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Continuum soft actuators based on reprogrammable geometric constraints
Journal Pre-proof Continuum soft actuators based on reprogrammable geometric constraints Sihwa Oh, Se-Um Kim, Sooyoung Yeom, Hogyeong Kim, Sunwoo Kim, Jun-Hee Na
PII: DOI: Reference:
S2352-4316(20)30024-9 https://doi.org/10.1016/j.eml.2020.100649 EML 100649
To appear in:
Extreme Mechanics Letters
Received date : 31 October 2019 Revised date : 21 December 2019 Accepted date : 7 February 2020 Please cite this article as: S. Oh, S.-U. Kim, S. Yeom et al., Continuum soft actuators based on reprogrammable geometric constraints, Extreme Mechanics Letters (2020), doi: https://doi.org/10.1016/j.eml.2020.100649. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2020 Published by Elsevier Ltd.
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Continuum soft actuators based on reprogrammable geometric constraints
Na1,3*
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Sihwa Oh1, Se-Um Kim2, Sooyoung Yeom3, Hogyeong Kim1, Sunwoo Kim4, and Jun-Hee
Department of Electrical, Electronics and Communication Engineering Education,
1
Chungnam National University, Daejeon 34134, Republic of Korea
Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia,
2
PA 19104, USA.
Department of Convergence System Engineering, Chungnam National University, Daejeon
3
34134, Republic of Korea
Department of Construction Engineering Education, Chungnam National University,
4
Daejeon 34134, Republic of Korea
Correspondence *Prof. Jun-Hee Na (email: [email protected])
Abstract
Although numerous soft actuators have been developed to generate diverse and dexterous
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morphing such as branching, bending, and twisting, continuum manipulation with increased degrees of freedom still relies on the coactivation of multiple actuators. We demonstrate continuum soft actuators that exhibit a higher number of deformation modes in a single actuating unit. Our devices consist of an elastomer composite embedded with micro liquid
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droplets and an array of resistive heating elements to locally drive the liquid-vapor phase change of adjacent liquid droplets. The elastomer composite body only inflates in the vicinity of a resistive heating element in the on-state while other segments, including those near inactive elements, serve as rigid constraints, such that the bending direction can be systemically changed depending on the state of the individual resistive heating elements in the embedded array. We show that our continuum soft actuators permit fully continuous motions, including rotations, via a simple operating scheme. 1
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Keywords: Continuum soft actuators, active geometric constraints, phase-change actuators
1. Introduction
Many creatures with their complex, evolved natural motions and mechanisms have served to inspire soft actuators that achieve delicate locomotion and morphing. Pioneering studies have established strategies for the design and the fabrication of soft actuators, exploring their potential applications in biomimetic and artificial organs [1,2]. Programming soft materials have traditionally hinged on geometric asymmetry [3,4] and/or the use of anisotropic functional materials [5–7], with the stimuli for their actuation spanning diverse inputs including electric or magnetic fields [8–11], temperature [6,12], and pneumatic or hydraulic inflation [13–17]. Today, a gamut of primary actuation, including one-directional expansion [3], bending [18–20], twisting [4,21–23], and rotation [24] have been demonstrated. However, soft actuators based on such inhomogeneity are primarily limited to the actuation of the single degree of freedom (DOF).
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Continuum soft actuators are a class of high-level actuators that overcome the aforementioned issue of the DOF restrictions by leveraging multiple, assembled actuators that work collectively to induce complex motion [25,26]. Several continuum actuators draw inspiration from the actuation mechanisms at work in organs, including octopus’ tentacles and elephant trunks
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[27,28], wherein a coactivation of antagonistic muscle groups affords these appendages nearly infinite DOF. They organize similar frameworks that, for instance, could comprise an inner actuating body surrounded by a series of tendons [29,30]. However, since prevalent technologies integrate multiple actuation units, they lack an innate simplicity and scalability, which is highly desirable for any such platform. When looking to use multiple inputs in a single body to increase the DOF, strong asymmetries that are indispensable in controlling the actuating 2
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direction and the working capacity may be reduced. Although recent literature has demonstrated multistate actuation within a single body [31–33], the capability of precisely controlling the
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actuating direction with a wide range of the displacement has far remained elusive. We describe a novel type of continuum soft actuators via a monolithic body that works based on localized inflation. These actuators afford active control over the direction of actuation and in doing so, achieve multi-dimensional complex motions despite their simple morphologies. They are comprised of an elastomer composite with embedded liquid droplets and an array of resistive heating elements to drive a liquid-vapor phase change. Inflation, driven by the liquidvapor phase change, occurs locally in the vicinity of each resistive heating element in the embedded array, and as such can be used to systemically program local strain mismatches without the need for any associated, passive geometric constraints. We show that the ability to individually control and actuate each resistive heating element in the array can direct various modes of actuation, overcoming the issue of the DOF restrictions in conventional systems [34,35], thereby providing a powerful platform for the design of reconfigurable structures.
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2. Actuator configuration and operation principle
Strategies for continuum actuation are illustrated in Figure 1. Without any geometric constraints, the liquid-vapor phase change results in isotropic expansion of the elastomer composite (λh = λv), where λh and λv denote the expansion ratio along the horizontal direction and the vertical
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direction, respectively (Figure 1a(1)). In this configuration, the bending direction and the curvature of the elastomer composite have been programmed by applying patterns of passive constraints. For instance, when a layer of passive constraint is applied, λh near the constraint is restricted (λh-in < λh-out) due to the contrast in stiffness, and the elastomer composite undergoes the bending toward the constraint (Figure 1a(2)). However, these approaches have so far been limited to the one-dimensional actuation [34,36–39]. Resistive heating elements in our actuators, 3
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on the other hand, depending on whether they are in their off- or on-states, can respectively assume the role of either a constraint or an actuating unit. For instance, when the segments of
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the upper layer (U) or the lower layer (L) act as active geometric constraints, this system has two DOF that is the bending toward U and L (Figure 1a(3)). In this way, a more significant number of actuation modes can be directed as the number of individually tunable resistive heating elements increases. One exemplary actuator configures a rod-like body with a 2 by 2 array of resistive heating elements that are parallelly aligned along the length of the actuator, working as a 4-segments actuator (Figure 1b). In this scheme, the bending direction lays within the single plane (the x-y plane), and it varies depending on the state of segments. We note that further increase of DOF is mostly limited at higher numbers of segments and complexity. In other configurations, e.g., two-folds actuators, classical actuators have trilayer structure (constraint/actuator/constraint) with the patterned gaps (Wo) in either the top and bottom passive constraint to program the locations of folding nodes. Without locally controlling the inflation, the actuation occurs synchronously at all nodes (Figure 2a). Based on our concept, actuators of active geometric constraints can assume the same function when segments form several
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independent nodes along the length of the actuator (Figure 2b). Unlike passive constraint analogs, the resistive heating elements in our actuators address independent and reprogrammable nodes, thereby allowing the overall system to manage various modes of actuation. Indeed, such variation in the configuration of resistive heating elements will provide
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diverse aspects of actuation.
