1 Introduction

Strokes are a common cause of long-term upper limb disability. Approximately 80% of stroke survivors suffer upper limb dysfunction, severely affecting their daily lives [1]. Medical research has shown that this group of patients can accelerate their upper extremity rehabilitation by rebuilding neurological function in the brain through extensive repetitive motion [2]. However, most existing upper limb rehabilitation training is performed manually by physicians, making the process labor-intensive, time-consuming, and expensive. With the development of rehabilitation robotics, many researchers have proposed a rigid exoskeleton [3,4,5]. These exoskeletons have a rigid frame aligned with the upper limb skeleton and can precisely assist with complex movements of the upper limb joints. However, the exoskeleton has a bulky structure, is incompatible with human movement, and can cause discomfort due to its complex system and rigid frame.

Consequently, some researchers have developed frameless soft robotic suits that are structurally lightweight, compliant, and comfortable [6]. These suits made using compliant materials, such as cables [7,8,9], elastomers [10,11,12], and textiles [13], are purported to be clothing-like robots that wrap around the body and work in parallel with muscles.

Among these, textile actuators have contributed to rapid developments in soft wearable devices owing to their foldability, flexibility, zero initial stiffness, and high power-to-weight ratio. O'Neill et al. [14,15,16] designed fabric pneumatic actuators to assist shoulder abduction. Thalman [17] used multiple rectangular fabric actuators arranged along a non-extendable fabric for elbow flexion assistance. Park et al. [18] and Realmuto et al. [19] proposed flat and helical pneumatic actuators to assist forearm pronation and supination, respectively. Bartlett [20] presented a soft device for wrist flexion and extension.

Researchers [13, 21, 22] have designed different actuators to assist various upper limb joints. However, most studies [16,17,18, 23] focused on flexion assistance in only one upper extremity joint. Some studies [24] focus on assisting two joints but usually use different actuator structures, which is poorly generalized for other joints. In addition, most studies simplify the modeling by cylindrical and prismatic assumptions [25,26,27]. There are fewer studies on actuator deformation. Hence, designing an actuator for multi-joint bi-directional assistance remains challenging.

This study proposes a fabric-based bi-directional actuator that can assist the flexion and extension of the elbow, wrist, and finger. We also provide a mathematical model to predict the deformation and output torque, and this model further guides actuator parameter design. We determined the geometric parameters of the actuators based on the required torque and motion range for the flexion/extension of the elbow, wrist, and fingers in adults. Furthermore, we characterized the effect of the input pressure and initial angle on the output torque and validated the theoretical model. Additionally, we developed a 3-DOF soft robotic suit based on the proposed bi-directional actuator. Preliminary results demonstrate that the suit can assist with elbow, wrist, and finger flexion/extension. The main contributions of this study are as follows:

  1. (1)

    Proposal of a fabric-based bi-directional actuator to assist the elbow, wrist, and finger flexion/extension.

  2. (2)

    Modeling, validation, and characterization of the proposed actuator.

  3. (3)

    Integration of a 3-DOF soft robotic suit, including elbow, wrist, and finger flexion/extension.

2 Actuator Design, Modeling, and Characterization

2.1 Actuator Design and Fabrication

Unlike the existing actuators that focus on either flexion or extension assistance of a single joint of a human’s upper limb, such as the elbow [17], wrist [20], and fingers [13], the proposed actuator uses bending and straightening bladders to achieve bi-directional motion, as shown in Fig. 1a. The bending and straightening bladders are mounted on the dorsal and ventral sides for flexion and extension, respectively. Figure 1b demonstrates that the actuator can adapt to different upper limb joints (elbow, wrist, and fingers) by simply changing the structural parameters.

Fig. 1
figure 1

a Structure of the fabric-based bi-directional actuator. The actuator bends when the bending bladder is pressurized, and the actuator straightens when the straightening bladder is inflated. b Bi-directional actuators for elbow, wrist, and finger, integrated into a 3-DOF soft robotic suit

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The above-mentioned flexion and extension actuators are derived from fabric bladders. The bladder comprises two pieces of composite textile. Each composite fabric contains two thin layers: a hot-melt material and stretch-resistant flexible material, as shown in Fig. 2a. In this study, we chose thermoplastic polyurethane (TPU)–fabric composite as the hot-melt and stretch-resistant flexible material, respectively.

