A modular torsional actuator using shape memory alloy wires

Abstract

In this study, novel modular shape memory alloy wire–based torsional actuators were designed and fabricated. These shape memory alloy–based actuators provide rotational displacements. The mechanical and thermal properties of a single module shape memory alloy torsional actuator were characterized. Next, a modular shape memory alloy torsional actuator was configured by connecting single actuator modules in series. This modular actuator can be used directly as a soft or biologically inspired robot. Finally, the rolling motion and shape transformation of the modular shape memory alloy torsional actuator (soft robot) were demonstrated with a simple open-loop-based control scheme experimentally validating the novel mobility and actuation of the proposed actuator. For a control input, sequentially coordinated square waves of electric current were supplied to the shape memory alloy actuating units.

Keywords

Characterization shape memory alloy wire soft robot torsional actuator

Introduction

Novel shape memory alloy (SMA) wire–based torsional actuators were designed and fabricated in this study. SMAs are smart materials that possess two important thermo-mechanical properties: shape memory effect and pseudo-elasticity. An SMA material can be deformed easily by external forces to produce a large residual strain when it is below its transition temperature. The SMA material can then fully recover its original shape while contracting if it is heated above its transition temperature.

Through the cycling of these deforming and recovery processes, SMA materials can generate mechanical forces and displacements. As a result, SMA materials can be used to provide new actuation methods and motions for various applications, which were difficult to achieve previously with simple traditional actuators such as electromagnetic motors. The benefits of SMA actuators include low cost, small size, high strength-to-weight ratio, silent operation, and compliance compared to traditional electromagnetic motors. Thus, SMA actuators have been frequently used in the biomedical, aerospace, and robotic fields (Coral et al., 2012). Many non-invasive surgical devices (Mingyen et al., 2012) have been introduced that use SMA actuators. More recently, many robotic researchers have investigated new actuations and manipulations by applying SMA actuators to various robotic applications which include soft and biologically inspired robots (Gilpin et al., 2014; Kim et al., 2006; Lee et al., 2013; Wang et al., 2008).

SMA wire has been traditionally used to provide one-dimensional linear or bending motion. However, this motion is constrained by a typical maximum strain of 5%–8% for the wire (Gilberston, 2000; Song et al., 2000; Wang et al., 2008). Nitinol SMAs or nickel–titanium alloys are one of the most popularly used SMA materials. Furthermore, SMA wires can be made into coil springs by applying heat treatment processes. In contrast to the relatively small strain in linear SMA wires, SMA coil springs can provide considerable deformation (in some cases, more than 100%) depending on their resisting load and geometric configuration (An et al., 2012). More recently, SMA sheets or thin plates (Jamie et al., 2010; Jamie and Robert, 2012) have been used to produce torsional or folding motion which has been difficult to achieve with a single SMA wire or spring. Typically, these SMA sheet–based folding actuators are produced by applying additional machining processes such as laser cutting. SMA coil springs (An et al., 2012; Huai-Ti et al., 2011; Kim et al., 2006) and sheets (Gilpin et al., 2014) have been adopted for the rolling motion of soft or biologically inspired robots.

To use SMA materials as an actuator, the thermo-mechanical properties of the materials need to be understood. Thus, many researchers have investigated the characteristics of SMA actuators for modeling and control (Brinson, 1993; Chang et al., 2006; Ianagui and Tannuri, 2011; Jayender et al., 2008; Lederlé, 2002; Wang et al., 2012). SMA actuators typically can be modeled by considering the thermo-mechanical properties which include the transformation between the martensite and austenite phases, temperature dynamics, and the stress–strain relationship (Brinson, 1993; Chang et al., 2006; Jayender et al., 2008). Parameters for actuator modeling have also been identified or tuned experimentally in many studies (Ianagui and Tannuri, 2011; Wang et al., 2012). As a result, many control schemes for SMA actuators have been presented based on their theoretical or experimental models, or on ad hoc methods (Chang-Jun et al., 2004; Gilpin et al., 2014; Huai-Ti et al., 2011; Jayender et al., 2008; Kim et al., 2006). Furthermore, some researchers (Shin et al., 2004; Teh, 2008) have focused on the actuation frequency which could critically depend on the heating and cooling times of the SMA material.

