2.1. SRIG-Exo system description

The overall architecture of the SRIG-Exo system is shown in Figure 1, which presents the mechanical structure and sensing layout of the glove together with the detachable cable connector and linear actuator designs. The system consists of three main subsystems: the soft glove module, the linear actuation unit, and the control system.

Figure 1.

Overview of the SRIG-Exo device. The figure illustrates its main components, including the glove, detachable cable connector, and hardware box containing the linear actuator, battery, and control electronics. (a) Glove design showing embedded sensors and tendon routing. (b) Detachable cable connector assembly with connector 1 and connector 2, and the first and second joining parts where tendons from the glove and actuator are fixed, respectively. (c) CAD model of the compact lead-screw-driven linear actuator. (d) The SRIG-Exo glove worn on the user’s hand.

The soft glove module is fabricated from multilayer textile materials selected for comfort, flexibility, and mechanical strength. Flexible steel tendons run along the palmar side of the thumb, middle, and ring fingers to generate flexion forces. They pass along the phalanges and loop around the fingertips through low-friction Teflon guides to ensure smooth motion (Figure 1(a)). Pressure sensors embedded at the fingertips and bend sensors positioned on the dorsal surfaces of the fingers provide real-time feedback on user interaction and joint motion. The glove also incorporates a detachable cable connector, allowing quick attachment or replacement while maintaining precise cable alignment (Figure 1(b)). This is an essential feature for daily donning and doffing and for interchanging gloves of different sizes or materials.

The linear actuation unit employs a lead-screw-based underactuated mechanism (Figure 1(c)). A compact DC servo motor drives a threaded rod, coupled to a traveling nut, which converts rotational motion into linear displacement. A loop-type cable routing mechanism is integrated to automatically distribute tendon tension among multiple fingers, enabling adaptive grasping of objects with different shapes without the need for separate actuators. This configuration effectively realizes under-actuation, reducing both weight and energy consumption while improving grasp adaptability. Mechanical stoppers at both stroke limits, along with software-defined position and torque limits, ensure operational safety by preventing excessive cable displacement or over-tightening.

The control and power module are housed in a lightweight 3D-printed enclosure that can be mounted on the user’s waist belt or upper arm to minimize distal loading. This module integrates the microcontroller board, linear actuator unit, and battery. The intention-based control algorithm utilizes real-time inputs from the bend and pressure sensors to interpret the wearer’s motion intent. When voluntary finger bending or contact pressure exceeds the preset thresholds (detailed in Section 2.4), the controller issues proportional actuator commands to pull the tendons and assist the grasp. This produces an intuitive, user-initiated assistance response while maintaining safe and natural interaction.

The integration of these three subsystems results in a lightweight, wearable, and intention-responsive glove capable of assisting functional grasping for individuals with partial hand mobility. The combination of a detachable cable connector, loop-based under-actuation, and hybrid sensing control distinguishes it from conventional cable-driven gloves, which typically rely on multiple actuators, rotary spool mechanisms, single-sensor modalities, or EMG-based control strategies. These subsystems, together with the intention-based control framework, are described in detail in the subsequent sections.

Furthermore, to guide the mechanical design, actuation strategy, and control architecture of the SRIG-Exo, key quantitative design requirements were established. These requirements define target specifications for wearability, assistive force, motion range, control responsiveness, and user comfort, ensuring the device is suitable for rehabilitation and daily activities. Table I summarizes the quantified requirements. These requirements provide a clear benchmark for evaluating design choices for the SRIG-Exo system and also guide the experimental validation.

Table I.

Quantified design requirements of the SRIG-Exo.

A summary comparing the design requirements listed in Table I with the experimentally achieved results is provided in the discussion (see Section 4), validating the target specifications for glove weight, actuator performance, grasping force, finger motion, control responsiveness, donning/doffing time, and user comfort.

2.2. Mechanical design of the SRIG

The physical design of the soft robotic glove is illustrated in Figure 2. The glove itself is equipped with force sensing resistor (FSR) sensors (RP-C18.3-LT, Suzhou Leanstar Electronic Technology Co., Ltd., China) affixed to the underside of the fingertips and the bend (flex) sensors (FLEX 4.5, Suzhou Leanstar Electronic Technology Co., Ltd., China) positioned at the midpoints along the top side of the finger and artificial tendons routed in the thumb, middle, and ring fingers at the palmar side, respectively.