Fig. 2
figure 2

Components and fabrication of the fabric-based bi-directional actuator. a The main fabrication process of the fabric bladder and b assembly of the bi-directional actuator

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The fabrication of the fabric bladder is as follows. First, the two TPU–fabric composites were stacked: one on top of the other, to obtain a total thickness of 0.24 mm. We then laser-cut the desired TPU–fabric shape (shown as a rectangle here). Second, we placed an aluminum alloy of the same shape and size as a mold above the two TPU–fabric pieces (the mold has a thickness of 2 mm, a rectangular border shape, and a gap at one end for inserting the air tube). Next, a polyimide sheet was placed near the inner edge of the mold as a thermal barrier to prevent internal adhesion. To further ensure the consistency of the bladder, a spacer was placed between the two layers to isolate the top and bottom layers. Finally, the two pieces of TPU–fabric composite were heat-pressed at 200 °C to form a cavity pocket with a gap; the air tube was inserted at the hole and sealed with glue.

After inflating the internal air cavity, the fabric bladder expands and deforms into a shape similar to a pillow. If the bladder folds in half, its inflation and expansion will straighten and actuator stiffen axially; this is called the straightening bladder. Alternatively, if we lengthen and fold the fabric bladder into a corrugated shape, we obtain the bending bladder. The straightening and bending bladders were connected with a piece of textile, as shown in Fig. 2b, to fabricate the bi-directional actuator.

2.2 Actuator Modeling

We first studied the deformation–pressure characteristics to quantify the mechanical properties of the bi-directional actuators. Furthermore, we investigated the effects of input pressure and initial angle on the output torque of the actuator.

First, we analyzed the actuator flexion motion, as shown in Fig. 3a. Only the elbow is shown here as the wrist and fingers also use the same structure. We selected one of the lamellae as the object and established a three-dimensional coordinate system with center \(O\) of the layer as the origin (y-direction is inwardly perpendicular to the paper face). According to Timoshenko’s large deformation theory [28], the deflection of the actuator after deformation is as follows:

$$\begin{array}{c}z={a}_{00}\left({a}^{2}-{x}^{2}\right)\left({b}^{2}-{y}^{2}\right),\end{array}$$
(1)

where \(a\) and \(b\) are half the length and width of the thin layer, respectively. We use \((u,v)\) to denote the strain in the \((x,y)\) direction, because the deformation of the actuator leads to non-negligible stretching in the plane. Based on [28], we describe the thin-layer deformation function as follows:

$$\begin{array}{c}\begin{array}{c}u=x\left({b}_{00}+{b}_{10}{x}^{2}+{b}_{01}{y}^{2}+{b}_{11}{x}^{2}{y}^{2}\right)\\ v=y\left({c}_{00}+{c}_{10}{x}^{2}+{c}_{01}{y}^{2}+{c}_{11}{x}^{2}{y}^{2}\right),\end{array}\end{array}$$
(2)

where \({a}_{00}, {b}_{ij}, {c}_{ij}, \left(i,j=0, 1\right)\) are the parameters of the system of equations that require solving. The strain energy \(V\) within the thin layer after deformation consists of the following two components:

$$\begin{array}{c}V={V}_{b}+{V}_{e},\end{array}$$
(3)

where \({V}_{b}\) is the bending strain energy due to pure bending and \({V}_{e}\) is the tensile strain energy due to elongation within the neutral plane. From the principle of virtual displacement, it follows that:

$$\delta V-\delta \iint qzdxdy=0,$$
(4)

where \(q\) is the pressure inside the actuator. Jointly, Eqs. (2–4) lead to

$$\begin{aligned}Q&=V-\iint qz\mathrm{d}x\mathrm{d}y \frac{\partial Q}{\partial {a}_{00}}=0; \\ \frac{\partial Q}{\partial {b}_{ij}} & =0; \frac{\partial Q}{\partial {c}_{ij}}=0. \quad i,j=0, 1.\end{aligned}$$
(5)
Fig. 3
figure 3

