2.3.1. Structure Analysis

In order to perform rehabilitation exercises or grasp activities, the flexion–extension motion for each digit is essential. Among all the force transmission mechanisms for rehabilitation exoskeletons, the four-linkage mechanism is simple and accurate for motion control, and thus is adopted in this study. Figure 4a presents the schematic diagram of the exoskeleton mechanism for the index finger. Rotation mechanisms for the MCP and PIP joints in the hand exoskeleton are the same. Taking the MCP joint as an example first, the metacarpal bone serves as a fixed-base frame and the proximal phalanx functions as a phantom element; together, they form a closed-chain mechanism with linear actuator 1 and exoskeleton linkages. Linear actuator 1 is an active member and dominates the flexion–extension behavior of MCP. Four constant parameters, *m*, *n*, *α*, and *β* labeled in Figure 4b,c, are adopted to describe the relationship between the actuator and angle *φ*. The relation between the length of the linear actuator 1 (*l*) and *φ* can be expressed as:

$$\cos\phi = \frac{m^2 + n^2 - l^2}{2mn} \tag{1}$$

**Figure 3.** The workspace of the tip and DIP joint of the index finger. (**a**) The workspace of the index fingertip; (**b**) 2D view of the workspace of the index fingertip; (**c**) The workspace of the DIP joint; (**d**) 2D view of the workspace of the DIP joint.

 ∅ = <sup>2</sup> + <sup>2</sup> − 2 2 **Figure 4.** Sketch of exoskeleton structure for index finger. (**a**) Four-linkage mechanism of exoskeleton; (**b**) minimum angle of MCP joint; (**c**) maximum angle of the MCP joint; (**d**) minimum angle of PIP joint; (**e**) maximum angle of the PIP joint.

∅

 = + + − . = + + − The rotation angle of the MCP joint can be presented as *ψ* = *α* + *β* + *φ* − *π*. Similarly, *a*, *b*, *u*, and *v* are adopted for PIP joint-related rotation and the rotation angle of the PIP joint *ω* = *α* + *β* + *φ* − *π*. Grasping activities in daily life does not require the full rotational range of joints. To hold a cup with a diameter of ~10 cm, the angular rotation in MCP and

DIP is ~10 ◦ and ~45 ◦ , respectively, for the thumb, while the MCP and PIP joints rotate ~30 ◦ and ~60 ◦ , respectively, for the rest of the 4 fingers. In this consideration, the maximum rotation angle for MCP and PIP joints is designed to be 60 ◦ , which guarantees the safety of users and fulfills the needs for activities such as grasping and rehabilitation. With the above-mentioned understanding, Figure 4b,c illustrate the minimum and maximum lengths of the linear motor 1; meanwhile, Figure 4d,e show the minimum and maximum PIP joint rotation angles, respectively.

The overall design of the hand exoskeleton is presented in Figure 5a. Based on the preferences of the patient and suggestions of the doctor, the hand exoskeleton can either function independently or perform rehabilitation with support from the existing upperlimb exoskeleton system presented in Figure 6. The hand exoskeleton can be attached to the arm exoskeleton via a link module, which greatly diminishes the weight of the hand exoskeleton that a user needs to bear. Most components of the hand exoskeleton are realized via 3D printing utilizing polylactic acid (PLA), which is a low-density material. The strength of essential parts is verified via the FEA method (Supplementary Material, Figure S1). The structure strength meets the requirements of tasks such as rehabilitation and low-weight object holding.

**Figure 5.** Hand exoskeleton rehabilitation system. (**a**) Overview of the hand exoskeleton; (**b**) components in the index finger exoskeleton; (**c**) detailed illustration of the wearable controller; (**d**) the synergy of hand exoskeleton and the wearable controller.

– The hand exoskeleton contains 10 active DoFs and 3 passive DoFs in total. The motion of each digit can be controlled separately. Taking the index finger exoskeleton as an example (Figure 5b), there are 2 linear actuators selected for joint rotation, which are FIRGELLI L12-50-100-12-I (linear actuator 1) and L12-30-100-12-I (linear actuator 2). All 3 passive DoFs are shown in the insert of Figure 5a, aiming to adjust the relative position between the finger exoskeleton base and the thumb exoskeleton base. The rotation of passive joints can be constrained by tightening the bolts when comfortable angles are found for rehabilitation and grasping. More information regarding passive joints is presented in Supplementary Materials, Figure S2.

 The metacarpal exoskeleton, linear actuator 1, and proximal phalanx exoskeleton together form an open-chain mechanism. The metacarpal exoskeleton needs to be fixed to the human hand (via either a bandage or glove) to ensure the accurate control of joints.