Figure 2.

The SRIG-Exo: palmar (right side) and dorsal (left side) views of the soft glove showcasing its mechanical structure and integrated sensing components.

The tendon routing and under-actuation mechanism of the SRIG-Exo are illustrated in Figure 3, showing how a single motor drives multiple fingers through a looped cable configuration. The glove is primarily constructed from synthetic leather, with cut patches at the finger joints to enhance natural movement and comfort. It is essential to note that for optimal performance, custom-tailored gloves are recommended to fit the glove on the wearer’s hand precisely [Reference Secciani, Brogi, Pagliai, Buonamici, Gerli, Vannetti, Bianchini, Volpe and Ridolfi70].

Figure 3.

Schematic of the tendon routing and under-actuation mechanism. (a) Overview of the SRIG-Exo showing tendon paths, teflon tubes, and Bowden cables driven by a single motor. (b) Detailed routing for two fingers (finger a and finger B) through the detachable connector, illustrating the looped configuration between the glove and actuator.

The connected artificial tendons constructed from 0.6 mm diameter flexible steel cables (ɸ 0.6 mm 7 × 7, Taizhou Jianyi Stainless Steel Products Co., Ltd., China), combined with Teflon (PTFE), are chosen to minimize friction between the synthetic leather and the cables. Each tendon is assigned to a particular finger of the glove. The artificial tendon traverses along both sides (medial and radial sides) of the bottom of each finger, forming a loop rather than going through the center, indicating a dual-sided routing pattern. This tendon loop converges near the finger’s base, and the tendons follow the palm routing. This proximity to the volar side generates a moment arm around the finger joint’s axes, facilitating flexion and adduction movements [Reference Park, Heo, Kim and Na63]. In addition, a strap is stitched to the proximal phalanx of the thumb to support the abduction adjustments, as depicted in Figure 2 (left side), thereby enhancing the hand’s grasping ability [Reference Kelly, Tacy, Kesner and Harlan57, Reference Kang, Choi, Lee and Cho71]. The primary objective is to improve hand grip strength, particularly on the thumb, middle, and ring fingers.

A splint has been devised to secure the cables within the glove. Notably, the glove’s palm features an opening near the edges of the proximal phalanges of the fingers, as depicted in Figure 2 (right side). This opening feature serves a dual purpose: first, it enhances the range of tendon displacement, facilitating greater finger bending. Second, it simplifies the process of putting on and taking off the glove. Additionally, two Velcro (hook-and-loop) straps are incorporated into the palm to fasten the glove securely onto the hand. These straps provide added support to withstand the forces exerted by the tendons on the hand. These tendons pass through the palm routing of the glove and are shown in Figure 2 (right side).

Teflon tubes are used to reduce friction within the tendon routing paths, thereby enhancing the longevity of the designated routes by minimizing wear and tear. This Teflon works as a pulley-type mechanism, guiding the artificial tendons. All tendons originate from a detachable connector that links the actuator unit to the glove, as depicted in Figure 1(d). The electrical wires of the FSR sensor traverse through the top of the finger, positioned beneath the flex sensor. The electrical wires of both sensors are passed through the dorsal side of the glove to avoid hindrances, while the palmar side of the glove comes into contact with objects. As a human–machine interface, the mechanical design of the SRIG-Exo must prioritize safety and ensure mechanically transparent operation. Therefore, mechanical travel limits are integrated on both the glove (within the detachable connector) and actuator sides to ensure safe and durable performance. The detachable connector is positioned on the palmar side of the forearm and secured with Velcro straps. Power transmission cables run along the arm, enabling easy detachment of the glove from the hardware box for replacement or interchange with other gloves. The actuators, controller, and batteries are housed in a compact hardware box (Figure 1) that can be worn remotely for convenient use.

2.2.1. Mathematical modeling

The schematic of the finger kinematics and tendon routing is developed to derive the forward kinematics of the finger, as illustrated in Figure 4. Additionally, Figure 5 presents the schematic depicting the sensor placement and the method used for angle measurement via the flex sensor.

Figure 4.

Schematic of one-finger kinematic and tendon routing model (lateral side). The schematic drawing defines the tendons’ routing along each finger joint.

Figure 5.

Schematic drawing defining the insertion of the sensors and the angle measurement method using the flex sensor, where $\theta _{f}$ is the measured angle.

