Design and Experiment of a Hand Movement Device Driven by Shape Memory Alloy Wires

Hand is one of the most ﬂexible and useful organs of the human body. However, cases of hand function loss due to diseases and accidents abound, which brings a lot of inconvenience to patients’ lives. This paper introduced a ﬂexible hand movement device (HMD) driven by shape memory alloy (SMA) wires, which is compact, lightweight, and easy to use during activities of daily living (ADL). Firstly, we elaborated the design and modelling process, including the driving analysis of SMA wires. Secondly, the manufacturing process and testing method of the HMD are presented. Thirdly, the results of the experiment are discussed in detail. Through the experiment, we obtained the bending angle and operating space of ﬁngers. Moreover, the joint angle as well as the ﬁngertip force can be controlled using PWM. A maximum angular movement of 45 ° , 62 ° , and 71 ° can be generated at the metacarpophalangeal (MCP), proximal interphalangeal (PIP), and distal interphalangeal joints (DIP) of a ﬁnger using an SMA wire, respectively. Then, the operating space of the entire hand can be calculated based on the experimental results. Besides, an estimated 40 N of grasping force can be produced for a whole hand. In conclusion, this research indicates that the ﬁnger movement driven by the HMD is similar to a healthy person, which can meet the needs of ADL.


Introduction
Kinds of neural diseases, such as stroke, may result in the loss of hand function, which causes enormous damage to patients' physical and mental health [1][2][3]. Many studies have confirmed that rehabilitation therapy can limit stroke complications and facilitate brain remodeling [4][5][6]. us, researchers have designed and fabricated a variety of robots to assist rehabilitation progress. Primordially, Wege and Conti proposed some kinematic chain mechanism for hand exoskeletons [7,8]. But the rigid structures in the linkage mechanisms usually impede the therapeutic potential of robotics, which causes joint alignment issues and secondary joint damage [9].
To combat these shortcomings, cable-driven mechanisms, pneumatic actuators, and artificial muscles are rapidly utilized as an alternative. Under Chu and Patterson, most hand rehabilitation devices use pneumatic systems or cable systems as actuators [9]. Hyunki In et al. designed a wearable robot called the Exo-Glove with a soft tendon routing system. e fingers were pulled by Bowden cable actuated by motors. Lucas et al. [10] proposed an EMGcontrolled pneumatic cable-driving hand exoskeleton in 2004. It was lightweight, and adjustable, but inconvenient to carry around because of the bulgy pneumatic pistons and other affiliate devices.
With the development of novel artificial muscles, pneumatic artificial muscle (PAM), twisted and coiled polymer (TCP) muscles, and SMA are increasingly being used in prosthetics and rehabilitation as actuators.
PAM has been widely used in the industrial and scientific field due to its high strength and small weight. However, it exhibits a highly nonlinear relationship between contraction and pulling force, which makes it difficult to model and control [11]. Besides, commonly used PAM actuators are relatively bulky and take up a lot of space, which is not convenient to install and carry around. Lokesh et al. proposed iGrab [12] in 2017, which was powered by TCP muscles. e device is lightweight but the output force still needs improvement. A study by Matheus et al. benchmarked grasping and manipulating forces and found that most objects of daily living weigh less than 1.5 Kg [13]. In terms of the research conducted by Wu et al. [14], the maximum tensile force of the TCP muscle is only 4.5 N, which is quite low compared to high stress [15] SMA (∅ 0.3 mm, 40 N). Besides, the total diameter of the coiled TCP muscles is 1.24 ∼ 1.41 mm( ± 0.02), which is thicker than SMA wires (0.3 mm). ASR glove [16] was proposed by Alireza et al. in 2017; it was actuated by SMA and could provide a grasping force of more than 40 N, which was sufficient for ADLs. However, the joint angles still need improvement.
In general, there are some terminologies which generally completes the power criteria of different actuators. However, there is no universal standard for measuring actuators. e judging criteria are depending on what the author uses the actuator for [17]. In [18], the trade-off between force output and the actuation speed is the main issue in rehabilitation. Compared to TCP muscles, SMA wires can exert higher stress. Apart from this, the pseudoelasticity and shape memory effect (SME) of SMA are very useful in neurology and neuromuscular rehabilitation applications [18]. e SME enables the SMA to integrate the sensor with actuator which can simplify the structure. Moreover, by exploiting the hysteretic properties, we can control and dampen unwanted involuntary movements during the actuation process to improve stability [18]. But there are a few studies that used SMA as actuators for hand rehabilitation because it is difficult to design a soft and pliable exoskeleton to fit well with SMA wires and the hand. Furthermore, the limited strain of the SMA wires stops it from being used as actuators [19]. To overcome this shortcoming, we designed a novel range extender mechanism to magnify the limited strain. Above all, it is very urgent to study the anatomical structure of human hands and design a new flexible exoskeleton structure driven by SMA wires. However, the current research on the new structure and design method is not innovative enough.
Based on the abovementioned design, we came up with an idea to actuate the finger in a way that is flexible and lightweight. As is known to us all, the pulley mechanism can be used to enlarge the displacement, so it can enlarge the shrinkage of the SMA wires. However, because the SMA wire has high hardness and does not fit well with the pulley, we use ropes instead. To connect the ropes and SMA wires, we designed some connection mechanisms. erefore, 3D printed range extenders which consist of the structures mentioned above are designed to amplify the displacement of the SMA wire. To increase the energy conversion rate, we wrap the SMA wires in the insulation tube to reduce the heat radiation. e rest of the paper is organized as follows: the structural design and model establishment is elaborated. en, the manufacturing process and testing methods are listed. e results of the experiments and the discussion are included in the results and discussion.