3. Results and discussion
3.1. Fabrication process and characterization method Our actuators are fabricated through the emulsification of ethanol (EtOH) in the prepolymer of Ecoflex described previously [35]. Prepolymer mixtures of elastomer composites were prepared 4
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by mixing two components of Ecoflex 00-50 (A and B) (Smooth-On) in a 1:1 ratio, stirring the mixture for 2 min, adding 30 wt.% of ethanol (≥ 94.5 %, Daejung Chemicals & Metals Co.),
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and forming ethanol-in-Ecoflex emulsion by another stirring for 2 min. Resistive heating elements were prepared by winding a Ni-Cr resistive wire (80 wt.% of Ni and 20 wt.% of Cr) of 0.25 mm diameter and 450 mm length onto a 2.5 mm diameter wrench. The pitch and the length of the Ni-Cr coil are 15 mm and 75 mm, respectively. Pairs of resistive heating elements were placed in a glass mold (15 mm width, 75 mm length, and 25 mm height). The prepolymer mixture was then cast in the glass mold and cured at room temperature for 3 hours. Two pairs of resistive heating elements (2 by 2) with the distance between adjacent resistive heating elements of d = 7 mm are finally composed in 15 mm width, 75 mm length, and 15 mm height elastomer composites. In the case of the other actuators that use patterns of passive constraints, we used a Korean traditional paper of Hanji. It is a durable, flexible, and resilient material, and found to promote excellent bonding with elastomer composites, such that it prevents delamination and failure during the actuation. These passive constraint actuators employed one pair of resistive heating elements (1 by 2) with the distance between them of d = 10 mm. The
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dimension of elastomer composite was 15 mm width, 75 mm length, and 10 mm height. A rigid layer of Hanji is then placed on the cast prepolymer before the curing process. In the case of the trilayer structure, we first placed the patterns of Hanji on the bottom surface of the glass mold, cast prepolymer, and covered the prepolymer with the other patterns of Hanji.
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Resistive heating elements were connected to the DC power supply (DP832A; RIGOL). As applying voltages, actuators were imaged using an action camera (FDR-X3000; Sony) and a thermal camera (One Pro LT; FLIR). Bending curvatures of actuators were measured from the obtained photographs using the curvature measurement tool (https://imagej.net/Kappa) in ImageJ.
3.2. Actuation characteristics 5
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We first examine the actuation mechanics in our actuators. When using the concept of the geometric constraints, the actuation primarily arises from the contrast in stiffness between the
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soft body and the constraint. As a reference, we first characterized a classical passive actuator (hereafter referred to as the bi-layer (BL)-actuator) that has a rigid layer on the one side of the elastomer composite (Figure 3a). Hanji, which was used as a rigid layer, has a much smaller thermal expansion coefficient (αr = 2×10-4 K-1) and higher Young’s modulus (Er > 1 GPa) compared with those of the elastomer composite (αs = 1.31×10-2 K-1 and Es = 83 kPa). It leads to a significant strain difference under the actuation. The radius of bending curvature, Rp is estimated with the ratio (η) of the thickness of the rigid constraint (Lr) to the thickness of the soft body (Ls) as described previously by Timoshenko and Stoney [40–42],
,
(1)
Where ϵ is the contrast in stiffness between the soft body and the rigid constraint (Er/Es), and
𝑅 ≅
𝐿
𝐿.
(2)
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From Equation 2,
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εm is the strain mismatch. In the BL-actuator, ηϵ ≫ 1 and 1 + η ≈ 1. Therefore,
𝜂 𝜖,
(3)
and ηo for the maximum Rp is derived as, 6
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2/𝜖 .
