Fabrication and Structure. Sheath-driven yarn muscles consist of two parts, a high mechanical strength polymer core and a CNT-layer sheath that is infiltrated with silicone elastomer. Actuator performance varies when using different polymer fibers, such as a polyimide (PI), nylon 6,6, and Kevlar. The nylon 6,6 polymer is a monofilament fiber and the PI and Kevlar are yarns which contain three and one-hundred 10-micron-diameter fibers, respectively. The mechanical properties of these polymer fibers are listed in Table S1. The fabrication of a sheath-driven electrothermal muscle is schematically illustrated in Fig. 1. Except for the polymer coating step that results in polymer infiltration into the CNT sheath, in going from Fig. 1c to 1d, this process is analogous to that previously used to make sheath-run electrochemically powered artificial muscles31. As an example of a typical fabrication method, which was used unless otherwise indicated, a highly aligned 20-mm-diameter PI yarn was first twisted with 7 turns/cm under an isobaric mechanical load of 14 MPa (Fig. 1a). Then the twisted polymer yarn was transferred to a vertical stage with opposite yarn ends fixed (Fig. 1b). Thereafter, a 5-layer, 20-cm-long, 5-cm-wide CNT sheet was wrapped around the polymer yarn as a cylinder, so that the CNT alignment direction was parallel to the polymer fiber direction. By inserting twist into this forest-drawn CNT sheet stack from opposite cylinder ends, two opposite cones were formed until the CNT sheet cylinder was twisted onto the polymer yarn (Fig. 1c). After the wrapping process, silicone elastomer resin was uniformly coated on the CNT sheet (so as to infiltrate the resin into the CNT sheath), which is shown in Fig. 1d. After curing the silicone elastomer resin at 60℃ for 12 h and inserting twist into the sheath-core yarn to obtain complete coiling, using the same tensile load as used for yarn twist, a coiled sheath-driven electrothermal artificial muscle was obtained (Fig. 1e). SEM images for sheath-driven muscles are shown in figs. S1&S2. Hybrid yarn muscles were made using a previous described method19,20,33. A CNT yarn fully infiltrated with PDMS, which is called a hybrid yarn, is noted as [email protected], a sheath driven muscle with PDMS-infiltrated CNT as sheath and PI polymer as core is expressed as [email protected]
An additional process is needed for making a sheath-driven muscle that has a twisted CNT yarn core. In order to avoid infiltration of the silicone elastomer into the CNT core, paraffin wax was used as sacrificial material to fill the twisted CNT yarn34. Due to the incompatibility of silicone and paraffin wax, the silicone resin fully infiltrated into the sheath, without penetrating into the twisted CNT core. Since silicone has a high melting temperature of 450℃ (fig. S3), we can remove the paraffin wax without melting the silicone by heating the muscle at 180℃ in vacuum to volatilize the paraffin wax.
The twist density is defined as the number of inserted twisted turns divided by the original fiber length. The applied tensile stress was obtained by dividing the applied force by the cross-sectional area of the non-loaded, non-actuated, fully-twisted muscle, as measured immediately before the onset of coiling. The spring index is defined for the non-actuated muscle as the ratio of the average coil diameter to the total muscle diameter. The sheath-core ratio (SCR), which is defined as the sheath thickness divided by the core diameter, is about 0.37 unless otherwise indicated. Contractile stroke is defined as the change of the length of the loaded muscle divided by the non-actuated length of the loaded muscle. Stroke rate is contractile stroke divided by the cycle time. The applied input power density is the input power divided by the total muscle weight. Work capacity is the contractile work divided by the total muscle weight. Contractile power density means the contractile mechanical work divided by the contraction time.
Twisted muscles and homochiral coiled muscles contract when input power is on, and expand when input power is off. For a homochiral thermally-powered coiled hybrid yarn muscle (Fig. 2a), comprising a volume changing guest infiltrated throughout the muscles volume, thermal expansion of the muscle on increasing temperature transfers some of the yarn twist to the twist of yarn coiling, which causes the muscle to contract. For a sheath-driven muscle with hybrid sheath (Fig. 2b), volume expansion of the hybrid sheath in driven by electrothermally heating the yarn sheath, which causes the yarn to untwist by transferring yarn twist to an increased twist of coiling.