Structural Design and Model Establishment
For human hands, each finger can be viewed as a serial open kinematic chain, which consists of three joints and links. e MCP joint has two rotational degrees of freedom (DoF), and the PIP and DIP joints have one DoF each, as shown in Figure 1. To simplify the modelling process, the MCP joint is regarded as a rotating joint with only one rotational DoF. erefore, each finger can be considered as a three-revolute joint robotic manipulator, as shown in Figure 1.
According to the different starting points of the muscle, the muscles can be divided into internal and external muscles. e internal muscle is mainly responsible for finetuning the balance of the joint. And the external muscle (FDP, FDS, and EDC) is the power source of finger motion. During finger flexion, the contraction of the FDP drives the movement of the joints together with internal muscles. During finger extension, the contraction of EDC contracts against the passive resistance of the FDP, which makes three finger joints rotate synchronically to complete finger extension [20]. e schematic diagram of the finger muscles is shown in Figure 2.
To better simulate the motion of the human fingers, the structure of the finger exoskeleton should mimic the biological structure. SMA, which have a shape memory effect, are widely used as artificial muscle actuators for bionic devices. By applying heat, SMA wires can be shortened through phase transformation, which can take the place of human muscles to activate the finger flexion and extension.
But there is an important limitation of SMA wires: low strain rate compared to its initial length which requires longer wires. To overcome this shortcoming, a novel range extender mechanism is designed to enlarge the driving displacement of SMA wires, as shown in Figure 3.
A pully block consists of two fixed pullies and three free pullies are used to enlarge the stroke of the SMA wire to six times the original (as seen in Figure 3(c)) which is long enough to actuate the finger. In this way, the HMD is more compact and lightweight, and its portability and comfort level is improved, compared with the ASR glove [16]. Besides, PE lines are used for directly pulling the finger to abduct and adduct. It can withstand large tensile forces without breaking. And it is tight and wear-resistant, has good plasticity, and will not get tangled up. In this way, the effectiveness of the device is well guaranteed. e rope on the dorsal side and palmar side of the finger is equivalent to the EDC and FDP, respectively, which imitate the physiological structure of the human hand. e schematic diagram of the hierarchical structure in the glove is shown in Figure 4. e range extenders are stuck between two layers of textile by adhesive. e distal end of the range extender is connected to the fingerstall fixed on the fingertip through PE lines; the other end is fixed at a wiring ring at the elbow through the SMA wire. e activation of each finger needs two SMA wires (one for the flexion, and the other one for extension); thus 10 SMA wires are required for a hand, as shown in Figure 5.
By applying a voltage to two ends of the SMA wire, it thermally contracted and then the pullies were pulled in the range extender. ereby, the PE line is actuated, and then the finger is pulled to flexion and extension. Due to the physiological structure of the finger, when we pull the distal 2 Journal of Robotics  phalanx of the finger, the three joints will rotate synchronously. e relationship between tendon displacement and joint angle is articulated in this section. As shown in Figure 6, we built a bidimensional model of the fingers on the sagittal plane, and the fingers are modeled as a 3-link kinematic chain.
e tendon displacement during flexion can be extracted from joint angles: where x represents the tendon displacement (mm), l 1 , l 2 , and l 3 are the thickness of the MCP, PIP, and DIP joints (mm), respectively. θ 1 , θ 2 , and θ 3 are joint angle (°) of MCP, PIP, and DIP joints, respectively.
Dividing the x obtained above by the strain rate can get the theoretical length of SMA wires; then because of the pulley mechanism inside the range extender, the length required is 6 times shorter. Besides, since we fold the SMA wires in half, the actual length is then doubled: where μ represents the shrinkage of the SMA wires, ε represents the magnification of the shrinkage of the SMA wire by the range extender, and L Act min is the minimum actual length of the alloy wire for a single finger.
SMA wire is a novel flexible actuator. Both the shape memory effect and the superelasticity arise from martensitic transformations [21]. During the heating process, when the temperature reaches a specific value, the martensitic crystal phase is transformed into austenite crystal phase, which is stable at higher temperature, and the structure becomes more compact and therefore the SMA wire contracts to its original length and produces shrinkage stress. erefore, it can be used to actuate the finger motion.
Power can be applied to both ends of the SMA wire through a power supply. Because of the heating effect of the current, the temperature rises, and then the phase transformation occurs. us, the temperature is very important for the activation process. e relationship between the temperature and the applied voltage is shown as follows: which can be simplified as where m SMA � ρ SMA πr 2 SMA l SMA is the weight of the SMA wire, r SMA is the density of the SMA wire, l SMA is the length, c p is the specific heat, T is the temperature, t is time, U is the voltage, R � ρ R l SMA /πr 2 SMA is the resistance of the SMA wires, ρ R is the resistivity, τ is the PWM ratio, h is the heat convection coefficient, A � 2πr SMA l SMA is the heat transfer area of the SMA wire, and T 0 is the ambient temperature. e relationship of heat convection coefficient temperature is a linear function, according to [22].
where h 1 is baseline heat transfer coefficient and h 2 is correction heat transfer coefficient. According to [23], the phase transformation during heating can be described as where σ is the terminal stress when the transformation is over, σ 0 is the initial stress, D � (D m − D a ) · η + D a is the elastic modulus, D m and D a are the elastic modulus of martensite and Austenite, respectively, η is the shape memory factor (between 0 and 1), ε 0 is the initial strain, Θ is  Journal of Robotics 5 the thermoelastic coefficient, Ω(η) � −ε L D(η) is the shape memory modulus, and ε L is the maximum residual strain of the SMA wire. e performance parameters of SMA wires are shown in Table 1.