(4)
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𝜂
We used a 0.5 mm thick Hanji to get the value of η close to ηo under the given parameters (~0.054 in case of Ls = 10 mm), wherein BL-actuators render the highest bending curvature. In the other actuators that employ active geometric confinements, the material composition of the on-segment (the actuating unit) and the off-segment (the constraint) is identical (ϵ ~ 1), and these segments are in similar dimension (η ~ 1) (Figure 3c). The Timoshenko model may not be valid in this regime. Instead, we applied a beam bending model based on the difference in the thermal expansion ratio. In this case, the radius of the bending curvature, Ra is found to be smaller than that of passive constraint, Rp. However, we note that this approach can afford extended bending modes. A numerical analysis was carried using a general-purpose nonlinear analysis program (Ansys Inc.) to evaluate the voltage-dependent bending curvature (see Supporting Information Numerical Analysis). We found that the bending curvature linearly increases as the temperature increases, and the experimental results are in good agreement with
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the numerical analysis (Figure 3b, 3d, and 3e). When the applied voltage of 5 V drives the actuation of the BL-actuator, the bending curvature is saturated as 29 m⁻¹ at 480 s, and the bending is released as 5.2 m⁻¹ at 1280 s after the removal of the applied voltage (see Supporting Information Figure S5a). Here, the bending time (rising time), Tr, is determined as the time that
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the bending curvature increases from 10 % (8 m⁻¹) to 90 % (26.58 m⁻¹) of the bending range under the heating. Similarly, the releasing time (falling time), Tf, is the time that the bending curvature decreases from 90 % to 10 % of the bending range. Tr and Tf were measured to be 230 s and 290 s, respectively. Since Tf is associated with the dissipation of heat, this value can fluctuate depending on the ambient temperature. Figure 3f shows bending curvatures of passive and active constraint under the continuous cycles of the on-state (5 V, ~70 oC) and the off-state 7
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(0 V, ~25 oC). During the cycles, the on-state shows a stable maximum curvature of ~30 m-1 (passive constraint) and ~20 m-1 (active constraint) while the releasing process leaves a modest
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hysteresis. It is due to the insufficient time for releasing heat inside the elastomer composite. The remnant curvature completely disappears after ~25 min, indicating the actuator is fully capable of the reversible operation. 3.3. Continuum actuation
As described above, continuum actuation with active geometric constraints relies on the individual manipulation of resistive heating elements. The liquid-vapor phase change locally occurs around the on-state resistive heating elements, and the other of the off-state remains as rigid constraints to induce the contrast in stiffness. In 4-segments actuators, we denote each resistive heating element in 2 by 2 array as inputs I0, I1, I2, and I3, respectively (Figure 4a). We first consider a series of inputs, Ii, as a binary variable, that is 1 at the on-state when 5 V is applied, or 0 at the off-state. When one input is the on-state, the banding occurs toward the opposite direction of the position of the input. We represented the bending direction as a vector. For instance, the output vector from the input of [I3, I2, I1, I0] = [0, 0, 0, 1] points southeast (SE)
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(Figure 4b and 4c). Similarly, output vectors from [I3, I2, I1, I0] = [0, 0, 1, 0], [I3, I2, I1, I0] = [0, 1, 0, 0], and [I3, I2, I1, I0] = [1, 0, 0, 0] point southwest (SW), northeast (NE), and northwest (NW), respectively. The productions from multiple on-states are the sum of output vectors. In case of [I3, I2, I1, I0] = [0, 0, 1, 1], the bending direction is SE + SW = south (S). Since inputs
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are not completely decoupled, several outputs yield overlapped results. For instance, both cases of [I3, I2, I1, I0] = [0, 0, 0, 1] and [I3, I2, I1, I0] = [0, 1, 1, 1] are identically SE. We also note that the cases of [I3, I2, I1, I0] = [0, 1, 0, 1] and [I3, I2, I1, I0] = [1, 0, 1, 0] are the un-actuated state (X) because the bending direction from each input is opposite. Therefore, four digitized inputs are decoded into nine outputs that consist of eight actuated states – east (E), SE, south (S), SW, west (W), NW, north (N), and NE, and one un-actuated state X (Figure 4b and see Supporting 8
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Information Table S2 and Movie S1). However, n inputs can be decoded up to n2 output states when all inputs are completely decoupled.
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Since both the input and output states are represented as an array of four elements, the actuating behavior also can be described with simplified Boolean expressions of their truth table. The bending along four principal directions (NW, NE, SW, and SE) corresponds to the binary outputs [O3, O2, O1, O0], respectively, where Oi is 1 at the actuated state (5 V) and 0 at the unactuated state (0 V). The Boolean function following the truth table of Oi[I3, I2, I1, I0] (see Supporting Information Table S3) is given as,
∑𝑚 ,
𝑂 𝐼 ,𝐼 ,𝐼 ,𝐼
(6)
where mk are minterms and k ∈ {1, 3, 5, 7} for i = 0, k ∈ {2, 3, 10, 11} for i = 1, k ∈ {4, 5, 12, 13} for i = 2, and k ∈ {8, 10, 12, 14} for i = 3. Oi is then simplified from Karnaugh map (see Supporting Information Figure S7) as, 𝑂 𝑂
𝑂 𝑂
𝐼𝐼 𝐼𝐼
𝐼𝐼 . 𝐼𝐼
(7)
Our 4-segments actuators exhibit a linear behavior when multiple inputs work simultaneously
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with different values of applied voltages. The magnitude of output vectors is proportional to the applied voltage, and thus the sum of output vectors of two adjacent inputs can get arbitrary magnitude and the direction on the associated quadrant. For instance, when the voltages (V2, V3) are applied to two adjacent inputs [I2, I3], the actuating direction is (V2, V3) and the distance 𝑉 in the quadrant that is defined with two output vectors, NE [0, 1, 0, 0] and NW [1,
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is 𝑉
0, 0, 0] (Figure 4d). In this way, fully continuous actuation can be achieved within the 2dimensional plane. In case that two inputs are in the opposite direction (e.g., [I0, I2] or [I1, I3]), antagonistic interaction occurs according to the difference of applied voltages (Figure 4e). We next demonstrate that the sequential modulation of [I3, I2, I1, I0] allows fully continuous control of bending direction, which have been rarely achieved due to the complexity in 9
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fabrication (Figure 5a). We propose a counter-clockwise rotational motion by sequentially applying combination of inputs as [I3, I2, I1, I0] = [0, 0, 1, 0], [0, 0, 1, 1], [0, 0, 0, 1], [0, 1, 0, 1],
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[0, 1, 0, 0], [1, 1, 0, 0], [1, 0, 0, 0], [1, 0, 1, 0], and [0, 0, 1, 0], and each state was lasted for 45 s (Figure 5b and 5c). According to the operation principle described in Figure 4, this sequence gives [0, 0, 1, 0] = SW, [0, 0, 1, 1] = SW + SE = S, [0, 0, 0, 1] = SE, [0, 1, 0, 1] = NE + SE = E, [0, 1, 0, 0] = NE, [1, 1, 0, 0] = NW + NE = N, [1, 0, 0, 0] = NW, and [1, 0, 1, 0] = NW + SW = W. The experimental results of the rotation and the displacement agree well, as illustrated in Figure 5d and 5e (see Supporting Information Movie S2). We highlight that the variation of the applied voltage between inputs renders fully continuous state of the displacement at any given rotation angle. It must be the first way to realize atypical rotational and linear motion simultaneously within a single actuator.