In Figure 4, $\theta _{f,i}$ (i = 1, 2, 3) denote the joint angles of the metacarpophalangeal (MCP), proximal interphalangeal (PIP), and distal interphalangeal (DIP) joints, respectively. Similarly, $L_{f,i}$ represent the lengths of the proximal, middle, and distal phalanges, and the black circles $J_{f,i}$ indicate the corresponding finger joints. Notably, in the schematic of Figure 4 and in the forward kinematics and total finger flexion equations, indexed variables are written explicitly (e.g., $\theta _{f1}$ – $\theta _{f3}$ , $L_{f1}-L_{f3}$ ) for improved readability.

The flexor tendon is routed along the palmar side of the finger through small guiding tubes fixed at the midpoints of each phalanx, as illustrated in Figure 4. Accordingly, $l_{t,i}$ denote the tendon path lengths from the palm to the proximal phalanx, from the proximal to the middle phalanx, and from the middle to the distal phalanx, respectively. $\gamma _{i}$ represent the angles influenced by the tendon path geometry. The flexor tendon is shown in maroon color, the routing path for the tendon is shown in light blue, and the gray rectangles represent the straps that support the tension on the finger.

The geometric parameters $l_{t,i}$ can be determined from the geometry of the glove. The distances between the Teflon guide tubes mounted at the midpoints of adjacent phalanges, as well as between the palm-mounted guide tube and the proximal phalanx, are fixed by the glove design. The parameter $h_{i}$ denotes half of the finger thickness at i-th phalanx. For the default fully extended configuration ( $\theta _{f1}=\theta _{f2}= \theta _{f3}=$ 0°), the tendon path lengths are expressed in Eq. (1) as:

(1) \begin{equation}l_{t,i}=l_{i,a}+l_{i,b},\quad {i}= 1, 2, 3.\end{equation}

The tendon routing geometry introduces the angles $\gamma _{i}$ , which are computed using the law of cosines as given in Eq. (2):

(2) \begin{equation}\gamma _{i}=cos^{-1}\left(\frac{\left(\left(h_{i}\right)^{2}+\left(l_{i,a}\right)^{2}\right)+\left(\left(h_{i+1}\right)^{2}+\left(l_{i,b}\right)^{2}\right)-\left(l_{t,i}\right)^{2}}{2\sqrt{(\!\left(h_{i}\right)^{2}+\left(l_{i,a}\right)^{2}) (\!\left(h_{i+1}\right)^{2}+\left(l_{i,b}\right)^{2})}}\right),\quad {i}= 1, 2, 3.\end{equation}

During finger flexion, variations in joint angles $\theta _{f,i}$ result in changes in the tendon path lengths due to cable displacement. The change in tendon length for each segment is approximated in Eq. (3) as:

(3) \begin{equation}{\unicode{x1D6E5}} l_{t,i}=l_{t,i}-\frac{D_{C}}{3},\quad {i}= 1, 2, 3.\end{equation}

where $D_{C}$ denotes the total cable displacement and can be computed using Eq. (12).

Accordingly, the variation in the tendon routing angles is given by Eq. (4):

(4) \begin{equation}{\unicode{x1D6E5}} \gamma _{i}=cos^{-1}\left(\frac{\left(\left(h_{i}\right)^{2}+\left(l_{i,a}\right)^{2}\right)+\left(\left(h_{i+1}\right)^{2}+\left(l_{i,b}\right)^{2}\right)-\left({\unicode{x1D6E5}} l_{t,i}\right)^{2}}{2\sqrt{(\!\left(h_{i}\right)^{2}+\left(l_{i,a}\right)^{2}) (\!\left(h_{i+1}\right)^{2}+\left(l_{i,b}\right)^{2})}}\right),\quad {i}= 1, 2, 3.\end{equation}

Now, the joint angles $\theta _{f,i}$ corresponding to the MCP, PIP, and DIP joints can be calculated using Eq. (5) as:

(5) \begin{equation}\theta _{f,i}= {\unicode{x1D6E5}} \gamma _{i}-\gamma _{i},\quad {i}= 1, 2, 3.\end{equation}

The forward kinematics of a single finger in the planar workspace are then expressed in Eqs. (6) and (7) as follows:

(6) \begin{equation}X= L_{f1}cos\theta _{f1}+L_{f2}cos (\theta _{f1}+\theta _{f2})+L_{f3}cos (\theta _{f1}+\theta _{f2}+\theta _{f3})\end{equation}