–

 The metacarpal exoskeleton, linear actuator 1, and proximal phalanx exoskeleton together form an open-chain mechanism. The metacarpal exoskeleton needs to be fixed to the human hand (via either a bandage or glove) to ensure the accurate control of joints.

**Figure 6.** The combination of the hand exoskeleton and the existing upper-arm rehabilitation system. (**a**) Picture of the whole system; (**b**) side view of the hand exoskeleton mounted on upper-arm rehabilitation system; (**c**) bottom view of the hand exoskeleton mounted on upper-arm rehabilitation system.

Consider the interaction and force transmission between the hand and wearable exoskeletons, fingers and exoskeleton are tightened by the presence of elastic silica gel (inset of Figure 5b). The exoskeleton rotation axes and finger rotation axes are lined up to minimize the possible relative sliding between exoskeleton linkage and human phalanges. Regarding the friction between linkages and actuators, miniaturized bearings are adopted. For each digit, 4 thin-film pressure sensors are sandwiched between the silica gel (both dorsal and palmar sides) and digit holder. In addition, 3 IMUs are installed in the exoskeleton in the labelled position of Figure 5b. Adopting the design of the hand exoskeleton, a wearable controller without an actuator is assembled with a pressure sensor and IMUs installed in the positions labelled in Figure 5c. This wearable controller is designed for HMI, which is thoroughly discussed in Section 3.

Although the hand exoskeleton is developed based on one subject, the fitness of people with different phalanx/digit lengths is considered in this design. Representative anthropometric data are considered first; however, a complete and convincing segment data sheet is rare in the literature. Thus, the phalanx lengths of 20 subjects were measured. The height of subjects ranged from 152 to 191 cm. Based on the measurements, a length-adjustment mechanism was designed. To ensure a comfortable rehabilitation experience for different people, the rotation axes of the PIP joints (DIP joint for the thumb) of the hand exoskeleton and the human hand need to be aligned first and then the length of the metacarpal exoskeleton is adjusted via the sliding chute of the metacarpal exoskeleton (Supplementary Materials, Figures S3–S5) to align the rotation axis of the MCP joints (Figure 4a). The metacarpal exoskeleton, linear actuator 1, and proximal phalanx exoskeleton together form an open-chain mechanism. The metacarpal exoskeleton needs to be fixed to the human hand (via either a bandage or glove) to ensure the accurate control of joints.

Based on the Monte Carlo method, Figure 7 represents the DIP joint workspace (*A*) of the index finger, which is driven by the exoskeleton. Considering the entire workspace *B* of the DIP joint (Figure 3d), the two workspaces present the following relationship *A* ⊂ *B*, which guarantees the safety of the exoskeleton user in all circumstances.

′′

**Figure 7.** Workspace of exoskeleton worn by index finger. (**a**) The DIP joint workspace of the index finger driven by index finger exoskeleton; (**b**) 2D view of the DIP joint workspace for the corresponding index finger exoskeleton.

⊂

#### 2.3.2. Kinematic Analysis

0 , <sup>1</sup> , <sup>2</sup> , <sup>3</sup> , <sup>4</sup> , <sup>5</sup> To execute rehabilitation training or grasp tasks precisely, joint space trajectory planning is needed to describe each joint angle variation with respect to time. Moreover, angular velocity and angular acceleration of both MCP and PIP joints during the rotation process need to be constrained to avoid the possibility of finger injury. To guarantee a gentle acceleration for each finger joint, a quintic polynomial is adopted for the trajectory planning of each joint. The quintic polynomial contains 6 coefficients (*C*0, *C*1, *C*2, *C*3, *C*4, *C*5), which constrain the angle, angular velocity, and angular acceleration. The corresponding angle, angular velocity, and angular acceleration of both joints meet the following requirements:

$$\begin{cases} \psi(t) = \mathbb{C}\_0 + \mathbb{C}\_1 t + \mathbb{C}\_2 t^2 + \mathbb{C}\_3 t^3 + \mathbb{C}\_4 t^4 + \mathbb{C}\_5 t^5\\ \psi'(t) = \mathbb{C}\_1 + 2\mathbb{C}\_2 t + 3\mathbb{C}\_3 t^2 + 4\mathbb{C}\_4 t^3 + 5\mathbb{C}\_5 t^4\\ \psi''(t) = 2\mathbb{C}\_2 + 6\mathbb{C}\_3 t + 12\mathbb{C}\_4 t^2 + 20\mathbb{C}\_5 t^3 \end{cases} \tag{2}$$