Prototype Manufacturing and
Testing Methods e prototype of the HMD is shown in Figure 7. e SMA wires used in this experiment are from Dongguan Baohong Metal Material Co., Ltd. (shop570466789.taobao.com), which is 0.3 mm in diameter. To fabricate the HMD, we used a pair of cotton gloves as the base. e base of the range extender is 3D printed using resin (made from Somos ® GP Plus, http://www.dsmsomos.com) and assembled by bolts. Outside the range extender, the PE lines (Camilo flagship store, Dyneema) are fixed on the cotton glove by Velcro tapes (VELCRO ® Brand Fasteners). As we know, the cross section shape of the forearm is not a regular circle. To better fit the shape of the arm, we use flexible materials to act as wiring rings. e wiring ring which is fixed near the elbow is 3D printed using flexible TPU. It consists of two halves, connected by bolts. An insulating tube is used to block the heat on the SMA wires during the actuation and prevent it from scalding the skin.
Reference [20] gives the range of motion of each finger joint, seen in Table 2. Table 3 depicts the thickness of the knuckles of a 21-year-old woman. Substituting the data in Tables 2 and 3 into equation (1) gives the length of the SMA wires that we need. Considering the errors in the experiment, the SMA wires that we used are 600 mm long. erefore, the effective length of the SMA wire is 300 mm because we folded them in half. Assuming that the strain rate of the SMA wire is 4%, the theoretical displacement of the PE lines when activated is 72 mm.
To verify the driving effect of the HMD, we designed several experiments to study the relationship between the finger bending angle over time and applied voltage. e operating space of fingers is also calculated. To control the fingers to reach different joint angles, we used PWM pulse to activate the SMA wires, and the maximum fingertip force during the process is measured by a pressure sensor.
A DC power supply is used to drive the fingers to bend, each SMA wire passed through a current of 1 A. A highspeed camera is used to record the bending angle of the joints under different driving voltages. After analyzing the data, we got graphs of the angles with time and the relationship between them. We measured the length of each knuckle, as shown in Table 4. Subsequently, the operating space of the fingertip can be obtained.
We also recorded the fingertip force using a pressure transducer to see if the device can generate enough grip strength. So we activate the fingers under different voltages, and the fingertip forces can be seen on the PC. e experimental setup is shown in Figure 8.
Mechanically, the final design encompassed a system that includes a DC power supply (IT6722 A 80 V/20 A/ 400 W from ITECH Electronics Co., Ltd.), HMD, pressure sensor (ZNBSQ-V 24 V 0∼10 V Bengbu Zhongnuo Sensor Co. Ltd.), and PC (as shown in Figure 9). On the premise of satisfying the requirements, the smaller the current, the longer the service life. Besides, at high heating rates (>100°C/min), the stress increases with a significant decrease in strain [24]. erefore, we use a current of 1 A to activate the SMA wires. e experimental results show that it can meet the requirements of the driving frequency of the HMD in reference [10].