(7) \begin{equation}Y= L_{f1}sin\theta _{f1}+L_{f2}sin (\theta _{f1}+\theta _{f2})+L_{f3}sin (\theta _{f1}+\theta _{f2}+\theta _{f3})\end{equation}

The finger flexion angle $\theta _{f}$ is approximated as the cumulative contribution of the MCP, PIP, and DIP joint angles, expressed in Eq. (8) as:

(8) \begin{equation}\theta _{f}= \theta _{f1}+\theta _{f2}+\theta _{f3}\end{equation}

It should be noted that the assumptions are made for simplifying the derivation of the theoretical model for finger kinematics. In addition, the other related parameters, such as the mechanical play of components, steel cables looseness and flexibility, glove stretching, and glove customization to fit the wearer’s hand, are not included, which can significantly affect the kinematics when the user wears the glove.

The geometric kinematic model can be used as a theoretical design guide to estimate the functional RoM of the fingers and to assess workspace feasibility based on user-specific finger anthropometric parameters and a given cable displacement. By relating cable displacement to joint angles (Eqs. (1)–(5)), the model enables estimation of the finger flexion ranges in Eq. (8). Furthermore, the forward kinematic formulation (Eqs. (6) and (7)) can be used to verify that the achievable fingertip workspace covers common grasping postures required for ADL. The model can also estimate finger motion velocities by derivation of Eq. (8) and support qualitative assessment of cable displacement distribution across finger joints.

2.2.2. Simulation of the finger kinematic model

Figure 6 illustrates the simulated kinematics of the middle finger derived from the theoretical model (Eqs. (6)–(7)). The simulation assumes phalange lengths of 3.5 cm (proximal), 2.9 cm (middle), and 2.6 cm (distal), with corresponding half-thickness heights as 1 cm, 0.9 cm, and 0.8 cm, respectively, and a Teflon tube of 0.5 cm. The RoM for the MCP, PIP, and DIP joints were set as 85°, 107°, and 70°, respectively [Reference Lee and Jung72]. The total cable displacement $D_{\textit{cable}}$ was distributed among the three phalanges over a range of 0–7 cm.

Figure 6.

Simulated kinematics of the finger based on the theoretical model: (a) MCP, PIP, and DIP joint angles and total finger flexion as a function of cable displacement; (b) corresponding fingertip trajectory calculated using forward kinematics.

Under these conditions, the MCP, PIP, and DIP joints achieved maximum flexion angles of approximately 85°, 107°, and 70° at cable displacements of 6.52, 6.73, and 4.87 cm, respectively, resulting in a total finger flexion of about 262°. The fingertip followed a smooth curling trajectory in the x–y plane, moving from the initial extended position ( $X_{0}$ , $Y_{0}$ ) = (0, 0) cm to the fully flexed position ( $X_{f}$ , $Y_{f}$ ) = (−2.89, 0.31) cm, with a total planar displacement of approximately 11.9 cm. In this idealized model, the PIP and DIP joints began flexion only after cable displacements of about 0.91 cm and 0.54 cm, respectively, reflecting geometric thresholds. These simulations assume symmetric tendon routing, equal distribution of cable displacement among phalanges, and neglect mechanical effects such as cable friction, glove compliance, slack, and fit. However, these factors are inherent in practical experiments and inevitably influence the measured results.

2.3. Linear actuator-based under-actuation mechanism

The glove is an underactuated soft wearable robot where stable grasping is achieved with the development of the adaptive grasping mechanism in the actuator, as shown in Figure A2. Ensuring stability in grasping enables the thumb and fingers to effectively hold onto objects by conforming to their shapes while distributing contact forces across each finger to enhance the grip. In the glove, U-shaped tubes can be installed at the tips of the fingers and between fingers near the MCP joint, forming a loop mechanism to facilitate adaptive grasping [Reference In, Kang, Sin and Cho17]. However, inspired by the study [Reference Kim, Jeong, Kang and Cho73], which utilized a slider-tendon linear actuator with a movable pulley mechanism, we incorporated this approach in our actuator to enable adaptive grasping and achieve stroke amplification.