For novel modular SMA wire–based actuators, we first have to consider linear and arc-shaped SMA actuating units, which can provide linear and rotational motions as shown in Figure 1(a) and (b), respectively. These actuating units are then rigidly attached to supporting elements to deliver actuator forces or torques to an object. These supporting elements can be used to mount an actuator on an object or to extend the actuator into a modular configuration. Because the linear displacement of the actuator may relatively be limited for use in many applications particularly when compared to electromagnetic motors, in this study, we focused on a torsional actuator that can provide rotational motion using a relatively larger displacement (∼0 ≤ θ ≤ θ^*; θ^* = maximum rotation angle). The designed torsional actuator has three phase states based on the thermo-mechanical properties of the SMA as shown in Figure 1(c). In State I (the deformed martensite phase), the actuating unit is initially deformed into an arc shape by loading at ambient temperature. Heating the SMA unit, the actuating unit then restores its original linear shape while contracting in State II (the austenite phase). By cooling the SMA unit, the actuating unit is extracted while keeping its previous heated shape in State III (cooled martensite). Moreover, the proposed SMA actuating units can easily be extended to parallel, serial, or multi-dimensional modular configurations as shown in Figure 2 such that we can increase the forces/torques of the actuator or provide new customized motion. First, a one-dimensional torsional actuator was constructed in a parallel configuration, as shown in Figure 2(e), to experimentally characterize the proposed novel torsional SMA actuator. The mechanical and thermal actuator properties were investigated. Then, this one-dimensional actuator was extended to a serially connected modular torsional actuator, as shown in Figure 2(g), which can be directly used in a soft or biologically inspired robot with a higher degree of freedom. Moreover, the rolling locomotion of a soft robot and the transformation of a robot shape from a horizontally straight posture to a circular posture were demonstrated with a simple open-loop control scheme.

The remaining part of this article is organized as follows. We discuss the structure of the torsional actuator in section “SMA actuator.” A one-dimensional torsional actuator in a parallel configuration is then characterized in section “Actuator characterization.” We demonstrate a serially connected modular torsional actuator (a soft robot) in section “Demonstration of a modular configuration: soft robot.” Finally, we provide conclusions in section “Conclusion.”

SMA actuator

This section describes the structure of the SMA wire–based actuators. In the proposed design, a single SMA actuator module comprising an SMA actuating unit and two supporting elements is shown in Figure 1. One end of the actuating unit is attached rigidly to the supporting element which supports the actuating unit and provides a connection to other mechanism or object. The actuating unit is made of a linear or deformed arc-shaped SMA wire which can provide force/torque through the shape memory effect. In this case, the actuating unit can be arranged as a single coil wire or as an array. Furthermore, a single actuator module can be extended to one-dimensional or multi-dimensional configurations as shown in Figure 2.

Next, a modular actuator is fabricated with SMA wires. Figure 1(a) and (b) shows how an SMA wire can be configured to produce linear and rotational motions. For the linear motion shown in Figure 1(a), an actuator is simply constructed by attaching a straight actuating unit (SMA wire) to the supporting elements in series without deformation in the SMA wire. This linear actuating configuration is similar to a prismatic joint and an actuator between two links in a manipulator robot. For rotational motion shown in Figure 1(b), an arc-shaped SMA actuating unit is used, deformed from a straight SMA wire. The actuating wire unit can be attached to supporting elements in parallel or at an oblique angle. As shown in Figures 1(c), 2(a), and (b), two supporting elements in the torsional actuator are initially aligned to have a non-zero (oblique) angular displacement, θ = θ^*, in State III where it is below the transition temperature with no external force. By applying an external force, the two supporting elements are easily positioned with a small or zero angular displacement, θ = ∼0°, as shown in Figures 1(c), 2(c), (d), (e), and (g), in State I where the SMA wire is still below its transition temperature. If the SMA wire is heated above the transition temperature by supplying an electric current, the SMA wire is contracted while recovering its original (or memorized) linear shape such that the two supporting elements are positioned to produce torque and rotational motion with an angular displacement of θ = θ^* in State II as shown in Figure 1(c). This torsional actuator can provide torque and rotational motion similar to a revolute joint and actuator with a limited range of orientations.