Mathematical model of the actuators. a Flexion of the actuator on the elbow. b Force analysis and boundary conditions for flexion of the actuator. Consider the middle part adjacent to the two pieces of the actuator contact force. The deformation of each side of the follows: Eq. (2), but only half along the length direction, similar to half a pillow, c adjacent actuator distance before bending, d extension of the actuator on the elbow, e force analysis and boundary conditions for extension of the actuator, and f actuator self-contact region

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Equation (5) is a set of nine nonlinear equations containing the coefficients \({a}_{00}, {b}_{ij}, {c}_{ij}, \left(i,j=0, 1\right)\). Upon solving this set of equations, we can obtain all coefficients. The values are substituted in Eq. (1) to obtain the deformation function of the actuator.

Subsequently, we created a flexion torque expression (Eq. (6)), where \(S\) represents the contact area of the adjacent layers and \(L\) is the length of the force arm; \(N\) is the number of thin layers and \(n=N-6\) is the number of layers involved in bending; \(\theta\) is the bending angle of the actuator and \(c\) is the distance between adjacent actuators (Fig. 3c)

$$\begin{array}{c}M=PSL\end{array}$$
(6)
$$\begin{array}{c}L=\frac{\left(n-1\right)c}{\phi }+a\end{array}$$
(7)
$$\begin{array}{c}\frac{\varphi }{2}=\frac{\phi }{2\left(n-1\right)}=\frac{\uppi -\theta }{2\left(n-1\right)}.\end{array}$$
(8)

Moving the coordinate system \(xyz\)-0 along the \(x\)-axis by length \(L\) and rotating \(\frac{{{\uppi } - \varphi }}{2}\) counterclockwise around the \(y\)-axis to \(x^{\prime}y^{\prime}z^{\prime}{-}O\), we obtain

$$\begin{array}{c}{z}{\prime}=xcos\frac{\varphi }{2}+{a}_{00}\left({a}^{2}-{x}^{2}\right)\left({b}^{2}-{y}^{2}\right)\mathrm{sin}\frac{\varphi }{2}-L\mathrm{cos}\frac{\varphi }{2}.\end{array}$$
(9)

Let \(x=0\). Then, the actuator self-contact range is expressed as

$$\begin{array}{c}S={\int }_{-b}^{b}\left[\begin{array}{c}{a}_{00}{a}^{2}\left({b}^{2}-{y}^{2}\right)\mathrm{sin}\frac{\uppi -\theta }{2\left(n-1\right)}\\ +Lcos\frac{\uppi -\theta }{2\left(n-1\right)}\end{array}\right]\mathrm{d}y.\end{array}$$
(10)

Finally, we can obtain the expression for the flexion torque:

$$\begin{array}{c}M=P\left[\frac{\left(n-1\right)c}{\uppi -\theta }+a\right]*\\ \left[{\frac{4}{3}a}_{00}{a}^{2}{b}^{3}\mathrm{sin}\frac{\uppi -\theta }{2\left(n-1\right)}+2bL\mathrm{cos}\frac{\uppi -\theta }{2\left(n-1\right)}\right].\end{array}$$
(11)

Furthermore, for the joint extension (Fig. 3d), we also developed a torque expression conditioned on geometric parameters, internal pressure \(P{\prime},\) and bending angle \(\theta\)

$$\begin{array}{c}{M}{\prime}={F}_{p}\frac{{a}{\prime}}{2}\end{array}$$
(12)
$$\begin{array}{c}{F}_{p}={F}_{c}\mathrm{cos}\frac{\theta }{2}\end{array}$$
(13)
$$\begin{array}{c}{F}_{c}={P}{\prime}{S}{\prime}.\end{array}$$
(14)