Figure 2c shows the time dependence of contractile stroke for a coiled neat CNT muscle, a coiled hybrid [email protected] muscle, and a coiled sheath-driven [email protected] muscle when a 0.05 Hz, 10.4 kW/g square-wave power input is used to drive actuation. At this low frequency, a [email protected] muscle provides a 23.2% contractile stroke, which is 1.2 times that for a thermal [email protected] muscle (20.1%) and 23 times that for a thermal neat CNT muscle (1.0%, fig. S4a). The spring indices for these muscles are 1.55, 1.56, and 1.6, respectively. The nearly identical spring indices are important for this comparison, since muscle stroke increases with increasing spring index. The yarn diameter for sheath-driven muscle, hybrid muscle, and CNT muscle were 68 mm, 78 mm, and 68 mm, respectively. Hence, the yarn surface area that is available for environmental cooling is similar. Nevertheless, the cooling time needed to reduce the contractile stroke by 90% for the [email protected] muscle (1.9 s) is much shorter than for the [email protected] muscle (9.0 s). When the frequency increased to 1 Hz, the stroke (5.4%) for the hybrid [email protected] muscle was much lower than the stroke for 0.05 Hz actuation, while the stroke for 1 Hz actuation (14.3%) (Fig. 2d, fig. S5a, Movie. S1) for the [email protected] muscle was close to the stroke for 0.05 Hz actuation.
The frequency dependencies of contractile stroke and contractile power density for the above sheath-driven muscle and hybrid muscle are shown in Fig. 2e. These results are for an applied power that is constant (10.4 kW/g) during muscle actuation. The contractile stroke decreases with increasing frequency for both muscles, since the input energy per cycle is inversely proportional to frequency. For both muscles (fig. S6), the contractile efficiency, calculated by dividing the contractile work per cycle by the input energy per cycle, increases with increasing frequency and increasing isobaric tensile stress. For an 8 Hz square-wave power, the [email protected] muscle can provide a contractile stroke of 7.3% (fig. S5b, Movie. S2), which is 7 times that for the hybrid [email protected] muscle (Fig. 2e, fig. S7d, 1.04%). Because of the decreased cooling time for the sheath-driven muscle, the contractile power density dramatically increases with increasing frequency. A maximum power density of 12.1 kW/kg was obtained at 8 Hz, which is 10 times the maximum power density for the hybrid [email protected] muscle (1.2 kW/kg at 2 Hz). The corresponding maximum stroke rate, defined as contractile stroke divided by the cycle time, is 57.6%/s at 8 Hz (fig. S5c) for the sheath-driven muscle, which is 8.7 times the maximum stroke rate for the hybrid muscle (6.6%/s at 2 Hz, fig. S5c).
For a 78-mm-fiber-diameter [email protected] muscle and a 68-mm-fiber-diameter [email protected] muscle, Fig. 2f shows the contractile stroke and work capacity as a function of applied tensile stress for these muscles for a 1 Hz square-wave power input. These results show that the load lifting capability of the sheath-driven muscle is higher than for the hybrid muscle. At this frequency, a maximum output work capacity of 1.63 kJ/kg was obtained for the [email protected] muscle, which is 2.9 times that for the [email protected] muscle (0.56 kJ/kg). The work capacity for the [email protected] muscle increased to 2.73 kJ/kg for a 0.3 Hz square-wave power input (fig. S5d). Although the sheath-driven yarn muscle shows much higher performance than the hybrid muscle, the weight percent (20 wt %) of PDMS to the CNT is approximately the same for the [email protected] muscle and for the [email protected] muscle, and the spring index for these yarn muscles were both about 1.55.
As shown in fig. S8, the sheath-driven muscle shows a similar contractile stroke (23.2%) as a hybrid muscle (21%) when a 0.05 Hz, 10.7 kW/g square-wave voltage is applied, where the input power is normalized to total muscle weight. However, when using a 1 Hz, 10.7 kW/g square-wave power input, the contractile stroke for a sheath-driven muscle (15.1%) is about 3.1 times that for a hybrid muscle (Fig. 3a).
The value of the sheath-core ratio (SCR) is important. Too low a SCR means that the sheath is not thick enough to affect the dimensions of the muscle core. Too high a SCR increases the electrothermal energy needed to power actuation and increases the time required to cool the sheath, which degrades high frequency actuation. The effect of SCR on actuation for a [email protected] muscle is shown in Fig. 3b. While the SCR little affects stroke for a frequency of 0.1 Hz, increasing the SCR produces a larger stroke decrease at higher frequencies. Figure 3c shows the effect of SCR on the tensile stress dependence of contractile stroke and work capacity for an actuation frequency of 0.1 Hz. These results show that the highest contractile work capacity for this low actuation frequency was obtained for an intermediate SCR of 0.37.
Since muscle stress generation is also important for powering soft robotics, we also measured isometric stress generation, using the apparatus in Fig. 3d. The isometric stress first increases and then decreases with increasing applied pre-strain (fig. S9a). The maximum generated isometric stress during actuation for a [email protected] muscle was 11 MPa for a pre-strain of 25%. The frequency dependence of the generated stress is shown in Fig. 3e for an isometric pre-strain of 25%. Actuation was driven by a 15 V/cm square-wave voltage. These results show that the generated stress decreases with increasing frequency, which is a consequence of the decreased heating time at increased actuation frequency (fig. S9b). For 1 Hz actuation, the sheath-driven muscle generated a stress of 3.5 MPa, which is 5.9 times that for a hybrid muscle (0.6 MPa, Fig. 3e). The diameters for the sheath-driven and hybrid muscles were 45 and 51 mm, respectively.