In this study, a single torsional SMA actuator module and a serially connected modular torsional actuator in array form were demonstrated. Thus, a torsional actuator prototype was first constructed (Figure 3) using an actuating unit in a one-dimensional wire array to form 28 coils as shown in Figure 2. This wire array is an extension of a single coil wire actuating unit to increase the force/torque capacities as previously discussed. Next, a serially connected modular torsional actuator prototype was constructed (Figure 4) by extending the proposed single module actuator, which consists of eight actuating units and nine supporting elements. This modular torsional actuator can be used directly as a soft or biologically inspired robot, which will be discussed in section “Demonstration of a modular configuration: soft robot.”

Actuator characterization

In this section, the single module actuator is characterized experimentally, especially the torsional spring constants, mechanical responses, thermal response speeds for several different given input currents, and resulting temperatures.

Mechanical characterization

The torsional spring constant of the actuator was investigated to characterize the stiffness. Two different spring constants were considered for the actuator: (1) the actuated spring constant at State II where the actuator is on and the resting position is θ ≈ 60° and (2) the unactuated spring constant at State I or III where the actuator is off. In addition, three different cases were considered to measure the unactuated spring constant: Case 1 in which the actuator is rotated counterclockwise with a resting position of θ ≈ 60°, Case 2 in which the actuator is rotated counterclockwise with a resting position of θ ≈ 0°, and Case 3 in which the actuator is rotated clockwise with a resting position of θ ≈ 0°. Our experimental setups for measuring spring constants are shown in Figure 5. One supporting element of the actuator was fixed and external force was applied to the other supporting element. Torque is estimated using a load cell which is mounted on a micrometer motion stage. The resulting angular displacements were measured as shown in Figure 6. As a result, the respective actuated and unactuated spring constants, k_a = ∼0.14 Nm/rad and k_u = ∼0.04 Nm/rad, respectively, were obtained with linear regression. This result shows that the torsional spring constant increases by 250% when the actuator is on. Note that the unactuated spring constant is approximated to be 0.04 Nm/rad even though the spring constant in Case 3 is slightly larger compared to Cases 1 and 2. Also note that mechanical instability is observed for larger displacement (>∼0.15 rad) in Case 3.

Furthermore, elastic beam theories (Benham et al., 1996) could be used to find an approximated torsional spring constant, which may be used to verify our experimentally determined spring constants. Toward this goal, a slender cantilever beam was considered with length L_b, Young’s modulus E, and the second moment of the cross section I. By applying the lateral force P at the tip of the beam and assuming a small deflection, the torsional spring constant k at the tip can be determined with the angular deflection ϕ and the moment M as given in equation (1)

\begin{array}{l} ϕ (L_{b}) = \frac{P L_{b}^{2}}{2 E I} \\ k = {\frac{M}{ϕ} |}_{t i p} = \frac{P L_{b}}{ϕ (L_{b})} = \frac{2 E I}{L_{b}} \end{array}

(1)

Considering a simple actuating unit with 28 slender wires and applying the SMA wire properties provided in Table 1 to equation (1), we can determine the respective unactuated and actuated spring constants at the tip of the actuator: k_u = 0.0328–0.0468 Nm/rad and k_a = 0.0877–0.0971 Nm/rad. Our analytically simplified model–based spring constants could be used to verify the experimentally determined spring constants despite some deviations between the simple analytical results and the experimentally determined values.

Table 1.

Properties of a nitinol SMA wire.

Properties	Value
Wire length (L_b)	18 mm
Radius of the wire	0.25 mm
Young’s modulus (State II: austenite)	75–83 GPa
Young’s modulus (States I and III: martensite)	28–40 GPa

SMA: shape memory alloy.