The fundamental concept of this mechanism mirrors that of the differential mechanism [Reference Gerez and Liarokapis54], that is, the distribution of pulled tendon length across multiple fingers. Opting for a fully actuated mechanism in the glove would provide precise control over finger movements and enhance grasping capabilities. However, it is essential to consider that this approach may result in higher costs and increased weight due to the requirement for separate motors for each finger. Therefore, this system incorporates a single rotary motor (Dynamixel XM430-W210, Robotis Co., Ltd., Korea), as depicted in Figure A1.

The motor drives lead screw rods with standard threads (ACME threads) featuring a lead screw diameter of 5 mm. This induces linear movement of a rectangular-shaped lead nut as the rod rotates. The actuator’s force output is transmitted through a slender steel cable, as the actuator is designed exclusively to generate tension in the cable. The linear movement of the lead nut can change the displacement of the routed cables to maximize the kinematics of each finger and assist in the equal distribution of forces in the cables. On the motor side, the lead screw is supported by a radial-axial bearing, whereas on the end-effector side, it relies on a radial bearing for support. Limit sensors (Tiaihua, Shenzhen Weixin Technology Co., Ltd., China) are employed to detect the end positions of the lead nut; no encoders are utilized, and only the end positions are monitored. For a visual representation of the various actuator components, refer to Figure A1.

In soft wearable exoskeletons, pretension can lead to discomfort or injury and may also increase friction along the tendon paths, resulting in hampered efficiency [Reference In, Kang, Sin and Cho17]. The proposed actuator eliminates the need for a pretension mechanism, as its lead screw rod and rectangular nut mechanism, combined with cable fixation, prevent cable derailment, allowing tendon slackening to be disregarded. The linear movement, achieved through the lead screw rod and nut mechanism, can firmly lock the fingers’ position. Therefore, this approach eliminates the need for an extra clutch-based component or additional locking system. Moreover, disengaging the motor from its holding position reduces the required control effort and the consequent power consumption.

The actuator requires a 100 mm stroke, which is sufficient to assist with grasping in ADLs [Reference In, Kang, Sin and Cho17]. The adopted stroke amplification mechanism minimizes the overall length of the actuator design. In this gear mechanism, the primary drive gear transmits the motion to two secondary gears, establishing a direct connection that induces them to rotate in reverse, as depicted in Figure A1. Additionally, the main drive gear is linked to two additional secondary gears via the first set of gears, resulting in these latter two gears rotating in the same direction as the main gear. The thumb gear with finger gear ratio is selected according to the first-hand postural synergy detailed in the paper [Reference Xiloyannis, Cappello, Khanh, Yen and Masia15].

A counterclockwise lead screw is securely fastened to the secondary gear. In contrast, a clockwise lead screw is connected to the additional final gear, as illustrated in Figure A2. These lead screws tension the cable when the main drive rotates clockwise. Conversely, when the main drive rotates counterclockwise, the opposite action occurs.

The cable displacement is directly linked to the slider’s linear movement and the cable’s length, which interacts with the pulley. This unique relationship arises from the looped cable mechanism. In this mechanism, the cable follows two distinct paths, ascending and descending, which are closely tied to the linear motion of the actuating slider. The total linear movement range of the slider (rectangular-shaped lead nut) is denoted by $S$ is expressed in Eq. (9) as follows:

(9) \begin{equation}S= L_{t}-l_{s}\end{equation}

Here, $L_{t}$ represents the total length between the motor plate and end support plate, and $l_{s}$ represents the length of the rectangular-shaped lead nut measured along its direction of motion (as illustrated in Figure A2). The $D_{\textit{stroke}}$ of the cables is given as:

(10) \begin{equation}D_{\textit{stroke}}= 2S\end{equation}

In Eq. (10), $D_{\textit{stroke}}$ represents the total linear displacement of the end-effector cable.

The lead of the slider $L_{S}$ can be calculated as:

(11) \begin{equation}L_{S}= n_{S}p \,(i_{G})\end{equation}

Here in Eq. (11), the gear ratio $i_{G}$ is defined as the ratio of the number of teeth on the main drive gear $T_{Gm}$ (i.e., motor gear) to the number of teeth on the lead screw gear $T_{Gs}$ . $n_{S}$ represents the number of threads starts on the screw, and $p$ is the pitch of the threaded screw.

