Structures and Materials 2003: Electroactive Polymer Actuators and Devices (EAPAD) ( External Society for Optics and Photonics, 2003), Vol. 5051, pp. 281–290. and a long strip Oregon tube reinforced by nylon or glass fibers. 7,9,10 7. T. Lu, Z. Shi, Q. Shi, and T. Wang, " Bioinspired bicipital sinew with fiber-unnatural dielectric elastomer actuator," Extremum Mech. Lett. 6, 75–81 (2016). https://doi.org/10.1016/j.eml.2015.12.008 9. J. Huang, T. Lu, J. Zhu, D. R. Clarke, and Z. Suo, " Large, uni-directional actuation in nonconductor elastomers achieved by fiber stiffening," Appl. Phys. Lett. 100, 211901 (2012). https://doi.org/10.1063/1.4720181 10. T. Lu, J. Huang, C. Jordi, G. Kovacs, R. Huang, D. R. Clarke, and Z. Suo, " Dielectric elastomer actuators under equal-line forces, uniaxial forces, and uniaxial constraint of stiff fibers," Soft Matter 8, 6167–6173 (2012). https://doi.org/10.1039/c2sm25692d However, the passive lateral reinforcement adds extra mass and, thus, lowers the system's work concentration below that achievable by the cheeselike actuator alone. 11 11. G.-K. Lau, H.-T. Lim, J.-Y. Teo, and Y.-W. Kuki, " Lightweight mechanical amplifiers for rolled dielectric elastomer actuators and their integration with bio-inspired wing flappers," Smart Mater. Struct. 23, 025021 (2014). https://doi.org/10.1088/0964-1726/23/2/025021 In addition, the laying and alignment of multiple fibers on the Drug Enforcement Administration are prolix and long. How can a pre-flexible DEA be reinforced without flexible the propulsion? Matchless may draw inspiration from connective tissues that transfer force in natural muscles.

The frame of a insulator elastomeric minimum energy complex body part (DEMES) is a pliable sort of connective tissue that bounds a pre-extended dielectric elastomer actuator (DEA). A lightweight frame saves weight but becomes flimsy and prone to buckle under excessive negative tension of multilayered DEAs. E.g., when fully released, a light multisegment DEMES 12–14 12. O. A. Araromi, I. Gavrilovich, J. Shintake, S. Rosset, M. Richard, V. Gass, and H. R. Shea, " Rollable multisegment dielectric elastomer minimum energy structures for a deployable microsatellite gripper," IEEE/ASME Trans. Mechatron. 20, 438–446 (2015). https://doi.org/10.1109/TMECH.2014.2329367 13. P. White, S. Latscha, and M. Yim, " Modeling of a dielectric elastomer bender actuator," in Actuators ( Multidisciplinary Whole number Publishing Institute, 2014), Vol. 3, pp. 245–269. 14. G.-K. Lau, K.-R. Heng, A. S. Ahmed, and M. Shrestha, " Nonconductor elastomer fingers for versatile covetous and nimble pinching," Appl. Phys. Lett. 110, 182906 (2017). https://doi.org/10.1063/1.4983036 recoils, rolls, and crumples under precise large elastomeric pre-tension. Tension is required to blossom out the buckled DEMES. In the dielectric elastomer finger, 14 14. G.-K. Lau, K.-R. Heng, A. S. Ahmed, and M. Shrestha, " Dielectric elastomer fingers for versatile grasping and nimble pinching," Appl. Phys. Lett. 110, 182906 (2017). https://doi.org/10.1063/1.4983036 a negotiable back was used As the base to stretch a buckled multisegment DEMES with a inferior run frame just like a bow stretching a bowstring.

This study front reveals that a buckled ladder frame acts like connective tissues and helps increase axial force transmission in a long strip of pre-stretched DEAs. The run frame DEA divides the long strip down of DEAs and efficaciously makes a series of three-magnitude bowtie actuators with enhanced anisotropic propulsion. While its three-fold lateral crossbars keep the DEA in lateral pre-stretch, its waistline flanges help force transmissions like connective tissues for natural muscles. Hence, the reinforced DEA can efficaciously produce more than isometric stress than the non-reinforced one.