Our sheath-driven muscles exhibit good cyclability. Figure 3f shows results obtained when a [email protected] muscle was cycled 1000 times by applying a 1 Hz square-wave voltage, while a mechanical load of 15.6 MPa was applied. The inset shows the time dependence of contractile stroke for the first three cycles and for the last ten cycles. After 1000 cycles, the stroke of 14.3% decreased by only 5.6% of that for the first cycle, which demonstrates that the sheath-driven muscle has excellent cyclability.
Fast actuation mechanism
In order to more deeply understand why the sheath-driven muscle shows much faster actuation than a hybrid muscle having the same diameter, the time dependence of temperature changes for sheath-driven muscle and hybrid muscle were measured using a thermal infrared camera. For these comparative measurements, the peak surface temperature for these muscles was regulated to be the same (150℃), by using a different constant voltage for the square-wave voltage input for the sheath-driven muscle and the hybrid muscle. When cycled using a 1 Hz square-wave voltage, the sheath-driven muscle cools faster and provides a larger contractile stroke than the hybrid muscle (Fig. 4a and Fig. 4b). Although the sheath-driven muscle and hybrid muscle have the same diameter of 65 mm, the sheath-driven muscle cools to ambient temperature (16℃) within 0.5 s, which is to a lower temperature than for the hybrid muscle (30℃) with the same cooling time. The sheath-driven muscle provides a contractile stroke that is 1.4 times that obtained for a hybrid muscle (9%).
Since temperature measurements using a thermal infrared camera only provides information on the muscle surface, the temperature distribution along the muscle radius is needed. Theoretical modeling was used to predict the temperature profile along the radial direction. For a fully-infiltrated hybrid muscle, the input electrical energy is uniformly delivered to the whole muscle, and therefore the initial temperature from muscle surface to center is nearly the same (fig. S10). As shown in Fig. 4d and 4e, the sheath temperature varies between 286℃ and 60℃ during 1 Hz continuous square-wave actuation cycles, while the muscle core temperature fluctuates only between 180℃ and 150℃ (Movie. S3). This indicates that the high actuation rate for the sheath-driven muscle results since temperature changes during cycling are largely localized on the sheath, which drives the actuation. The temperature profile for sheath-driven muscle can be optimized by changing the sheath-core ratio (fig. S11).
By using the infrared-camera-measured surface temperatures, we calculated the heat transfer coefficients for sheath-driven muscles and hybrid muscles by applying Newton's cooling law:
where t is the heat transfer coefficient35. T1 and T2 are the surface temperatures of actuated and non-actuated states, respectively. For the same diameter sheath-driven and hybrid muscle (70 mm), the heat transfer coefficient for the sheath-driven muscle and hybrid muscle were 0.151 and 0.207, indicating that the sheath-driven muscle cools faster than the same diameter hybrid muscle.
Thus, there are two reasons that sheath-driven muscle can operate at high frequencies. Firstly, the hybrid CNT sheath delivers thermal energy to itself, which improves the heating process. During cooling process, the CNT network in the sheath accelerates thermal transport rate between hybrid sheath and ambient air, which enables fast cooling. On the other hand, due to the big difference of thermal conductivity between hybrid sheath and polymer core36,37, the thermal energy delivered to the polymer core in first few cycles is mostly trapped in the polymer core during next heating-cooling cycles. Hence, the exchange of thermal energy is largely restricted in the hybrid sheath.
Demonstration of crawling robot
A robot that crawls in a pipe was designed and implemented to demonstrate the use of the high frequency actuation of our sheath-driven artificial muscles. The robot was made of silicone elastomer (SYLGARD 184, Dow Inc.) and actuated by [email protected] muscles with yarn diameter of 287 μm and spring index of 1.63. The robot has a total length of 55 mm and can crawl inside a 10-mm-diameter pipe. As shown in Fig. 5a, the robot consists of four rhombic modules made of silicone struts, and powered by muscles that are along a rhombic diagonal. The two end modules are larger in diameter, so they can clamp on the pipe surface, while the smaller diagonal inner modules provide actuation but no clamping. Upon electrothermal heating, the artificial muscles contract, causing the module to shrink in the muscle length direction and expand in the perpendicular direction. The four modules are connected in series along the diagonal direction and can be electrically heated individually. The working principle of the robot imitates the inchworm mechanism. First, the anterior clamping module is heated to clamp against the pipe, then the middle modules are heated to pull the posterior forward. Afterwards the posterior clamping module is heated and the other modules are afterwards allowed to cool to complete a cycle. Figure 5b shows the robot crawling between two parallel walls. When operated using a 0.25 Hz, 1 V square-wave voltage input, the robot has a crawling speed of 7.5 mm/min (Movie. S4).