The displacement of the cable $D_{\textit{cable}}$ per one rotation of the motor can be expressed by Eq. (12) as:

(12) \begin{equation}D_{\textit{cable}}= 2L_{S}\end{equation}

The linear speed of the end-effector cable $V_{\textit{cable}}$ is

(13) \begin{equation}V_{\textit{cable}}= D_{\textit{cable}}\left(\frac{\omega _{M}}{60}\right)\end{equation}

Here in Eq. (13), $\omega _{M}$ denotes the angular velocity of the motor in revolutions per minute (rpm).

The formula for calculating the torque required to raise the load of a lead screw nut (given in Chapter 8 of [Reference Budynas and Nisbett74]) was modified to include the gearing transmission efficiency, representing the relationship between motor dynamics and slider dynamics of the actuator, as follows:

(14) \begin{equation}\tau _{M}= \frac{F_{S}d_{m} }{2}\left(\frac{L_{S}+\pi fd_{m}\, sec\alpha _{l}}{\pi d_{m}-fL_{S}\, sec\alpha _{l}}\right)\frac{1}{e_{G}}\end{equation}

Here in Eq. (14), $\tau _{M}$ is the motor torque, $F_{S}$ is the slider force, $d_{m}$ is the mean thread diameter, $L_{S}$ is the lead of the slider (see Eq. (11)), $f$ is the screw friction coefficient, $\alpha _{l}$ is the thread geometry parameter, and $e_{G}$ is the spur gear efficiency (typically 95–98%). Pulley friction and mass are neglected due to the lightweight design and bearing support. The contribution of the thrust collar bearing friction is also neglected for simplicity, as it is small compared to the screw-and-nut thread friction in the actuator under consideration.

The tension in the cable can be determined from Eq. (15) as follows:

(15) \begin{equation}F_{\textit{cable}}=\frac{F_{S} }{2n_{B}}\end{equation}

where $n_{B}$ is the number of movable pulleys for the cable stroke amplification mechanism (see Figure A1).

This actuator model can be used to guide stroke sizing, gear ratio selection, and motor choice for the underactuated mechanism. The cable displacement relationships (Eqs. (9)–(13)) can be employed to determine the slider stroke required to achieve the desired cable displacement for finger flexion. The torque/tension model (Eqs. (14)–(15)) can be used to estimate the motor torque needed to generate the required cable tension, or conversely, to determine cable tension for a given motor torque. The model can also help verify that the designed actuator provides sufficient displacement and force capability to support the intended tasks.

2.4. Intention-based control system

Given that the intended users of the robotic glove are individuals with weak hands and mild-to-moderate stroke impairment, the affected individuals may be able to move their fingers partially but lack the strength to grasp objects effectively. As such, the controller input commands should be designed to be as simple as possible to accommodate this user group. We implemented a sensor-based force assistance controller, enabling dynamic control of the grasping strength in response to the user’s intent, as detailed in the schematic provided in Figure 7.

Figure 7.

The intention-based control system of the SRIG-Exo.

The proposed intention identification method relies on the signals from two types of sensors, utilizing the hybrid sensing technique. The first are bending sensors, which are positioned at the top of the fingers, and the latter are FSRs fixed at the fingertips level (see Figure 2). These FSRs and bend sensors operate with a constant voltage of 3.3–5 V, and variations in current are monitored through an amplifier PCB board. This approach enables the recognition of human intentions by analyzing the wearer’s partial finger movements, fingertip touch, and voluntary grip control. It facilitates assisted grasping with the robotic glove. The microcontroller processes the filtered signal from the FSRs and bend sensors and controls the intelligent motor using a straightforward thresholding technique.

The estimated finger poses can be mathematically analyzed by considering the lead of the rod and the gearing ratio with the motor. Calculating the displacement of the flexor/extensor cable during operation becomes straightforward using Eq. (12) since the angular motion of the motor is known. Finally, the forward kinematics Eqs. (6) and (7) can determine the finger pose.

The control algorithm identifies the desired control input for triggering the motor based on the wearer’s estimated finger bending and fingertip force. The algorithm commands assistance force only when the estimated finger bending and fingertip force exceed the predetermined threshold. A study by [Reference Bjorksten and Jonsson75] indicates that the estimated force surpasses 5% of the maximum voluntary contraction (MVC) fingertip force, which the user can sustain for a minimum of 1 h without experiencing substantial fatigue. It is essential to understand that the exact degree of finger bending varies based on factors such as hand anatomy, flexibility, and joint health. However, when people make a fist, the fingers often achieve a significant degree of flexion. In this case, the maximum voluntary bending (MVB) can be in the range of 90° or greater for some individuals. Older adults and individuals with weak muscles have different MVC, MVB, and estimated force surpassing percent values. Therefore, we can modify Eq. (16) by considering suitable values for these variables based on the individual’s capabilities.