4. Concluding remarks
In summary, we have shown that our reprogrammable actuators are capable of increasing DOF by incorporating multiple inputs in one geometry. The vaporization of liquid droplets in the
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elastomer composite locally occurs adjacent to the resistive heater, such that each segment assigned to resistive heating elements can change the role of the actuating unit and the rigid constraint. Our actuators will especially be suitable for the works that require versatile, highly sophisticated control of the actuation direction owing to several remarkable characteristics: i)
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The structure as well as the actuating behavior of our actuators are not limited to the case discussed here but can change widely depending on the molds and corresponding configuration of resistive heating elements. ii) Since the actuation is driven by the voltage and the magnitude is controlled by the value of the applied voltage, our actuators control the actuation direction and magnitude precisely. iii) The scalability can be readily accessed because of the simplicity in the actuator configuration, the fabrication process, and the operating scheme without bulky 10
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accessories. The proposed actuators, in turn, outlines a powerful strategy for the design of freeform, actuatable, and reconfigurable soft structures via appropriate material selection and
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intelligent design. Therefore, we anticipate that this platform will be applied in a broad class of soft actuators and biomimicry devices.
Acknowledgements This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (NRF-2017R1D1A1B03029573).
Author contributions S.O., S.-U.K., and J.-H.N. designed the research; S.O., S.-U.K., S.Y., H.K., S.K. conducted the research and interpreted the results; J.-H.N supervised the research and interpreted the results; S.O., S.-U.K., and J.-H.N. prepared the manuscript.
Competing financial interests The authors declare that they have no competing financial interests.
Additional information Supplementary information is available in the online version of the paper. S.O. and S.-U.K. contributed equally to this work. Correspondence and requests for materials should be addressed to J.-H.N.
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W. Yim, J. Lee, K.J. Kim, An artificial muscle actuator for biomimetic underwater propulsors, Bioinspir. Biomim. 2 (2007) S31–S41. https://doi.org/10.1088/1748-
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freedom actuator based on a novel cylindrical ionic polymer-metal composite material, in: 2011 15th Int. Conf. Adv. Robot., IEEE, 2011: pp. 435–440. https://doi.org/10.1109/ICAR.2011.6088584.
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elastomers, Adv. Mater. 25 (2013) 205–212. https://doi.org/10.1002/adma.201203002. J.-H. Na, A.A. Evans, J. Bae, M.C. Chiappelli, C.D. Santangelo, R.J. Lang, T.C. Hull, R.C. Hayward, Programming reversibly self-folding origami with micropatterned photo-crosslinkable polymer trilayers, Adv. Mater. 27 (2015) 79–85. https://doi.org/10.1002/adma.201403510. [35]
A. Miriyev, K. Stack, H. Lipson, Soft material for soft actuators, Nat. Commun. 8 (2017) 596. https://doi.org/10.1038/s41467-017-00685-3.
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M. Amjadi, M. Sitti, Self-sensing paper actuators based on graphite-carbon nanotube hybrid films, Adv. Sci. 5 (2018) 1800239. https://doi.org/10.1002/advs.201800239.
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E. Hawkes, B. An, N.M. Benbernou, H. Tanaka, S. Kim, E.D. Demaine, D. Rus, R.J. Wood, Programmable matter by folding, Proc. Natl. Acad. Sci. 107 (2010) 12441– 12445. https://doi.org/10.1073/pnas.0914069107.
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folding with shape memory composites, Soft Matter. 9 (2013) 7688. https://doi.org/10.1039/c3sm51003d. [39]
B. An, D. Rus, Designing and programming self-folding sheets, Rob. Auton. Syst. 62 (2014) 976–1001. https://doi.org/10.1016/j.robot.2013.06.015. G.G. Stoney, The Tension of Metallic Films Deposited by Electrolysis, Proc. R. Soc.
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https://doi.org/10.1017/CBO9780511754715.
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Figure 1. Strategies for continuum actuation via reprogrammable geometric constraints. (a) Schematic illustrations of the isotropic expansion without geometric constraints (1), the unidirectional bending by the passive geometric constraint (2), and the extended bending modes via actively switching the role of segments in the elastomer composite (U and L) between the
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actuating unit and the rigid constraint based on the localized vaporization of liquid droplet fillers (3). Here, λ is the expansion ratio, α is the thermal expansion coefficient, L is the thickness, and E is Young’s modulus. Subscripts of r, s, U, and L depict the rigid layer, the soft body (elastomer composite), the upper layer, and the lower layer, respectively. (b) Exemplary actuation of 4-
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segments actuators comprising a 2 by 2 array of resistive heating elements. On-segments inflate while off-segments act as a rigid constraint to vary the bending direction.
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Figure 2. Asynchronous two-folds actuation. (a) Two-folds actuation occurs synchronously at all nodes when passive constraints are implemented. This is a single DOF actuation. Here, the width of the patterned gap is denoted by and Wo. (b) Asynchronous two-folds actuation via active geometric constraints. Each folding node, which is defined by configuring resistive heating elements separately along the length direction of actuators, can individually be
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manipulated.
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Figure 3. Actuation mechanics based on the contrast in stiffness. (a) Schematic diagram of BL-actuators. The thickness of the rigid layer (left blue) and that of the elastomer composite (right translucent) are denoted by Lr and Ls, respectively. (b) The experimental (top) and 20
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numerical calculation (bottom) results of the bending of BL-actuators at several conditions of the temperature (0, 35, 55, and 75 °C). In numerical results, the color bar is total deformation ∆𝑦
∆𝑧 . (c) Schematic diagram of 2-segments actuators
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of x, y, and z vectors as ∆𝑥
incorporating active geometric constrains. The off-segment (left) and the on-segment (right) have an identical material composition and similar thickness. (d) The experimental (top) and numerical calculation (bottom) results of the bending of 2-segments actuators at several conditions of the temperature (0, 40, 65, and 75 °C). (e) The bending curvature of BL-actuators and 2-segments actuators as a function of the temperature. (f) The bending curvature of BLactuators and 2-segments actuators under multiple cycles of the on-state (70 °C) and the off-
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state (25 °C). The states were switched every 5 min.