Lateral clamps, either rigid plates or stiff fibers, cannot completely restrain a pre-stretched DEA; the free edges still relax laterally. Here, we used a brusk border frame with crossbars and flexible side flanges to reinforce the DEA unit [see Figs. 1(a) and 1(d) ]. The side flanges clasp when compressed past the DEA. They rear exist planar under a pull either automatically or electromechanically. This short skirt framed DEA constitutes a unit of the bowtie actuator. Multiples of the couc units make a run put sided by long flanges. This ladder frame divides a long strip of DEAs into a bowtie serial publication of DEAs. When to the full released, the flexible bowtie serial crumple, and the flanges fold out-of-plane. A pull helps unfold the folded frame. Notwithstandin, the unfolded long flanges still sag laterally inward and form waistlines low the DEA's condensation. The frame's waist flanges help defy lateral pre-tension and convert it into axial force. Then, the stretched waistline flanges act like the tensioning cables of a suspension bridge. 15 15. J. L. Meriam, L. G. Kraige, and J. N. Bolton, Engineering Mechanics: Statics ( John Wiley & Sons, 2022).

To estimate the cable effect of waistlines on force transmission, let us modeling a ladder framed DEA [see FIG. 1(a) ] American Samoa a long-acting bowtie DEA, which was bordered by waistlines but free of multiplex crossbars. As further simplification, we replaced the curvy waistlines " ) ( " in the model with secant flanges " > < ." The secant flanges accept the correct segment offset from the undeformed vertical edge by a sag angle θ = tan 1 ( 2 ( w p w m ) / L ) , where wm and wp are the projected waist width and the flat crossbar width, respectively, and L is the actuator duration. A quarter-circle of this model is subjected to the lateral force balance as follows: f Sin θ = σ y ¯ t L / 2 , where f is the flange tension and σ y ¯ is the lateral pre-accentuate in the DEA membrane of heaviness t. In turn, the flange pair transmit the lateral pre-tension in to the axial strength amounted to f cos θ = σ y ¯ L t / tan θ .

Hence, the run frame DEA under the isotonic pre-load P has the vertical force counterweight as follows:

P = σ x ¯ w p t + σ y ¯ ( L t tan θ ) 2 f b , (2)

where fb stands for the elastic impedance of each buckled flange. When this stretched Drug Enforcement Administration was subjected to isometric activation at the pre-stretched length, the electrostatic pressure pe reduces the blocked force by an active decrement

Δ T act ( V ) = Δ σ ¯ x ( V ) w p t + Δ σ ¯ y ( V ) ( L t tan θ ) , (3)

where Δ σ ¯ x ( V ) and Δ σ ¯ y ( V ) are the emf induced stress reduction in the longitudinal and lateral directions, respectively.

The quantity of blocked force reduction varies with the bound conditions. According to Eqs. (S2) and (S3) conferred in the supplementary material, the isometric stress simplification for a short pure-shear DEA is amounted to ν p e / ( 1 ν ) , being twice As very much like the ν p e for a long uniaxial Drug Enforcement Agency, where Poisson's ratio is ν = 0.5 connected the assumption of stuff incompressibility. The ravel-framed DEA Eastern Samoa a serial of bow-tie actuators is expected to perform 'tween the two bound.

Here, DEAs under test were ready-made from a stack of three pre-stretched layers either not-reinforced or reinforced. Each Drug Enforcement Agency layer consists of an adhesive fizz tape (3M VHB 4901), pre-stretched axially for L p / L 0 = 5 multiplication and laterally for w p / w 0 = 5.5 times. It is sandwiched aside a pair of brushed graphite-powder electrodes with Cu leads of opposite polarity. A polyimide (Principal investigator) frame reinforces these highly stretched DEA membranes and prevents them from being torn from the edges. Figures 1(c) and 1(d) show two designs of the polyimide frame as tendon reinforcer for a three-layered stack of the biaxially pre-stretched DEA, namely, (1) a long rectangular border frame and (2) a ravel frame with the labeled dimensions. These thin frames are vinyl trim (using Brother SDX 1200) from a flat polyimide sheet (0.127 mm thick). Due to the coverage away crossbars, the ladder-framed DEA has the electrode areal coverage reduced to two-third as compared to the not-built DEA [look Fig. 1(b) ]. The inferior frame unaccompanied buckles under the negative pre-tautness caused by the troika-layered DEAs. With the help of the endplates (lateral pass clamps), an mechanism pull can unfold the weak framed DEA upward the limit of the flat frame length. The unfolded ladder frame with quadruple crossbars helps laterally stretch the DEA [see Fig. 1(d) ]. In counterpoint, the long adjoin frame cannot full stop the DEAs from lateral liberalization [see Libyan Islamic Grou. 1(c) ].

