Soft robots, an emerging supplement for rigid robots, have attracted huge attention from both academia and industry. The development of soft robots is rapidly evolving with complimentary activities covering architecture design, assembling, modeling, and control [1
Most of those soft robots are driven by soft actuators or known as artificial muscles which can serve torsion, tensile, or bending motion pneumatically, thermally, electrically, or by other methods [3
]. Pneumatic artificial muscles (PAMs) have large actuation force, high power density, and fast respond speed [8
]. PAMs can exhibit high strain up to 90%, generating peak power densities over 2 kW/kg [10
]. Dielectric elastomers (DEs) can generate a large strain up to 24% when subjected to an electric field, while the power density reached 80 W/kg [1
]. Hydrogels can achieve a large strain (up to approximate to 40%), and deliver a remarkable volumetric power density of 30.77 mW/cm3
Recent literature reports a novel type of soft actuator which used twisted and coiled polymer (TCP). These artificial muscles have been intensely studied due to their high strength, high work density, and ease of access. TCP muscles are converted from inexpensive commercial polymer fibers used for fishing line and sewing thread so they are cheap as well [16
These coiled muscles can generate large strain of 49% without hysteresis, exceeding the maximum stroke of human skeletal muscles [16
]. Soft robot modules driven by TCP muscles were developed and could be easily assembled and fabricated. These modules produce maximum bending angle of 40° in any direction, and reversible radius of curvature reaching 0.23 mm−1
]. Integrated systems have been proposed, including musculoskeletal system [19
], robotic hand [21
], power generation systems [23
], and robotic skin, in which the TCP muscles are embedded within the soft silicone skin as linear actuators, allowing the skin to generate desired movements without noise [25
The actuation mechanism of TCP muscles under simulation could be regarded as following steps: (a) during fabrication process, twist is inserted into nylon fibers, then wrap highly twisted fibers around a mandrel to make them coiled, which enables them to amplify tensile stroke; (b) during actuation process, TCP muscles will untwist when subjected to heat because of the positive axial and negative radial thermal expansion coefficient, resulting in a torque that decreases inter-coil separation. The torque will transfer into ‘recovery force’ when two ends of the TCP muscles are fixed to prevent rotating while the twist number inserted in fabrication process turning into length change of TCP muscles, generating actuation stroke and; (c) during recovery process, TCP muscles will twist again and return to unactuated state when the temperature drops.
Therefore, it is concluded that the actuation performance is highly related to how TCP muscles are made. Through single-helix approximation method, it is proved that torsional stroke depends on twist number inserted into the fiber and is independent of fiber diameter [26
]. While other studies report that the performance of TCP muscles can also be affected by other factors such as annealing stress, arrangement of fibers, turns per a length, weight per a fiber, and temperature of heat treatment [27
]. The influence of twisting speed and plies number on the performance of TCP was discussed thoroughly [31
]. It is found that low coiling speed will introduce variation of actuation performance while the twisting frequency close to the natural frequency of the TCP muscles. The use of spandex was introduced as another approach to improve TCP performance [32
]. By adjusting those fabrication parameters, various of actuation strain can be obtained. For example, it is shown that the strain can be improved from 3% to 10% by increasing annealing stress [29
]; and optimal coiling load can lead to achieve highest muscle stroke up to 40% [32
As explained above, actuating characteristics of TCP muscles are mainly determined by few fabrication parameters. However, there is a lack of studies demonstrating the reasons for coils forming of TCP muscles and the quantitative relationship between tensile actuation and fabrication load, which may contribute to the further improvement of TCP performance.
In this study, we adopt the theory of elastic bar and present a model showing the quantitative relationship between tensile actuation and fabrication parameters. As mentioned in [16
], larger actuation strain of TCP can be achieved by increasing twist number inserted into the fibers. However, overtwisted fibers will form curls or improper coiling before wrapping them around a mandrel. Therefore, we identified the critical load and twist of coils forming as key factors and considered these fabrication parameters when deriving the actuation equations of TCP muscles. Firstly, in Section 2.1
, the relationship between maximum twist number and fabrication load is derived based on elastic rod theory. Such a relationship explains how the factors like the fiber elastic modulus, fiber shape, and dimensional size could influence the maximum twist number. Now we have the expression of maximum twist number by using fabrication load as independent variable. Therefore, the quantitative relationship between tensile actuation and maximum twist number can be derived. By doing so, we can propose the function between tensile actuation and fabrication load. Secondly, in Section 2.2
the quantitative relationship between tensile actuation and maximum twist number are proposed based on Frenet frame. Finally, the relationship between tensile actuation and fabrication load is obtained. We validated the model through TCP muscles made of silver-coated Nylon 6 fiber under different fabrication load. Recovery stress and maximum stroke of the samples are measured during heating by using a dynamic mechanical analyzer (DMA). The proposed model was also evaluated in terms of the quantitative prediction of the tensile stroke.
