is attached in the forearm module, in which the Z0 axis is coincide with the rotation axis of F/E movement. Here, the motion angles of wrist F/E and R/U are represented by θ1 and θ2, respectively. The associated D-H parameters for RTD are listed in Table 1.

Table 1. Parameters of the modified D-H method for RTD.

In general, the homogeneous transformation matrix between two adjacent frames, namely and , is conventionally described as:

i−1iT=[Cθi−Sθi0ai−1SθiCαi−1CθiCαi−1−Sαi−1−Sαi−1diSθiSαi−1CθiSαi−1Cαi−1Cαi−1di0001]    (24)

where Sθi, Cθi, Sαi, and Cαi represent sinθi, cosθi, sinαi, and cosαi, respectively. Therefore, by substituting the D-H parameters of RTD into Equation (24), the transformation matrix 01T and 12T can be obtained, then the transformation matrix between frame and frame is calculated by:

02T=01T21T=[Cθ1Sθ2Cθ1Cθ2−Sθ10Sθ1Sθ2Sθ1Cθ2Cθ10Cθ2−Sθ2000001]    (25)

According to the discussion above, the point B of hand module in frame is calculated by:

0BP=[0BPx0BPy0BPz1]=02TB2P =[Cθ1Sθ2Cθ1Cθ2−Sθ10Sθ1Sθ2Sθ1Cθ2Cθ10Cθ2−Sθ2000001][2BPxPyBPzB1]    (26)

In terms of the obtained coordinate value of point B, the distance between A and B after a certain wrist movement is:

dAB=(0BPx−0APx0)2+(0BPy−0APy0)2+(0BPz−0APz0)2    (27)

while the initial distance between A and B is:

d0=(0BPx0−0APx0)2+(0BPy0−0APy0)2+(0BPz0−0APz0)2    (28)

then the actual extension value of spring can be expressed as follows:

For RTD, the resistance module includes four rope-spring kits, whose initial endpoint positions of A and B in base frame are given by:

A=[A1A2A3A4]=[-124012-1240-12-12-4012-12-40-12]    (30) B=[B1B2B3B4]=[4212.5124212.5-1242-12.51242-12.5-12]    (31)

As mentioned before, the available range of F/E movement θ1∈[-75◦,70◦], and the range for R/U motion θ2∈[-20◦,35◦]. Based on previous analysis, the elastic deformations of four springs under different motion patterns can be calculated, the relationships between spring elongations and motion angles are exhibited in Figure 8.

Figure 8. Variations in spring elongation of the rope-spring (A) kit 1, (B) kit 2, (C) kit 3, and (D) kit 4.

In addition, the applied force of each group of two rope-spring kits can be calculated by:

where x is the spring elongation, k is the spring constant given by:

To investigate the influence of resistance levels on human muscle activity, two spring modules with different stiffnesses were employed in this work. According to Equations (32, 33) and the physical parameters of adopted extension springs listed in Table 2, the available resistant force of RTD for each motion patterns can be obtained. As presented in Table 3, the types of low and high resistance denote the conditions using springs with wire diameters of 0.8 and 1.0 mm, respectively.

Table 2. Physical parameters of the adopted extension springs.

Table 3. Available resistant force for each motion pattern of RTD.

3.3 Data acquisition system

As presented in Figure 9, the two exoskeleton devices are combined with respective data acquisition systems to evaluate their practical function. Notably, AFD and RTD are both equipped with two posture sensors, respectively distributing in the aforementioned installation platforms of hand and forearm modules. The required fixation for DRF could last a long time, thus a temperature module is attached in the forearm module of AFD, for monitoring the temperature variation of patient wearing the exoskeleton. The corresponding joint angle and temperature data are transmitted into a STM32 microcontroller, which is an information processing and exchanging center that communicated with computer based on a WiFi module. As to the RTD, the resistant effect is examined by an additional sEMG acquisition device, in which the electrodes (i.e., the red, green, and yellow ones) should be placed in the outer skin of forearm for bioelectric signal detection. The computer serves for data collection and visualization, the relevant joint angle and the cumulative exercise times will be calculated and displayed in real time, resulting to more intuitive observation for the patient and more quantitative supervision for the attending doctor.

Figure 9. Hardware architectures of the data acquisition systems for AFD and RTD.