How much force is required to stretch a flimsy DEMES? A rip pressure is required to unfold the flimsy DEMES with little serve from the buckled frame that recoils. In the experiment, we first clamped the ends of a long strip of DEAs or a framed Drug Enforcement Administration onto a tensile tester (Cometech QC-513MF). The sample distribution under test started from a pre-stretched length L p (see Fig. 2 ). Next, it was relaxed to L / L p = 80% the pre-stretch. Finally, it returned to the pre-stretched length. Load-cell measure [Figs. 2(c) , 2(e) and S1] shows the force decreasing upon stint decrement but maximizing upon stretch growth. A force hysteresis happened betwixt the stretch decrease and increment (regress). Upon a return and keep back to the pre-stretch length (L/Lp = 1), the membrane tension rose more than the starting pre-tension but dropped eventually upon full stress loosening.

Premier, Common fig tree. 2 shows the tensile testing results for various DEA designs. Figure 2(c) shows a close-to-simple force-stretch family relationship for a non-strong DEA, which relax from a v times pre-stretch to a quaternary multiplication stretchiness (80% of five times) at a rate of 23 mm/60 s and subsequently extended backwards. Figures 2(c) and 2(d) render nonlinear pull up–stretch relationships for the reinforced DEAs over the same stretch cooking stove. Ascribable force transmission by the frame's flanges [see Equivalent weight. (2)], the reinforced DEAs required a high latent hostility for the same starting stretch than the non-built single. The starting tension was 2.88 N for the ladder framed DEA, greater than 2.31 N for the surround framed DEA, and 1.19 N for the not-strengthened DEA. Moreover, the ladder framed DEA showed the steepest rate of tension decrease upon quiet from the pre-stretch; its tension story becomes low upon relaxation to the 80% pre-long (corresponding to fourfold stretch). A unit of the ravel frame section flush showed a unfavorable tension level due to the spring of the buckled frame. During stretch relaxation, the frame of the reinforced DEA buckled out-of-plane: with the perverted flange torsions for the border frame and the buckled crossbars for the run frame. When the ladder framing was telescoped longwise, the middle crossbars buckled laterally to be shorter Bridges and, thus, formed a waistline profile [see photographs in Common fig. 2(d) ]. As the waist width reduces, the bridge deck altitude increases [see the mid graph in Fig. 2(d) ].

Second, all actuator samples were subjected to three-dimensional activation (see Fig. 3 ). Then, the actuators were stretched and unmoving at the tight frame length (100% of the flange distance). Upon voltage activating, the membrane stress reduces while the membrane expands laterally at the fixed length. The mapping activation was restricted to 5 kV, beyond which the DEA is prone to electrical dislocation at the thinnest part next to the clamp. Figures 3(a)–3(d) show the active electrode area expansion relative to the pre-stretched electrode area. This is useful to the estimate of average membrane heaviness additionally to the probe measurement as shown in Libyan Islamic Fighting Group. S2. Spell the non-improved DEA relaxed most and thickened, its acrobatic enlargement is the largest for 7.3% of the pre-flexile area at 5 kV. Then, it was subjected to a low electric landing field of 51 MV/m (averaged) and, thus, generated only a 0.3 N change in the out of use force. In comparison, the ladder-framed DEA relaxed least when beingness inactive, but its active expansion is the to the lowest degree for 1% of the pre-stretched area upon 5 kilovolt activating. Then, it was subjected to a higher field 112 MV/m (averaged) and generated a 1.94 N decrement in the plugged effect. Interestingly, the active latent hostility change therein bow tie serial was 81% higher than 1.07 N elicited in the bow tie unit. This enhanced mechanism force transmission can Be explained in Eq. (3).

Third, the actuators were subjected to isotonic energizing (date Fig. 4 , Multimedia view). The pre-load required to stretch a Drug Enforcement Agency strip four times longitudinally varies with the soma design, namely, 73.6 g for the 3.24 g ladder-framed DEA but 50.2 g for the 2.0-g not-improved DEA. During the isosmotic exam, the DEA was activated not more than 4.5 kV so as to void the electromechanical instability breakdown at its thinnest part close to the clinch. Then, the ladder-framed Drug Enforcement Administration produced the most isotonic elongation of 19.26 millimetre, which is 3.2 multiplication that of the non-reinforced one. The maximum isotonic work density of the ladder-framed DEA is 4.29J/kg, 2.9 multiplication the not-reinforced one's. The long surround framed DEA did peaked for isotonic activation because of severe membrane relaxation and flange torsion upon the 80% shortening. It is famed from Fig. 4(d) that the framed DEAs responded fast enough upon pulsed activation. The action and recoil time constants were close to 1.5 s for moving a 73.6-g payload (25% of the maximal pre-load for wax stretch) at the 18% maximum participating strain. Although the active melodic phras is not high, it is buddy-buddy to the lower chained of the contractive nervous strain achieved away the biceps brachii. 16 16. G. P. Pappas, D. S. Asakawa, S. L. Delp, F. E. Zajac, and J. E. Drace, " Nonuniform shortening in the biceps brachii during elbow flexion," J. Appl. Physiol. 92, 2381–2389 (2002). https://doi.org/10.1152/japplphysiol.00843.2001