3

 () = 2<sup>2</sup> + 6<sup>3</sup> + 12<sup>4</sup> <sup>2</sup> + 20<sup>5</sup> 0 We assume 10 s is required for MCP and PIP joints to rotate 60 ◦ , taking *t*<sup>0</sup> and *t<sup>e</sup>* as the start and end time for both joints, and the 6 parameters in Equation (3) are presented as follows:

$$\begin{cases} \mathsf{C}\_{0} = 0\\ \mathsf{C}\_{1} = \mathsf{y}'(t\_{0})\\ \mathsf{C}\_{2} = \frac{\mathsf{y}''(t\_{c})}{2} - \frac{3\mathsf{y}''(t\_{0})}{20} - \frac{3\mathsf{y}'(t\_{0})}{50} - \frac{\mathsf{y}'(t\_{c})}{25} + \frac{\pi}{300} \\ \mathsf{C}\_{4} = \frac{3\mathsf{y}''(t\_{0})}{200} - \frac{\mathsf{y}''(t\_{c})}{100} + \frac{\mathsf{y}'(t\_{0})}{125} + \frac{7\mathsf{y}'(t\_{c})}{1000} - \frac{\pi}{2000} \\ \mathsf{C}\_{5} = \frac{\mathsf{y}''(t\_{c})}{2000} - \frac{\mathsf{y}''(t\_{0})}{2000} - \frac{3\mathsf{y}'(t\_{0})}{10000} - \frac{3\mathsf{y}'(t\_{c})}{10000} + \frac{\pi}{50000} \end{cases} \tag{3}$$

To guarantee gentle and stable rehabilitation training with the exoskeleton, the speed and acceleration of the MCP and DIP joints are set to 0 for the start and end points. Based on the setup above, angle, angular velocity, and angular acceleration changes with respect to time are calculated for MCP and PIP joints, which are presented in Figure 8. Figure 9a presents the trajectory of the corresponding (index finger exoskeleton) DIP joint, and as can be seen, the trajectory exists completely inside the workspace of the index finger exoskeleton DIP joint (Figure 9b).

{ 

{ 

 

 

<sup>3</sup> = ′′ ( ) 20

<sup>3</sup> = ′′ ( ) 20

3 ′′ (<sup>0</sup> )

3 ′′ (<sup>0</sup> )

200

200

<sup>4</sup> =

<sup>4</sup> =

<sup>5</sup> = ′′ ( ) 2000

<sup>5</sup> = ′′ ( ) 2000

– – **Figure 8.** Trajectory planning for index finger exoskeleton MCP joint and PIP joint. (**a**–**c**) MCP joint angle, angular velocity, and angular acceleration variation with respect to time; (**d**–**f**) PIP joint angle, angular velocity, and angular acceleration variation with respect to time. – –

<sup>0</sup> = 0 <sup>1</sup> = ′ (<sup>0</sup> )

<sup>0</sup> = 0 <sup>1</sup> = ′ (<sup>0</sup> )

> − 3 ′ (<sup>0</sup> )

− 3 ′ (<sup>0</sup> )

+ ′ (<sup>0</sup> ) 125

+ ′ (<sup>0</sup> ) 125

10000

10000

− 3 ′ (<sup>0</sup> )

− 3 ′ (<sup>0</sup> )

50

50

− ′() 25 + 300

− ′() 25 + 300

− 2000

− 2000

 50000

 50000

+

+

+ 7 ′() 1000

+ 7 ′() 1000

− 3 ′() 10000

− 3 ′() 10000

<sup>2</sup> = ′′ (<sup>0</sup> ) 2

<sup>2</sup> = ′′ (<sup>0</sup> ) 2

20

20

− 3 ′′ (<sup>0</sup> )

− 3 ′′ (<sup>0</sup> )

− ′′ ( ) 100

− ′′ ( ) 100

− ′′ (<sup>0</sup> ) 2000

− ′′ (<sup>0</sup> ) 2000

**Figure 9.** Trajectory of index finger exoskeleton DIP joint to accomplish a grasp action; (**a**) 3D view of the trajectory; (**b**) trajectory of index finger exoskeleton DIP joint compared with the workspace of the DIP joint.

To ensure the fingers under the control of the exoskeleton move according to the previously determined trajectory, it is necessary to control the linear actuator precisely. Based on Figure 4 and Equation (1), the length of linear actuators 1 and 2 (Figure 5b) can be expressed as:

$$\begin{cases} l(t) = \sqrt{m^2 + n^2 - 2mn\cos[\pi - \alpha - \beta + \psi(t)]}\\ c(t) = \sqrt{a^2 + b^2 - 2ab\cos[\pi - u - v + \psi(t)]} \end{cases} \tag{4}$$

For the grasp action defined in this section, the displacement, velocity, and acceleration for linear actuators 1 and 2 are presented in Figure 10.