In order to validate the effectiveness of the proposed model, experiments were conducted through a prototype of the experimental.
Conductive silver coated Nylon 6 fiber (product number: #40024104600, Shieldex®, diameter: 0.6 mm, lineal resistance: 50 Ω m−1, mass: 0.37 g m−1) was used to fabricate TCP muscle. The thermo-mechanical tests of samples were conducted by DMA Q800 (TA Instruments, New Castle, DE, USA). The thermal distribution of TCP muscles during heating was captured by a thermal imaging Camera T630SC (FLIR® Systems, Inc., Santa Barbara, CA, USA). Microscope image was taken by digital microscope VH-S30 (KEYENCE, Osaka, Japan).
This paper concentrated on homochiral muscles whose chirality of fiber twist matches the coil’s chirality [16
]. For homochiral muscles, the direction of helical structure is the same to the fiber twist under the same rule (such as right-hand screw rule). These muscles tend to contract during heating. Silver coated Nylon 6 fibers were twisted before coiling, then wrapped around a mandrel of 1.38 mm diameter. The bottom end of Nylon fiber was loaded with a known weight which was free to move vertically, and rotation was prevented. The other end was twisted by an electrical DC motor. After that, the resulting samples were annealed at 140 °C for 90 min, then cooled to room temperature. Finally, the TCP muscles were obtained.
3.1. Thermo-Mechanical Properties Test of Silver Coated Nylon 6
The thermo-mechanical tests of samples were conducted by DMA Q800 (TA Instruments, New Castle, DE, USA) and carried out in tension mode at a frequency of 1 Hz. The temperature varied from room temperature up to 180 °C with a rate of 3 °C/min, while the length of fibers between clamps was 15 mm. We carried out such experiment to identify elastic modulus under various temperature of commercial purchased silver coated Nylon 6 fibers.
3.2. Strain of TCP Muscles under Different Fabrication Load
In this test, the fiber length is 500 mm and the TCP muscles had a non-loaded length of 42 mm. Samples were heated by applying electric current of 0.2 A. Strain of TCP muscles with different fabrication load was captured by a high-speed camera under different test stress. The upper end of TCP muscles was fixed, while the bottom end was attached to a weight.
3.3. Isometric Recovery Stress of TCP Muscles
TCP muscles were tested in DMA Q800 at constant strain of 30%, heating from room temperature up to 130 °C with a rate of 3 °C/min. TCP muscles tend to contract when heated, which bring about the change of recovery stress.
3.4. Recovery Strain of TCP Muscles During Heating
Recovery strain of TCP muscles change with temperature. TCP muscles were also tested in DMA Q800 at constant force of 0.8 N, heating from room temperature up to 140 °C with a rate of 3 °C/min. The experimental data were compared to theoretical model deduced from Equation (15). The relationship between temperature and actuation strain (shown in Equation (15)) can be validated through these experiments.
In this paper, an elastic-rod-theory-based model was established and validated for explaining the quantitative relationship between tensile actuation and fabrication load. For modeling building, firstly, the relationship between maximum twist number and fabrication load is derived based on elastic rod theory. The maximum twist number that could insert into the TCP muscles which directly determine the stroke of TCP depends on the fiber elastic modulus, dimensional size, and fabrication load applied during fabrication. Such a relationship explains how these factors could influence the maximum twist number. Next, the quantitative relationship between tensile actuation and maximum twist number are proposed based on Frenet frame. Finally, the relationship between tensile actuation and fabrication load can be obtained. The model can also be used to predict the tensile stroke as a function of temperature. For model validation and parametric study, TCP muscles made of silver-coated Nylon 6 fiber were fabricated under different fabrication load. Recovery stress, recovery strain, and maximum stroke of the samples with different fabrication load were measured during heating by using a dynamic mechanical analyzer. Finally, we evaluated the model in terms of the quantitative prediction of the tensile stroke. The theoretical predictions were in agreement with experimental results. The results show that the TCP muscles of 10.44 MPa fabrication load were capable of demonstrating maximum stroke of 52.6% with a specific work of 186.49 J/kg.
For real application, the model provides a guideline for choosing desired fiber materials, fiber shape, or dimensional size. Further works could be on improving of efficiency and building control strategy of TCP muscles. Therefore, those compliant, safe, non-noised, and cheap muscles can be used in rehabilitation robots, intelligent equipment, aquatic robots design, etc.