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Figure 4. Continuum actuation enabled by active geometric constraints. (a) Schematic illustration showing the configuration of resistive heating elements in 4-segments actuators as inputs [I3, I2, I1, I0]. (b) Exemplary actuation directions when considering a series of input as
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the binary state (the on-state and off-state). The output bending directions are represented as a vector. In case that two or more inputs are the on-state, the banding direction is expressed as the sum of the output vectors. Outputs also include the un-actuated state X. (c) Outputs that correspond to (b). Thermal images show that the temperature of the on-state input is higher than that of the off-state input. (d) Continuum actuation in the 2-dimensional plane via applying different values of voltages to two adjacent inputs. Output vectors are scaled by the applied 22
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voltage, and thus the sum of output vectors accordingly have arbitrary directions and distances in the associated quadrant defined by the two principal actuating directions. (e) Continuum
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actuation along one axis via manipulating two opposite inputs.
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Figure 5. Sequential control of inputs for rotational actuation. (a) Illustration of rotational motion via the sequential control of inputs [I3, I2, I1, I0]. (b) The chart flow and (c) the timing diagram of [I3, I2, I1, I0] to drive a counterclockwise rotation. (d) The displacement and the bending direction. The red circle and the green circle is the initial state at t = 0 and the bending
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of input combination of [0, 1, 0, 0] at t = 60 s, respectively. Here, each point was measured every 30 s. (e) Digital images in several time frames are showing the counterclockwise
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rotational actuation of the phase-change actuator. Red arrows denote the bending direction.
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PII: DOI: Reference:
S2352-4316(20)30024-9 https://doi.org/10.1016/j.eml.2020.100649 EML 100649
To appear in:
Extreme Mechanics Letters
Received date : 31 October 2019 Revised date : 21 December 2019 Accepted date : 7 February 2020 Please cite this article as: S. Oh, S.-U. Kim, S. Yeom et al., Continuum soft actuators based on reprogrammable geometric constraints, Extreme Mechanics Letters (2020), doi: https://doi.org/10.1016/j.eml.2020.100649. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2020 Published by Elsevier Ltd.
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Continuum soft actuators based on reprogrammable geometric constraints
Na1,3*
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Sihwa Oh1, Se-Um Kim2, Sooyoung Yeom3, Hogyeong Kim1, Sunwoo Kim4, and Jun-Hee
Department of Electrical, Electronics and Communication Engineering Education,
1
Chungnam National University, Daejeon 34134, Republic of Korea
Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia,
2
PA 19104, USA.
Department of Convergence System Engineering, Chungnam National University, Daejeon
3
34134, Republic of Korea
Department of Construction Engineering Education, Chungnam National University,
4
Daejeon 34134, Republic of Korea
Correspondence *Prof. Jun-Hee Na (email: [email protected])
Abstract
Although numerous soft actuators have been developed to generate diverse and dexterous
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morphing such as branching, bending, and twisting, continuum manipulation with increased degrees of freedom still relies on the coactivation of multiple actuators. We demonstrate continuum soft actuators that exhibit a higher number of deformation modes in a single actuating unit. Our devices consist of an elastomer composite embedded with micro liquid
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droplets and an array of resistive heating elements to locally drive the liquid-vapor phase change of adjacent liquid droplets. The elastomer composite body only inflates in the vicinity of a resistive heating element in the on-state while other segments, including those near inactive elements, serve as rigid constraints, such that the bending direction can be systemically changed depending on the state of the individual resistive heating elements in the embedded array. We show that our continuum soft actuators permit fully continuous motions, including rotations, via a simple operating scheme. 1
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Keywords: Continuum soft actuators, active geometric constraints, phase-change actuators
1. Introduction
Many creatures with their complex, evolved natural motions and mechanisms have served to inspire soft actuators that achieve delicate locomotion and morphing. Pioneering studies have established strategies for the design and the fabrication of soft actuators, exploring their potential applications in biomimetic and artificial organs [1,2]. Programming soft materials have traditionally hinged on geometric asymmetry [3,4] and/or the use of anisotropic functional materials [5–7], with the stimuli for their actuation spanning diverse inputs including electric or magnetic fields [8–11], temperature [6,12], and pneumatic or hydraulic inflation [13–17]. Today, a gamut of primary actuation, including one-directional expansion [3], bending [18–20], twisting [4,21–23], and rotation [24] have been demonstrated. However, soft actuators based on such inhomogeneity are primarily limited to the actuation of the single degree of freedom (DOF).
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Continuum soft actuators are a class of high-level actuators that overcome the aforementioned issue of the DOF restrictions by leveraging multiple, assembled actuators that work collectively to induce complex motion [25,26]. Several continuum actuators draw inspiration from the actuation mechanisms at work in organs, including octopus’ tentacles and elephant trunks
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[27,28], wherein a coactivation of antagonistic muscle groups affords these appendages nearly infinite DOF. They organize similar frameworks that, for instance, could comprise an inner actuating body surrounded by a series of tendons [29,30]. However, since prevalent technologies integrate multiple actuation units, they lack an innate simplicity and scalability, which is highly desirable for any such platform. When looking to use multiple inputs in a single body to increase the DOF, strong asymmetries that are indispensable in controlling the actuating 2
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direction and the working capacity may be reduced. Although recent literature has demonstrated multistate actuation within a single body [31–33], the capability of precisely controlling the
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actuating direction with a wide range of the displacement has far remained elusive. We describe a novel type of continuum soft actuators via a monolithic body that works based on localized inflation. These actuators afford active control over the direction of actuation and in doing so, achieve multi-dimensional complex motions despite their simple morphologies. They are comprised of an elastomer composite with embedded liquid droplets and an array of resistive heating elements to drive a liquid-vapor phase change. Inflation, driven by the liquidvapor phase change, occurs locally in the vicinity of each resistive heating element in the embedded array, and as such can be used to systemically program local strain mismatches without the need for any associated, passive geometric constraints. We show that the ability to individually control and actuate each resistive heating element in the array can direct various modes of actuation, overcoming the issue of the DOF restrictions in conventional systems [34,35], thereby providing a powerful platform for the design of reconfigurable structures.