Finger Bending Test.
We can get a series of pictures from the videos that we recorded. For the sake of brevity, only the index finger is discussed in detail, as shown in Figure 9. It can be seen that the device can perform about 6 rehabilitation exercises per minute. We meet the requirement of [25], five times per minute. Besides, compared to 3 or 4 times a minute in [26], we have greatly improved on this basis. Figure 10 shows the process of flexion of the fingers at different voltages. Since the voltages we used are higher than the voltage threshold to reach the phase transformation temperature, therefore, the maximum joint angle of fingers is the same and has nothing to do with the applied voltages. But we only recorded the joint angles in the first ten seconds after the voltage excitation for simplification. We can see that when we tune up the voltage, the movement will also accelerate. To this end, more rehabilitation exercises can be performed if we increase the voltage value in the experiment. Figure 11 shows the comparison between the theoretical joint angle and the experimental joint angle of the DIP joint over time under different driving voltage. We can see that the experimental joint angles are consistent with the theoretical angle.
Dr. Wenrui Chen used principal component analysis to analyze the three joints of a single finger and found that the three joint angles of a finger can be expressed linearly by a principal component vector [27]. e relationship among the finger joint angles is shown in equation (7).
erefore, when one of the joints rotates at a certain angle, the motion of other joints can be determined accordingly. For this experiment, the average value of the maximum joint angle of our joints at different voltages is  Table 5. e maximum joint angle of each joint of the finger during the experiment (regardless of the voltage value) is recorded in Table 6. e joint angles of the MCP, PIP, and DIP joints are related to each other, showing a proportional relationship among them in this experiment (Table 5), which is similar to the ratio obtained in [27], that is, and the experiment showed a capacity of activating the index finger to adduct. e current system is an underdriven system; the theoretical joint angles can be obtained based on the tendon displacement. But some experimental errors cause the shrinkage of the SMA wire to be wasted. For      Journal of Robotics example, due to the slack of the SMA wire and PE lines as well as the irregular shape of the arm, the tendons cannot always fit well with the surface of the arm. Besides, the shrinkage of the SMA wires is constantly changing with time and voltage. Besides, the friction in the mechanism also needs to be taken into consideration. In conclusion, the actual displacement of the PE line is different from the theoretical calculation. erefore, we assume that only a quarter of the displacement generated by SMA wires is in effect. at is, the shrinkage of the PE line is 18 mm.
Putting equation (8) and the thickness of the index finger (Table 3) into equation (1), we can get the following theoretical angular displacement of each finger joint: e experimental angular displacement of the three finger joints in the index finger is shown as follows: We can see that there are some deviations between the experimental joint angles and the theoretical ones; this is because of the individual differences in various persons. On the whole, the theoretical joint angles are almost consistent with the experimental one, which indicates the feasibility of our design.