{

() = √<sup>2</sup> +

<sup>2</sup> +

() = √

<sup>2</sup> − 2 [ − − + ()]

<sup>2</sup> − 2 [ − − + ()]

– – – – – – **Figure 10.** Displacement, velocity, and acceleration diagrams of the two actuators in order to rotate 60 ◦ in 10 s for MCP and PIP joints. (**a**) Displacement–time diagram of actuator 1; (**b**) velocity–time diagram of actuator 1; (**c**) acceleration–time diagram of actuator 1; (**d**) displacement–time diagram of actuator 2; (**e**) velocity–time diagram of actuator 2; (**f**) acceleration–time diagram of actuators 2.

#### **3. Hand Exoskeleton HMI Strategies**

#### *3.1. Hand Exoskeleton System Overview*

–

The overall control system is composed of four major parts, including the hand exoskeleton, host computer, slave computer (STM32-F329 microcontroller, manufactured by Zhengdianyuanzi Ltd., Guangzhou, China), and a wearable controller (Figure 11a). The host computer processes data collected by the slave computer and sends commands via the interface program developed in the QT environment. As shown in Figure 11b, the interface program possesses two basic functions including mode selection and data visualization. The slave computer integrates one analog-to-digital converter (ADC) and one serial port transmission module and controls the linear actuator via pulse width modulation (PWM).

– Considering the high real-time and high-resolution requirements for rehabilitation, thin pressure sensors (RP-C18.3-ST, manufactured by Aodong Ltd., Dunhua, China) and IMUs (IMU901, manufactured by Zhengdianyuanzi Ltd.) are selected for human–machine interaction, and the distribution of these sensors is illustrated in Figure 5. The thin-film pressure sensors selected are piezoelectric and their pressure reading can be calibrated via the resistance–voltage conversion relation:

$$\mathcal{U}\_0 = \left(1 + R\_{AO-RES} \times \frac{1}{R\_\chi}\right) \times 0.1\tag{5}$$

where *RAO*−*RES* represents the adjustable resistance and *R<sup>x</sup>* is the resistance that changes in real time with respect to pressure changes. The real-time pressure data collected by the sensor can be converted into an analog voltage (0~3.3 V) through the ADC module in the slave computer. The adopted IMU integrates a gyroscope, accelerometer, magnetometer, and barometer. The IMU outputs the variation of pitch, roll, and yaw angles via the Universal Synchronous Asynchronous Receiver Transmitter module (USART). In order to minimize the interference of 'abnormal data' (induced by shaking of the hand, random motion of the arm, etc.) while ensuring the reliability of data, an amplitude-limiting filtering algorithm (integrated into STM32) is utilized to constrain the steep variation in the data.

<sup>0</sup> = (1 + − ×

−

minimize the interference of 'abnormal data' (in

1 

) × 0.1

**Figure 11.** Control of the hand exoskeleton rehabilitation. (**a**) System overview of the hand exoskeleton; (**b**) interface program to control the hand exoskeleton.

#### *3.2. Control Modes for Rehabilitation and Daily Life Activity Assistance*

Stroke patients usually need a long rehabilitation period after surgery in order to recover from stroke-related complications such as hemiplegia. Patients' demands at different rehabilitation stages vary even for the same patient [14], thus, rehabilitation therapy should also be changed accordingly. Regarding this issue, human–machine interaction (HMI) technology is adopted to adjust rehabilitation therapy and control the motion of the hand exoskeleton based on personal needs. Three modes are designed for rehabilitation and daily life assistance, namely, robot-in-charge, therapist-in-charge, and patient-in-charge modes.

The robot-in-charge training strategy aims to help patients without the ability to move or exercise. In this mode, the hand exoskeleton guides the patient's hand along a preplanned path (proposed by doctors). The therapist-in-charge training strategy is suitable for patients in all recovery stages and requires a therapist to put on the wearable controller (Figure 5c). The angular rotation of the therapist's hand is mapped onto the patient's hand via tracking pitch, roll, and yaw angles obtained by IMUs. The patient-in-charge training strategy targets patients who are capable of low-intensity exercises. In this mode, two functions can be achieved, which are rehabilitation and daily activity assistance. A

wearable controller is required to be worn by one hand, while the hand exoskeleton is equipped with the other hand (Figure 5d). Utilizing deep learning and machine learning methods, data (collected by the wearable controller) can be correlated to different preplanned exoskeleton postures/actions. More information regarding the three modes is presented in the following sections.

move or exercise. In this mode, the hand exoskeleton guides the patient's hand along a

controller (Figure 5c). The angular rotation of the therapist's hand is mapped onto the patient's hand via tracking pitch, roll, and yaw angles obtained by IMUs. The patient

related complications such as hemiplegia. Patients' demands at dif-

–