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2. Actuator configuration and operation principle
Strategies for continuum actuation are illustrated in Figure 1. Without any geometric constraints, the liquid-vapor phase change results in isotropic expansion of the elastomer composite (λh = λv), where λh and λv denote the expansion ratio along the horizontal direction and the vertical
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direction, respectively (Figure 1a(1)). In this configuration, the bending direction and the curvature of the elastomer composite have been programmed by applying patterns of passive constraints. For instance, when a layer of passive constraint is applied, λh near the constraint is restricted (λh-in < λh-out) due to the contrast in stiffness, and the elastomer composite undergoes the bending toward the constraint (Figure 1a(2)). However, these approaches have so far been limited to the one-dimensional actuation [34,36–39]. Resistive heating elements in our actuators, 3
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on the other hand, depending on whether they are in their off- or on-states, can respectively assume the role of either a constraint or an actuating unit. For instance, when the segments of
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the upper layer (U) or the lower layer (L) act as active geometric constraints, this system has two DOF that is the bending toward U and L (Figure 1a(3)). In this way, a more significant number of actuation modes can be directed as the number of individually tunable resistive heating elements increases. One exemplary actuator configures a rod-like body with a 2 by 2 array of resistive heating elements that are parallelly aligned along the length of the actuator, working as a 4-segments actuator (Figure 1b). In this scheme, the bending direction lays within the single plane (the x-y plane), and it varies depending on the state of segments. We note that further increase of DOF is mostly limited at higher numbers of segments and complexity. In other configurations, e.g., two-folds actuators, classical actuators have trilayer structure (constraint/actuator/constraint) with the patterned gaps (Wo) in either the top and bottom passive constraint to program the locations of folding nodes. Without locally controlling the inflation, the actuation occurs synchronously at all nodes (Figure 2a). Based on our concept, actuators of active geometric constraints can assume the same function when segments form several
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independent nodes along the length of the actuator (Figure 2b). Unlike passive constraint analogs, the resistive heating elements in our actuators address independent and reprogrammable nodes, thereby allowing the overall system to manage various modes of actuation. Indeed, such variation in the configuration of resistive heating elements will provide
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diverse aspects of actuation.
3. Results and discussion
3.1. Fabrication process and characterization method Our actuators are fabricated through the emulsification of ethanol (EtOH) in the prepolymer of Ecoflex described previously [35]. Prepolymer mixtures of elastomer composites were prepared 4
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by mixing two components of Ecoflex 00-50 (A and B) (Smooth-On) in a 1:1 ratio, stirring the mixture for 2 min, adding 30 wt.% of ethanol (≥ 94.5 %, Daejung Chemicals & Metals Co.),
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and forming ethanol-in-Ecoflex emulsion by another stirring for 2 min. Resistive heating elements were prepared by winding a Ni-Cr resistive wire (80 wt.% of Ni and 20 wt.% of Cr) of 0.25 mm diameter and 450 mm length onto a 2.5 mm diameter wrench. The pitch and the length of the Ni-Cr coil are 15 mm and 75 mm, respectively. Pairs of resistive heating elements were placed in a glass mold (15 mm width, 75 mm length, and 25 mm height). The prepolymer mixture was then cast in the glass mold and cured at room temperature for 3 hours. Two pairs of resistive heating elements (2 by 2) with the distance between adjacent resistive heating elements of d = 7 mm are finally composed in 15 mm width, 75 mm length, and 15 mm height elastomer composites. In the case of the other actuators that use patterns of passive constraints, we used a Korean traditional paper of Hanji. It is a durable, flexible, and resilient material, and found to promote excellent bonding with elastomer composites, such that it prevents delamination and failure during the actuation. These passive constraint actuators employed one pair of resistive heating elements (1 by 2) with the distance between them of d = 10 mm. The
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dimension of elastomer composite was 15 mm width, 75 mm length, and 10 mm height. A rigid layer of Hanji is then placed on the cast prepolymer before the curing process. In the case of the trilayer structure, we first placed the patterns of Hanji on the bottom surface of the glass mold, cast prepolymer, and covered the prepolymer with the other patterns of Hanji.
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Resistive heating elements were connected to the DC power supply (DP832A; RIGOL). As applying voltages, actuators were imaged using an action camera (FDR-X3000; Sony) and a thermal camera (One Pro LT; FLIR). Bending curvatures of actuators were measured from the obtained photographs using the curvature measurement tool (https://imagej.net/Kappa) in ImageJ.
3.2. Actuation characteristics 5
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We first examine the actuation mechanics in our actuators. When using the concept of the geometric constraints, the actuation primarily arises from the contrast in stiffness between the
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soft body and the constraint. As a reference, we first characterized a classical passive actuator (hereafter referred to as the bi-layer (BL)-actuator) that has a rigid layer on the one side of the elastomer composite (Figure 3a). Hanji, which was used as a rigid layer, has a much smaller thermal expansion coefficient (αr = 2×10-4 K-1) and higher Young’s modulus (Er > 1 GPa) compared with those of the elastomer composite (αs = 1.31×10-2 K-1 and Es = 83 kPa). It leads to a significant strain difference under the actuation. The radius of bending curvature, Rp is estimated with the ratio (η) of the thickness of the rigid constraint (Lr) to the thickness of the soft body (Ls) as described previously by Timoshenko and Stoney [40–42],
,
(1)
Where ϵ is the contrast in stiffness between the soft body and the rigid constraint (Er/Es), and
𝑅 ≅
𝐿
𝐿.
(2)
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From Equation 2,
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εm is the strain mismatch. In the BL-actuator, ηϵ ≫ 1 and 1 + η ≈ 1. Therefore,
𝜂 𝜖,
(3)
and ηo for the maximum Rp is derived as, 6
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2/𝜖 .