In many applications, it has been quite popular to use an electrical current or the resulting heat to activate SMA actuators. The angular displacements (the orientation angle, α = θ/2) of the actuator as a function of time were examined to determine the actuation speed shown in Figure 7. Eight different input currents were applied ranging from 0.5 to 1.2 A, which includes the recommended 1-A input current for a nitinol SMA wire with a 0.25-mm diameter. Through observations, it was confirmed that the displacement response of the actuator is faster for a higher input current, whereas the response speed is slower for a lower input current. It takes less than 1 s to reach α = 40° from a resting position of α = 0° for the applied input currents of 0.8–1.2 A. For the input currents of 1.1–1.2 A, the actuation time to reach α = 50° from 0° was less than 0.7 s. We also found that lower input currents such as 0.5 A might not provide sufficient force to activate the actuator completely for a given time period. It is worthwhile to note that the mechanical actuation speed of the actuator increases as the magnitude of input current increases. However, it should also be noted that overheating the SMA wire using a higher input current can easily cause physical damages to the actuator such as wire melting and ultimately results in a loss of the shape memory effect.

Thermal characterization

One of the limitations in SMA actuators could be the relatively longer cooling time, which could critically limit the operation frequency of the actuator. The overheating approach has thus been used to provide a higher actuation frequency for high-speed applications. Increasing the input heating power can improve the actuator response time considerably. As a result, increasing the input heating power could resolve the limitations in actuation frequency. However, overheating can easily cause physical damage to SMA materials such that the shape memory effect can be ultimately lost as mentioned above.

Next, the thermal response of the actuator was investigated. Figure 8 shows the heating and cooling of the SMA actuating unit for five different input currents. The maximum temperature T_max is limited to ∼70°C to prevent physical damage to the SMA actuator for the applied higher input currents. The minimum temperature corresponds to ambient room temperature, T_a = 21°C–23°C. Temperature responses for the lower input currents below 0.7 A are not included here because they are considerably slow. Higher input currents significantly decrease the required time for the cooling and heating of the actuator as expected.

For further analysis, the heating speed was defined as the elapsed time to reach the maximum heated temperature (T_max = ∼70°C) starting from the ambient temperature (T_a = 21°C–23°C) for a given input current. Likewise, the cooling speed was measured from T_max to T_a; the activation start speed was measured from T_a to the activation start temperature (68°C), and the relaxation finish speed was measured from T_max to the relaxation finish temperature (42°C). Applying five different input currents, these four thermal response speeds are shown in Figure 9.

For 0.8, 0.9, 1.0, 1.1, and 1.2 A inputs, the heating speeds from T_a to T_max are 1.8, 0.31, 0.18, 0.11, and 0.077 s, respectively. The activation start and relaxation finish speeds are even faster than the heating speeds as desired. However, the cooling speeds from T_max to T_a are considerably slower (e.g. 3–10 times slower) compared to the heating speeds. More importantly, the actuation frequency of the SMA actuator critically depends on the heating, activation start, and relaxation finish speeds. Thus, by taking into consideration the heating, activation start, and/or relaxation finish speeds for a given input current, a control input can be derived for the actuator to achieve a higher frequency of actuation.

Demonstration of a modular configuration: soft robot

The proposed single module for a torsional SMA actuator was extended to a modular torsional actuator by connecting eight single actuator modules in series as shown in Figure 4. This serially connected modular torsional actuator can be used directly for a soft or biologically inspired robot. Our modular SMA actuator demonstrated shape transformation and rolling locomotion as shown in Figure 10(a) and (b), respectively. In this case, open-loop control algorithms were simply applied to validate the proposed design of the single and/or modular SMA actuator. Each actuating unit is independently and sequentially activated to achieve each task. The experimental results of this study verify that the actuator functions as designed such that rolling locomotion and shape transformation are easily achieved as expected.

Conclusion

In this study, we present a single module and modular SMA actuators using SMA wires. The single module actuator can easily be extended into several more versatile configurations. We then investigated the mechanical and thermal properties to characterize the actuator. From the results, we found that a higher current input is required to activate the actuator faster. More importantly, thermal response speeds should be coordinated properly to provide higher frequency actuation while preventing physical damage to the actuator. In addition, the torsional spring constants of the actuator were also estimated for dynamic modeling. In this case, we demonstrated rolling locomotion and shape transformation using simple open-loop control algorithms. Moreover, our results could be used to establish a dynamic model and more advanced control algorithms for the actuator to be carried out in future research.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (2012R1A1A1011457).

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