Here, \(a^{\prime}\) is half the length of the straightened bladder, \(b^{\prime}\) is half the width, and \(S^{\prime}\) is the self-contact area of the actuator. As shown in Fig. 3e, we establish \(xyz{-}O\) at the center of the actuator before deformation. By rotating the coordinate system \(xyz - O\) by \(\theta /2\) along the y-axis to \(x^{\prime}y^{\prime}z^{\prime} - O\), we obtain the following according to the coordinate transformation:

$$\begin{array}{c}{z}{\prime}=-x\mathrm{sin}\theta +{a}_{00}\left({{a}{\prime}}^{2}-{x}^{2}\right)\left({{b}{\prime}}^{2}-{y}^{2}\right)\mathrm{cos}\frac{\theta }{2}.\end{array}$$
(15)

Let \(x=0\). Then, the actuator self-contact range is expressed as

$$\begin{array}{c}S{\prime}={\int }_{-b}^{b}{a}_{00}{a{\prime}}^{2}\left({b{\prime}}^{2}-{y}^{2}\right)\mathrm{cos}\frac{\theta }{2}\mathrm{d}y.\end{array}$$
(16)

Finally, we can obtain the expression for the extension torque

$$\begin{array}{c}{M}{\prime}=\frac{2}{3}{a}_{00}{{a}{\prime}}^{3}{{b}{\prime}}^{3}{P}^{{\prime}\mathrm{cos}\frac{\theta }{2}\mathrm{cos}\frac{\theta }{2}}.\end{array}$$
(17)

2.3 Characterization

To determine the geometrical parameters of different joint actuators, we referred to the maximum torque and motion range of the elbow, wrist, and finger, as listed in Table 1 [29,30,31,32]. Due to the large individual differences, we have provided a reference range for the maximum torque. In addition, most studies only refer to fingertip forces; therefore, we calculated the maximum finger torque. Particularly, in the motion range, 0° indicates that the joint is straight, an increasing angle indicates inward flexion, and decreasing angle indicates outward extension. In addition, the motion range of the finger refers to the range reached by the proximal interphalangeal joints. Referring to the actuator model and demand of upper limb motion, the actuator geometrical parameters are listed in Table 2. We first determined the width \(2b\) and \({2b}{\prime}\) of each joint actuator to fit the human arm and finger dimensions [33, 34]. Other parameters, including the height \(2a\), length \({2a}{\prime}\), number \(N\), and distance \(c\), were determined considering the actuator shape, angle, and torque requirements. Furthermore, according to tests, the modulus of elasticity of the actuator material is 300 MPa and the Poisson's ratio is 0.256.

Table 1 Needs of flexion and extension for elbow, wrist, and finger
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Table 2 Geometric parameters of the bi-directional actuators for elbow, wrist, and finger
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Subsequently, we set up an experimental apparatus to characterize the effect of the pressure and initial angle on the actuator flexion/extension torque, as shown in Fig. 4.

Fig. 4
figure 4

Characterization of the actuators. a Experimental setup for the flexion torque of the actuator. b Experimental setup for the extension torque of the actuator

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In the flexion test (Fig. 4a), the initial bending angle \(\theta\) is set to 90°. The input pressure \(P\) increases from 0 to 300 kPa in steps of 30 kPa. The experimental results in Fig. 5a reveal that the torque increases as the pressure increases from 0 to 300 kPa. The elbow, wrist, and finger actuators provide 8.85, 1.82, and 0.18 \(\mathrm{N}\cdot \mathrm{m}\) torque, respectively, when the input pressure is 300 kPa; the corresponding model are 8.57, 1.85, and 0.17 \(\mathrm{N}\cdot \mathrm{m}\), respectively, which are in good agreement with the experimental results.

Fig. 5
figure 5

The characterization of actuators. a Effect of input air pressure on the flexion torque of the actuator with 90° angle. b Effect of initial bending angle on the flexion torque of the actuator with 180 kPa pressure. c Influence of input air pressure on the extension torque of the actuator with 90° angle. d Influence of initial bending angle on the extension torque of the actuator with 180 kPa pressure

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In addition, the effect of the initial bending angle on the actuator torque was investigated. A pressure of 180 kPa was maintained during bending. The initial angle was decreased from 150° to 15° in steps of 15°. The experimental results in Fig. 5b show that the torque decreases with the initial bending angle. When the bending angle is 150°, the elbow, wrist, and finger actuators provide torques of magnitudes 24.35, 4.45, and 0.32 \(\mathrm{N}\cdot \mathrm{m}\), respectively; the corresponding model predictions are 25.65, 4.29, and 0.23 \(\mathrm{N}\cdot \mathrm{m}\), respectively. The small discrepancy between the model predictions and experimental results is acceptable.