(4)
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𝜂
We used a 0.5 mm thick Hanji to get the value of η close to ηo under the given parameters (~0.054 in case of Ls = 10 mm), wherein BL-actuators render the highest bending curvature. In the other actuators that employ active geometric confinements, the material composition of the on-segment (the actuating unit) and the off-segment (the constraint) is identical (ϵ ~ 1), and these segments are in similar dimension (η ~ 1) (Figure 3c). The Timoshenko model may not be valid in this regime. Instead, we applied a beam bending model based on the difference in the thermal expansion ratio. In this case, the radius of the bending curvature, Ra is found to be smaller than that of passive constraint, Rp. However, we note that this approach can afford extended bending modes. A numerical analysis was carried using a general-purpose nonlinear analysis program (Ansys Inc.) to evaluate the voltage-dependent bending curvature (see Supporting Information Numerical Analysis). We found that the bending curvature linearly increases as the temperature increases, and the experimental results are in good agreement with
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the numerical analysis (Figure 3b, 3d, and 3e). When the applied voltage of 5 V drives the actuation of the BL-actuator, the bending curvature is saturated as 29 m⁻¹ at 480 s, and the bending is released as 5.2 m⁻¹ at 1280 s after the removal of the applied voltage (see Supporting Information Figure S5a). Here, the bending time (rising time), Tr, is determined as the time that
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the bending curvature increases from 10 % (8 m⁻¹) to 90 % (26.58 m⁻¹) of the bending range under the heating. Similarly, the releasing time (falling time), Tf, is the time that the bending curvature decreases from 90 % to 10 % of the bending range. Tr and Tf were measured to be 230 s and 290 s, respectively. Since Tf is associated with the dissipation of heat, this value can fluctuate depending on the ambient temperature. Figure 3f shows bending curvatures of passive and active constraint under the continuous cycles of the on-state (5 V, ~70 oC) and the off-state 7
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(0 V, ~25 oC). During the cycles, the on-state shows a stable maximum curvature of ~30 m-1 (passive constraint) and ~20 m-1 (active constraint) while the releasing process leaves a modest
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hysteresis. It is due to the insufficient time for releasing heat inside the elastomer composite. The remnant curvature completely disappears after ~25 min, indicating the actuator is fully capable of the reversible operation. 3.3. Continuum actuation
As described above, continuum actuation with active geometric constraints relies on the individual manipulation of resistive heating elements. The liquid-vapor phase change locally occurs around the on-state resistive heating elements, and the other of the off-state remains as rigid constraints to induce the contrast in stiffness. In 4-segments actuators, we denote each resistive heating element in 2 by 2 array as inputs I0, I1, I2, and I3, respectively (Figure 4a). We first consider a series of inputs, Ii, as a binary variable, that is 1 at the on-state when 5 V is applied, or 0 at the off-state. When one input is the on-state, the banding occurs toward the opposite direction of the position of the input. We represented the bending direction as a vector. For instance, the output vector from the input of [I3, I2, I1, I0] = [0, 0, 0, 1] points southeast (SE)
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(Figure 4b and 4c). Similarly, output vectors from [I3, I2, I1, I0] = [0, 0, 1, 0], [I3, I2, I1, I0] = [0, 1, 0, 0], and [I3, I2, I1, I0] = [1, 0, 0, 0] point southwest (SW), northeast (NE), and northwest (NW), respectively. The productions from multiple on-states are the sum of output vectors. In case of [I3, I2, I1, I0] = [0, 0, 1, 1], the bending direction is SE + SW = south (S). Since inputs
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are not completely decoupled, several outputs yield overlapped results. For instance, both cases of [I3, I2, I1, I0] = [0, 0, 0, 1] and [I3, I2, I1, I0] = [0, 1, 1, 1] are identically SE. We also note that the cases of [I3, I2, I1, I0] = [0, 1, 0, 1] and [I3, I2, I1, I0] = [1, 0, 1, 0] are the un-actuated state (X) because the bending direction from each input is opposite. Therefore, four digitized inputs are decoded into nine outputs that consist of eight actuated states – east (E), SE, south (S), SW, west (W), NW, north (N), and NE, and one un-actuated state X (Figure 4b and see Supporting 8
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Information Table S2 and Movie S1). However, n inputs can be decoded up to n2 output states when all inputs are completely decoupled.
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Since both the input and output states are represented as an array of four elements, the actuating behavior also can be described with simplified Boolean expressions of their truth table. The bending along four principal directions (NW, NE, SW, and SE) corresponds to the binary outputs [O3, O2, O1, O0], respectively, where Oi is 1 at the actuated state (5 V) and 0 at the unactuated state (0 V). The Boolean function following the truth table of Oi[I3, I2, I1, I0] (see Supporting Information Table S3) is given as,
∑𝑚 ,
𝑂 𝐼 ,𝐼 ,𝐼 ,𝐼
(6)
where mk are minterms and k ∈ {1, 3, 5, 7} for i = 0, k ∈ {2, 3, 10, 11} for i = 1, k ∈ {4, 5, 12, 13} for i = 2, and k ∈ {8, 10, 12, 14} for i = 3. Oi is then simplified from Karnaugh map (see Supporting Information Figure S7) as, 𝑂 𝑂
𝑂 𝑂
𝐼𝐼 𝐼𝐼
𝐼𝐼 . 𝐼𝐼
(7)
Our 4-segments actuators exhibit a linear behavior when multiple inputs work simultaneously
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with different values of applied voltages. The magnitude of output vectors is proportional to the applied voltage, and thus the sum of output vectors of two adjacent inputs can get arbitrary magnitude and the direction on the associated quadrant. For instance, when the voltages (V2, V3) are applied to two adjacent inputs [I2, I3], the actuating direction is (V2, V3) and the distance 𝑉 in the quadrant that is defined with two output vectors, NE [0, 1, 0, 0] and NW [1,
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is 𝑉
0, 0, 0] (Figure 4d). In this way, fully continuous actuation can be achieved within the 2dimensional plane. In case that two inputs are in the opposite direction (e.g., [I0, I2] or [I1, I3]), antagonistic interaction occurs according to the difference of applied voltages (Figure 4e). We next demonstrate that the sequential modulation of [I3, I2, I1, I0] allows fully continuous control of bending direction, which have been rarely achieved due to the complexity in 9
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fabrication (Figure 5a). We propose a counter-clockwise rotational motion by sequentially applying combination of inputs as [I3, I2, I1, I0] = [0, 0, 1, 0], [0, 0, 1, 1], [0, 0, 0, 1], [0, 1, 0, 1],
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[0, 1, 0, 0], [1, 1, 0, 0], [1, 0, 0, 0], [1, 0, 1, 0], and [0, 0, 1, 0], and each state was lasted for 45 s (Figure 5b and 5c). According to the operation principle described in Figure 4, this sequence gives [0, 0, 1, 0] = SW, [0, 0, 1, 1] = SW + SE = S, [0, 0, 0, 1] = SE, [0, 1, 0, 1] = NE + SE = E, [0, 1, 0, 0] = NE, [1, 1, 0, 0] = NW + NE = N, [1, 0, 0, 0] = NW, and [1, 0, 1, 0] = NW + SW = W. The experimental results of the rotation and the displacement agree well, as illustrated in Figure 5d and 5e (see Supporting Information Movie S2). We highlight that the variation of the applied voltage between inputs renders fully continuous state of the displacement at any given rotation angle. It must be the first way to realize atypical rotational and linear motion simultaneously within a single actuator.