4 Experiments and functional evaluation

Based on the design schemes presented above, the prototypes of AFD and RTD were established for function evaluation. The main bodies of these two exoskeleton devices, including the hand, wrist and forearm modules, were fabricated by 3D printing with the material of UV curable resin. As suggested in previous researches (Li et al., 2023), the joint motion and muscle strength are two indispensable indexes to track human states. To investigate the application performance of exoskeleton device on human movement, physical experiments were carried out on three healthy subjects (Subject 1: female, 45 kg, 1.62 m, 24 years old; Subject 2: male, 65 kg, 1.72 m, 30 years old; Subject 3: female, 48 kg, 1.67 m, 29 years old). The experimental protocol has been approved by the Ethics Committee of Zhongda Hospital Southeast University, and the subjects have given informed consent to participate in the experiments by signing a written agreement.

As presented in Figure 10A, the hand and forearm modules are worn by Subject 1 and the paired components are tied with Velcro types. Most electronic elements of the required data acquisition system for AFD are deployed to attach in the installation platforms, while some of them are carried by arm, including the portable battery module. To validate the feasibility in detecting and recording the motion ranges of different postures, several experiments under wrist, elbow and shoulder movements were systematically implemented. Notably, the key of wrist experiment focuses more on the reachable range of AFD, while the experiments of elbow and shoulder joint are mainly concentrated in the counting precision of exercise times.

Figure 10. Experimental conditions and wearing appearances of (A) AFD and (B) RTD.

The experimental conditions of RTD and the attachment of surface electrodes are exhibited in Figure 10B, where the red electrode serves as a signal reference, while the green and the yellow ones are applied for the actual bioelectric signal detection and placed on the corresponding skin region of muscle. To study the actual impact of RTD on muscle activities in different individuals, all three subjects participated in the resistance training experiments were equipped with RTDs customized to their forearm contours.

4.1 Attitude monitoring

In this work, the two groups of wrist movement were respectively performed for five consecutive times by experimenter, the posture data is recorded and the actual range of each action was calculated. As illustrated in Figure 11, the motion angle equals to zero when the wrist is at its neutral position, extension and ulnar deviation are defined as the positive direction, as opposite to the flexion and radial deviation. According to motion curves, it is apparent that the accessible ranges of AFD for flexion/extension and radial/ulnar deviation are all capable of covering the functional ROMs of wrist joint.

Figure 11. Motion curves based on (A) flexion/extension and (B) radial/ulnar deviation of the wrist joint.

As for the elbow and shoulder joints, different thresholds were defined for the judgment on whether the basic range requirement of a motion behavior is satisfied or not. The employed thresholds for each motion patterns of elbow and shoulder are listed in Table 4. In this work, a continuous movement that successively exceeds the upper threshold and the lower threshold is regarded as one time of complete training action. To estimate the counting precision and sensitivity on training times, the experiments were deliberately configured by establishing conditions in which half of the total repetitive motions were correctly counted, while the other half were not. As illustrated in Figure 12, 10 times of reciprocating motion for each pattern have been conducted. According to the experimental results of each motion pattern, only the first five times of action can be effectively counted, while the last five are failed. The results are as expected, hereby the monitoring function of elbow and shoulder postures AFD is demonstrated to be reliable.

Table 4. Range thresholds for each motion pattern of elbow and shoulder joint.

Figure 12. Motion curves based on (A) flexion/extension of the elbow joint, (B) abduction/adduction, (C) flexion/extension, and (D) internal/external rotation of the shoulder joint.

In contrast to previous studies that mainly focused on immobilizing fractured wrists using plaster splint or other fixation devices, the AFD introduces a novel, adjustable wrist exoskeleton mechanism. It provides stable protection for DRF while allowing limited joint movements to reduce muscle stiffness. Meanwhile, the AFD also offers effective motion data for rehabilitation exercises, contributing to better quantification of the active rehabilitation process in DRF patients.

4.2 Resistant influence

The neuromuscular system of a human body includes plenty of muscles and nerves, every movement of the body is realized based on the communication from the brain to muscles. The muscular system is comprised of several specialized cells named muscle fibers, and the predominant function of them is for contractility. In general, the activities of muscle fiber can be detected and digitalized by the electromyography (EMG). As one of the EMG technology, surface electromyography (sEMG) has been extensively applied in wearable technologies (Xiao et al., 2024) for clinical diagnosis and functional supervision of muscle rehabilitation.

Here, the contraction activities of extensor carpi ulnaris (ECU) and flexor carpi ulnaris (FCU) during F/E movement, flexor carpi radialis (FCR) and flexor carpi ulnaris (FCU) during R/U movement, were systematically investigated. ECU is a forearm muscle extending from the lateral epicondyle of the humerus to the posterior border of the ulna, it plays a crucial role in wrist extension. FCU is a flexor muscle that originates from the medial epicondyle of the humerus to the posterior border of the ulna, it is mainly associated with wrist flexion and ulnar deviation. FCR is emanated from the medial epicondyle of the humerus and extends distally to the base of the second metacarpal bone, it contributes to radial deviation of the wrist, facilitating movement toward the thumb side. The selected three muscles are distributed in a superficial layer of forearm, and the bioelectric signals of this superficial muscle are more effectively and evidently to be detected on the skin. The sEMG signals of muscles under different experimental conditions were monitored in real time based on a sEMG acquisition kit presented in Figure 9.