The gripping of the different objects required varying bending positions and grip forces. Therefore, the developed algorithm system includes the proportional force control condition where the force of at least one of the fingertips can increase or decrease the motor torque. The bending of fingers is auto-adjusted according to the shape of the grasped object due to the designed cable-loop system in the linear actuator, specifically for the ring and middle fingers. A simple open-loop controller can be used, considering the finger’s MVC fingertip force and MVB values. The device’s exerted fingertip assistance force for improving grasping can be set, for example, 0 to 30 N, following the proportional fingertip force value between 5% and 15% MVC. The intentional force of 5% and 15% of the MVC is selected as the threshold and saturation points, respectively [Reference Park, Heo, Kim and Na63]. A condition: when the estimated fingertip force of the user reaches or exceeds 15% of the MVC fingertip force, the controller would then increase the cable tension corresponding to 30 N, which is the maximum set value (MSV). The RoM for finger bending is determined by the MVB value, allowing fingers to bend from 0° and reach or exceed 90°. However, the shape of the object being grasped can influence the specific degree of finger bending. The relationship between an estimated fingertip force and the actuator control input duty cycle, as described in [Reference Park, Heo, Kim and Na63], is modified to incorporate finger bending for grasping control. The estimated intentional fingertip force $F_{I}$ and finger bending angle $\theta _{bent}$ are continuously monitored to interpret the user’s motion intention. The assistive motor command $u_{m,h}$ is generated proportionally to the normalized cable tension $C_{\textit{tension}-\textit{release}}$ , defined as:

(16) \begin{equation}C_{\textit{tension}-\textit{release}}=\begin{cases} \begin{array}{ll} -0.5, & \begin{array}{l} F_{I}\lt F_{thr} || \theta _{bent}\lt \theta _{thr}\\ \quad (\textit{release}) \end{array}\\ \dfrac{ F_{I}-F_{thr}}{0.1 \times F_{MVC}} , & \begin{array}{l} F_{thr}\leq F_{I}\lt F_{sat}\, \& \&\, \theta _{bent}\geq \theta _{thr}\\ \quad (\textit{proportional}\,\, \textit{assit}) \end{array}\\ 1, & \begin{array}{l} F_{I} \geq F_{sat}\, \& \&\, \theta _{bent}\geq \theta _{thr}\\ (\textit{saturation}\colon \mathit{\max }\,\, \textit{assist}) \end{array} \end{array} \end{cases}\end{equation}

The corresponding actuator command is expressed as:

(17) \begin{equation}{u_{m,h}}= C_{\textit{tension}-\textit{release}} \cdot\! \tau _{mot}\end{equation}

In Eq. (16), $F_{I}$ denotes the estimated intentional fingertip force, and $\theta _{bent}$ represents the measured finger bending angle of the wearer. The activation and saturation force thresholds are defined as $F_{thr} = 0.05F_{MVC}$ and $F_{sat} = 0.15F_{MVC}$ , respectively, where $F_{MVC}$ is the MVC fingertip force. The bending activation threshold is set as $\theta _{thr} = 0.1\theta _{MVB}$ , where $\theta _{MVB}$ denotes the MVB angle of the finger. The actuator torque corresponding to the maximum assistive force ( $F_{MSV}$ = 30 N) is represented by ^⋅ $\tau _{mot}$ in Eq. (17).

Eq. (16) captures both the tensioning and release behaviors within a unified formulation. When $F_{I}$ or $\theta _{bent}$ are below their activation thresholds, the controller enters release mode, relaxing the cable tension to allow voluntary finger extension. Once the bending and force exceed their thresholds, the controller transitions to assistive mode, generating proportional cable tension that scales linearly with $F_{I}$ until reaching the saturation limit $F_{sat}$ . This approach ensures intuitive and user-driven actuation, preventing unintended movements during inactivity while providing smooth, proportional assistance during active grasping. At saturation, the actuator delivers the maximum torque corresponding to $F_{MSV}$ .

Algorithm 1:

SRIG-Exo Intention-Based Cable Tension and Release Control