In addition, we tested the extension properties of the actuators, as shown in Fig. 4b. The initial bending angle was set to 90°. The input pressure was increased from 0 to 300 kPa in steps of 30 kPa. The results in Fig. 5c show that the elbow, wrist, and finger actuators provide 12.87, 3.35, and 0.25 \(\mathrm{N}\cdot \mathrm{m}\) extension torques, respectively, at a pressure of 300 kPa; the corresponding model predicted values are 11.81, 2.70, and 0.25 \(\mathrm{N}\cdot \mathrm{m}\), respectively, which are in good agreement with the experimental results.

Subsequently, we studied the influence of the initial angle on the extension torque. The input pressure is 180 kPa. The initial angle was decreased from 150° to 15° in steps of 15°. The results in Fig. 5d show that the elbow, wrist, and finger actuators provide extension torques of magnitudes 48.35, 17.36, and 1.53 \(\mathrm{N}\cdot \mathrm{m}\), respectively; the corresponding model predictions are 55.76, 12.75, and 1.20 \(\mathrm{N}\cdot \mathrm{m}\), respectively. The discrepancy between the model predictions and experimental results is acceptable.

Finally, we tested the maximum performance of the actuators, including the maximum motion range and torque, as presented in Table 3. The actuators can all be combined head-to-tail. Thus, the cited motion ranges of actuators are 0–180°. Comparing the results with those in Table 1 reveals that the actuator torques satisfy all requirements. The range of motion is slightly insufficient; however, it is adequate for most rehabilitation movements.

Table 3 Maximum performance of the actuators
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3 Soft Robotic Suits

To verify the performance of the actuators on the upper limb assist, we sewed bi-directional actuators on the elastic fabric to create an elbow module, as shown in Fig. 6a-1. As the wrist and hand actuators were close together, we assembled them into a monolithic module, the wrist-hand module, as shown in Fig. 6a-2. The modules were sewn with Velcro and a button for convenience and adaptability.

Fig. 6
figure 6

Integration and characterization of the soft robotic suit. a-1 Elbow module. a-2 Wrist hand module. b-1 The suit with integrated modules. b-2 Control screen. c Flexion and extension of elbow, wrist, and finger

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Further, the modules were integrated into a 3-DOF soft robotic suit with 251 g weight, as shown in Fig. 6b-1. We designed a control box that included power, an air pump, a valve, and a screen. The touchscreen control interface, in Fig. 6b-2, can realize on/off control and force adjustment of different rehabilitation movements. Figure 6c shows various rehabilitation movements of an adult male wearing a soft suit, such as elbow flexion (c-1), elbow extension (c-2), wrist flexion (c-3), wrist extension (c-4), finger flexion (c-5), and finger extension (c-6).

4 Conclusion and Future Work

This study presents the design, modeling, and characterization of a fabric-based bi-directional actuator for multi-joint flexion/extension. A mathematical model was developed to predict the deformation and output torque of the actuator. Compared with the most existing standard shape assumptions of actuators, we use the large deformation theory to solve the analytic function of the actuator surface. Based on the model and torque requirements, we modify the geometric parameters—without changing the structure—to design and fabricate the elbow, wrist, and finger bi-directional actuator. Finally, we develop a 3-DOF soft robotic suit integrated with the proposed actuator to assist with elbow, wrist, and finger flexion/extensions. Due to the high scalability of the proposed actuator, it is possible to extend assistance to other joints, such as the knee and ankle, by modifying the actuator parameters. In the future, we will explore variable-stiffness actuators to increase the actuator output force and provide a stable variable force for the impedance mode to enhance the rehabilitation training effect. Furthermore, the textile strain sensors will be integrated into the suit to monitor the assisted force and range of motion, achieving self-sensing.