For each experimental subject, the F/E and R/U movement of wrist under the condition without any resistance, the condition with low resistance and the condition with high resistance were required to be independently performed for five consecutive times. Compared with the early stage, the ROM for resistance training is limited to 55° for wrist flexion and 35° for wrist flexion, while radial deviation is limited to 15° and ulnar deviation to 25°. However, the directly detected bioelectric data may contain a significant amounts of noise and artifacts, which can negatively affect signal interpretation (Yin et al., 2024). Algorithmic intervention served as a popular strategy to reduce such distortions and enhance signal clarity. Here, the sEMG signals were further filtered by the wavelet transform algorithm, with the basis function of Daubechies (db4), the decomposition level of 2, and a sampling rate of 1,000 Hz. Wavelet transform offers an effective denoising method for electromyographic signals due to its time-frequency localization and multi-scale resolution, it removes noise while preserving signal details, enhancing signal-to-noise ratio and facilitating accurate analysis of EMG activity patterns. The eventually acquired sEMG signal data of one of the subjects are presented in Figure 13.

Figure 13. The sEMG signals of muscles under different motion patterns and experimental conditions: (A) F/E movement without resistance, (B) R/U movement without resistance, (C) F/E movement with low resistance, (D) R/U movement with low resistance, (E) F/E movement with high resistance, and (F) R/U movement with high resistance.

The integrated EMG (iEMG), a frequently-used feature extraction methods of sEMG signals, was employed as an evaluation index of the muscular contraction level. As described in Equation (34), iEMG is the mathematical integration of rectified EMG signals over a specified period of time, where T denotes the length of integration time window, and Data[t] is the EMG signal.

iEMG=∫0T|Data[t]|dt    (34)

The calculated iEMG values of different muscles under three experimental conditions are shown in Figure 14. The results demonstrate an apparent growth of muscle activation with the increase of external resistance applied in each motion pattern for all subjects. As depicted in Figure 15, compared to the experimental condition without any constraint, the iEMG values exhibit distinct patterns under varying resistance levels. Specifically, during the F/E movement, the iEMG values increase by approximately 35% and 22% for FCU and ECU under low resistance, respectively, and by approximately 91% and 86% under high resistance, respectively. Similarly, during the R/U movement, the iEMG values increase by approximately 12% and 31% for FCR and FCU under low resistance, respectively, and by approximately 37% and 82% under high resistance, respectively.

Figure 14. The iEMG values of different muscles: (A) FCU under F/E movement, (B) ECU under F/E movement, (C) FCR under R/U movement, and (D) FCU under R/U movement.

Figure 15. The average iEMG values of all subjects (Mean ± 1SD, N = 3) under different experimental conditions.

According to the experimental results of RTD, the application of an resistant force is essential for the patients with diverse muscular strength. Compared to previous studies that mainly focused on the passive motion of wrist joint under the assistance of exoskeleton robots, the RTD proposed in this study aims to enhance the active rehabilitation ability of DRF patients, which is of great significance for helping them regain normal function of wrist movement. Notably, the springs employed on the RTD can be freely replaced with ones of different stiffnesses according to the baseline muscle strength of patients. For patients with weak muscle strength (e.g., old patients or the patients in the early stage of rehabilitation), it is recommend that the RTD be equipped with low resistance. To continue gaining benefits from strength enhancing activities, the resistance force is required to be progressively increased.

In this section, the application performance of AFD and RTD for wrist rehabilitation were experimentally evaluated. The research focus lies in validating the joint monitoring function and exploring the resistance training influence of exoskeleton devices. Therefore, although the data were obtained from healthy human subjects, the summarized principles related to joint motion and resistance training can be generalized to patients suffering from DRFs with varying characteristics. However, despite the validated advantages, there are still some limitations to the current exoskeleton devices. Due to the physiological differences between healthy individuals and fracture patients, further integration of the exoskeleton devices with force/torque sensors is conducive to gain a deeper understanding of the wrist dynamics in DRF patients. Moreover, the exoskeleton device can be further integrated with additional mechanisms to automatically impose physical intervention that limit joint movement when the monitored force/torque data reach safety thresholds defined by doctors based on clinical experience during joint motion. Meanwhile, there are also some potential issues that could affect the application of exoskeleton devices. In clinical practice, patients may experience issues such as poor comfort and compliance when wear