4. Concluding remarks
In summary, we have shown that our reprogrammable actuators are capable of increasing DOF by incorporating multiple inputs in one geometry. The vaporization of liquid droplets in the
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elastomer composite locally occurs adjacent to the resistive heater, such that each segment assigned to resistive heating elements can change the role of the actuating unit and the rigid constraint. Our actuators will especially be suitable for the works that require versatile, highly sophisticated control of the actuation direction owing to several remarkable characteristics: i)
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The structure as well as the actuating behavior of our actuators are not limited to the case discussed here but can change widely depending on the molds and corresponding configuration of resistive heating elements. ii) Since the actuation is driven by the voltage and the magnitude is controlled by the value of the applied voltage, our actuators control the actuation direction and magnitude precisely. iii) The scalability can be readily accessed because of the simplicity in the actuator configuration, the fabrication process, and the operating scheme without bulky 10
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accessories. The proposed actuators, in turn, outlines a powerful strategy for the design of freeform, actuatable, and reconfigurable soft structures via appropriate material selection and
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intelligent design. Therefore, we anticipate that this platform will be applied in a broad class of soft actuators and biomimicry devices.
Acknowledgements This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (NRF-2017R1D1A1B03029573).
Author contributions S.O., S.-U.K., and J.-H.N. designed the research; S.O., S.-U.K., S.Y., H.K., S.K. conducted the research and interpreted the results; J.-H.N supervised the research and interpreted the results; S.O., S.-U.K., and J.-H.N. prepared the manuscript.
Competing financial interests The authors declare that they have no competing financial interests.
Additional information Supplementary information is available in the online version of the paper. S.O. and S.-U.K. contributed equally to this work. Correspondence and requests for materials should be addressed to J.-H.N.
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D. Rus, M.T. Tolley, Design, fabrication and control of soft robots, Nature. 521 (2015) 467–475. https://doi.org/10.1038/nature14543. S. Palagi, P. Fischer, Bioinspired microrobots, Nat. Rev. Mater. 3 (2018) 113–124.
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Figure 1. Strategies for continuum actuation via reprogrammable geometric constraints. (a) Schematic illustrations of the isotropic expansion without geometric constraints (1), the unidirectional bending by the passive geometric constraint (2), and the extended bending modes via actively switching the role of segments in the elastomer composite (U and L) between the
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actuating unit and the rigid constraint based on the localized vaporization of liquid droplet fillers (3). Here, λ is the expansion ratio, α is the thermal expansion coefficient, L is the thickness, and E is Young’s modulus. Subscripts of r, s, U, and L depict the rigid layer, the soft body (elastomer composite), the upper layer, and the lower layer, respectively. (b) Exemplary actuation of 4-
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segments actuators comprising a 2 by 2 array of resistive heating elements. On-segments inflate while off-segments act as a rigid constraint to vary the bending direction.
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Figure 2. Asynchronous two-folds actuation. (a) Two-folds actuation occurs synchronously at all nodes when passive constraints are implemented. This is a single DOF actuation. Here, the width of the patterned gap is denoted by and Wo. (b) Asynchronous two-folds actuation via active geometric constraints. Each folding node, which is defined by configuring resistive heating elements separately along the length direction of actuators, can individually be
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manipulated.
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Figure 3. Actuation mechanics based on the contrast in stiffness. (a) Schematic diagram of BL-actuators. The thickness of the rigid layer (left blue) and that of the elastomer composite (right translucent) are denoted by Lr and Ls, respectively. (b) The experimental (top) and 20
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numerical calculation (bottom) results of the bending of BL-actuators at several conditions of the temperature (0, 35, 55, and 75 °C). In numerical results, the color bar is total deformation ∆𝑦
∆𝑧 . (c) Schematic diagram of 2-segments actuators
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of x, y, and z vectors as ∆𝑥
incorporating active geometric constrains. The off-segment (left) and the on-segment (right) have an identical material composition and similar thickness. (d) The experimental (top) and numerical calculation (bottom) results of the bending of 2-segments actuators at several conditions of the temperature (0, 40, 65, and 75 °C). (e) The bending curvature of BL-actuators and 2-segments actuators as a function of the temperature. (f) The bending curvature of BLactuators and 2-segments actuators under multiple cycles of the on-state (70 °C) and the off-
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state (25 °C). The states were switched every 5 min.
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Figure 4. Continuum actuation enabled by active geometric constraints. (a) Schematic illustration showing the configuration of resistive heating elements in 4-segments actuators as inputs [I3, I2, I1, I0]. (b) Exemplary actuation directions when considering a series of input as
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the binary state (the on-state and off-state). The output bending directions are represented as a vector. In case that two or more inputs are the on-state, the banding direction is expressed as the sum of the output vectors. Outputs also include the un-actuated state X. (c) Outputs that correspond to (b). Thermal images show that the temperature of the on-state input is higher than that of the off-state input. (d) Continuum actuation in the 2-dimensional plane via applying different values of voltages to two adjacent inputs. Output vectors are scaled by the applied 22
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voltage, and thus the sum of output vectors accordingly have arbitrary directions and distances in the associated quadrant defined by the two principal actuating directions. (e) Continuum
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actuation along one axis via manipulating two opposite inputs.
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Figure 5. Sequential control of inputs for rotational actuation. (a) Illustration of rotational motion via the sequential control of inputs [I3, I2, I1, I0]. (b) The chart flow and (c) the timing diagram of [I3, I2, I1, I0] to drive a counterclockwise rotation. (d) The displacement and the bending direction. The red circle and the green circle is the initial state at t = 0 and the bending
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of input combination of [0, 1, 0, 0] at t = 60 s, respectively. Here, each point was measured every 30 s. (e) Digital images in several time frames are showing the counterclockwise
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rotational actuation of the phase-change actuator. Red arrows denote the bending direction.
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