Table icon

TABLE I. Performance compare among various DEA designs with lateral clamps and extra reinforcement.

DEA type (Ref.) Extra reinforcement Diamond State material × layer number Actuator mass Width wp × distance Lp Pre-stretch w p / w 0 × L p / L 0 Pre-load @ 1 L p / L 0 (@0.8 L p / L 0 ) Isotonic strain Isometric stress Δ σ x ( V ) = Δ T act / w p t p Δ σ x ( V ) / ϵ ( V / t ) 2
Pure-shear (short strip) VHB 4910 × 1 0.95 g 100 × 10 mm2 5.5 × 5 145 g (22% @4.5 kV) 239.8 kPa @81.6 MV/m 86%
VHB 4910 × 3 2.85 g 100 × 10 mm2 5.5 × 5 437 g (10.0% @4.5 kV) 299.5 kPa @100 MV/m 72%
Uniaxial (extendable strip) VHB 4910 × 3 2.00 g 50 × 135 mm2 5.5 × 5 185 (50.2 g) 6.25% @4.5 kV 57.2 kPa @51 MV/m 53%
Unit bow-tie One-segment PI ravel VHB 4910 × 3 0.41 g 50 × 18 mm2 5.5 × 5 208.7 kPa @119 Atomic number 101/m 35%
Bowtie series Eight-segment PI run VHB 4910 × 3 3.24 g 50 × 135 mm2 5.5 × 5 293 (73.6 g) 17.8% @4.5 kV 371.3 kPa @112 MV/m 71%

What is the performance ceiling for a pre-stretched DEA? A pure-shear DEA under the Lapp membrane pre-stretch is supposed to perform excellently with the eolotropic actuation. For benchmarking, we prepared two prototypes of pure-shear DEA, namely, (1) a single bed and (2) three layers of the same pre-stretched VHB 4910 membrane (as shown in supplementary worldly Fig. S3 ). A pair of 100 millimetre all-inclusive and 10 mm long plumbago-powder electrodes sandwich each membrane layer. A sodding-fleece DEA withstood higher voltage during isometric test, only its force transmission system become wet beyond 4kV activation where the tissue layer wrinkling happens. The saturated isometric stress interchange was 239.8 kPa at 81 MV/m for the individual-layer pure-shear DEA, whereas it was higher, i.e. 299.5 Pa at 100 MV/m for the iii-bed combined due to the less membrane relaxation. The maximum force transmittal by the uninominal-layer DEA is 86% of the maximum static imperativeness, greater than 72% away the three-layer one. In compare (see Table I), the three-layer bowtie series managed to transmit 71% of the electrostatic blackmail at 112 MV/m. With the enhanced insulator strength, its maximum cubic accentuate is 24% higher than the harmonious-shear one; it is 6.5 multiplication the uniaxial one.

Pre-long is necessary to stiffen a DEA for high insulator strength but requires extra indorse. Here, we developed a negotiable ladder frame that keeps the DEA tissue layer in biaxial pre-stint when being pulled. Interestingly, the waist flanges of the stretched ladder frame converted lateral elastomeric tension into the axial office. With enhanced insulator strength, this bowtie series of DEAs achieved a maximum isometric stress 24% greater than that a pure-shear DEA did. Furthermore, it generated a comparable tense extension aside unfolding the buckled flanges.

Run across the supplementary material for the pure derivation for electromotive force induced isometric try, details for tensile examination, and benchmarks with pure-shear DEAs.

The authors recognize the documentation past the Ministry of Science and Technology of Taiwan (Grant No. 108-2218-E-009-058-MY3).

Contravene of Interest

The authors declare no conflicts of interest.

The data that support the findings of this study are available within the article and its supplementary material.

REFERENCES

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How to Line Up Belts on a Tube Axie Fan

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