Operating Space When Wearing HMD
We can get the operating space at the end of the finger through Tables 4 and 5. By simplifying the framework of the fingers, we built a link coordinate frame for each joint, as shown in Figure 12, and subsequently built the kinematics of the manipulator based on the Denavit-Hartenberg (D-H) convention. e D-H parameter table of the finger is shown in Table 7.
Bring the joint angle in Table 5 into the link coordinate frame ( Figure 12, Table 7); the results are shown in Figure 13, which shows the achievable flexion/extension ranges of five fingers when wearing the HMD. en we can get the size of the object that can be grasped when wearing the device. e blue bands in Figure 13 represent the track set of fingertip movement trajectories, which is also the operating space at  Journal of Robotics the end of the finger. e pink dots indicate three finger joints (DIP, PIP, and MCP joints). e three short rods represent the three phalanxes, respectively (blue for proximal phalanx and middle phalanx, the red one for the distal phalanx). ey are all described in the sagittal plane. Figure 14(b) shows the posture of the hand when it is fully opened. Its original state is shown in Figure 14(a).
We found that the minimum radius of the sphere that can be grasped is 16 mm, which is about the diameter of a small ring, as shown in Figure 14(b). e subject can pinch thin slices of any thickness using HMD, like a piece of paper. Also, the patients can turn on and off the device easily due to the flexible wearable structure. From Table 6, It can also be found that the joint angles in this experiment have been improved compared to Lokesh's [12]. Besides, because of the novel range extender, we can use fewer SMA wires to achieve the same joint angle compared with Alireza's [16]. is has brought a significant reduction in costs. At the same time, the device uses a driving method that mimics human muscle, and there are no protruding parts like reference [10,28] did. us, the whole device is more lightweight, compact, and portable, which is more applicable to ADL.

PWM Control of Flexion Angle of HMD
To achieve the specific hand posture, we need to be able to control the finger joint angle to a certain degree. rough tuning the PWM power ratio, we can activate the finger joint angle to a certain degree. e experimental setup is shown in Figure 15.
Take the index finger as an example; we control the sum of the DIP, PIP, and MCP joint angles to a certain degree and stabilize for several seconds under different PWM pulse duty cycle; the relationship between the theoretical analysis and experimental results is shown in Figure 16. We can see that, through tuning the duty cycle of the PWM pulse, the HMD can activate the fingers to reach different joint angles and can be stable for a while. e higher the PWM duty cycle, the larger the stabilized joint angle can be reached.      e fingertip force is shown in Table 8. In the experiment, we used a pressure sensor to measure the fingertip forces. e results are as follows.
According to Table 8, the average fingertip force generated by each finger is about 8 N. Compared with the grip strength of 26.2 N produced by the five fingers when using   the HandSOME in reference [28], we have increased the fingertip force by 52.7%, which is capable of most ADL.

Conclusions
In this study, we proposed a hand movement device actuated by SMA wires. e suggested soft robotic glove uses a tendon-driven system and 3D-printed novel range extenders. e structure of the range extender and the HMD is explained in detail. Besides, we also experimentally verified that the voltage has a positive correlation with the speed of finger movement. e joint angles actuated by the proposed HMD are also sufficient for ADL and can be controlled to a certain degree through tuning the duty cycle of PWM pulse.
is device can provide reference values for other related research and can help the ADL of patients with hand defects. It can approximately generate a fingertip force of about 8 N, which is sufficient for most patients. e robustness and life cycle of the SMA wires as well as the numbers of SMA wires used will be investigated during fatigue tests in the future to improve the practical performance of the robot. And we will also work on how to improve the frequency of the device to further improve the rehabilitation process.

Data Availability
e data used to support the findings of this study are included within the supplementary information files.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.   PWM ratio 50% exp. PWM ratio 60% exp. PWM ratio 70% exp. PWM ratio 80% exp. PWM ratio 90% exp.