The specifications of the orthosis made by the spatial stiffness distribution design are determined as follows based on the results of previous studies and interviews with clinicians.

1) Portability: The orthosis including the actuators should weigh <500 g (Nycz et al., 2016; Ates et al., 2017; Lambelet et al., 2020) because it will be in constant use throughout the day. Thus, the number of actuators should be minimized.

The number of grasp types that the orthosis can assist with is limited because the underactuation of the orthosis is inevitable for portability. Because tripod grasp achieved by three fingers (i.e., the thumb, index finger, and middle finger) was similar with the grasping posture achieved by one of the postural synergies required for a tool use (Santello et al., 1988), it was considered that common objects can be grasped by the tripod grasp. Thus, the tripod grasp is selected for emulation using a single motor.

The orthosis comprises a passive elastic structure (including a beam) fabricated from thermoplastic polyurethane (TPU; Hyvision System, Inc. Seongnam, South Korea), an intention detection module, and a control module (Figure 2A). The orthosis has a total weight of 454 g, and it compactly fits on the affected hand and forearm. The passive elastic structure is made using a 3D printer (Cubicon Single, Hyvision System, Inc. Seongnam, South Korea) and reduces the number of actuators required by realizing the passive extension of fingers. The passive elastic structure allows independent donning/doffing of the orthosis and avoids joint compression during extension of spastic finger joints. The beam of the passive elastic structure where the fingers make contact is designed to optimize the stiffness for ensuring a sufficient grip aperture in the pre-grasping phase and minimizing the required antagonistic assistive force (T) for grasping. The passive elastic structure excluding the beam is designed as per the hand geometry of each user for comfort. Because of finger contracture in the affected hand, a 3D scanner (Sense2, 3D Systems Inc. Rock Hill, SC, United States) is used to scan the unaffected hand when the user grasps an 80-mm-diameter cylinder. The affected hand geometry is generated by mirroring the 3D scanning results assuming symmetry of the hands (Kulaksiz and Gözil, 2002). The thumb module is designed based on the affected hand geometry using the software Geomagic Freeform (3D Systems, Inc. Rock Hill, SC, United States) so that the palmar aspect of the thumb is rigidly fixed at the abducted posture as the user grasps an 80-mm-diameter cylinder.

The control module comprises a small motor (10 ∅ , 46.8 mm length, 64:1, 315172, MAXON Inc. Sachseln, Switzerland), cable (Power Pro, Shimano Inc. Caringbah, Australia), motor driver (446023, MAXON Inc. Sachseln, Switzerland), Arduino Micro, and battery (800 mAh-11.1v, PEAKPOWER Engineering Inc. Lakewood, United States). The cable contraction for active flexion of the beam is driven by a twisted string actuation (TSA) mechanism (Palli et al., 2013). The contraction length of the cable is adjusted by controlling the rotation angle ( φ ) of the motor. A contraction force (assistive force) is applied at routing structures of the beam. The battery continuously lasts for 170 min, and 2,260 cycles of active flexion were continuously achieved during that period. It was also confirmed that the orthosis could withstand ∼40,000 cycles of active flexion without break. The intention detection module comprises two force-sensing resistors (FSRs) (FSR01CE, OHMITE Manufacturing Co., Warrenville, IL, United States) that are respectively positioned on the beam and thumb module. In particular, the FSR on the beam (FSR_f) can sense the flexion force of the affected hand, and the FSR on the thumb module (FSR_g) can measure how much grip strength is applied to a grasped object.

Because stroke survivors cannot voluntarily extend their fingers because of extensor muscle weakness, the grasping and releasing intentions are detected solely using the FSR_f that can measure the flexion force. The grasping and releasing intentions are detected when the FSR_f detects a force that exceeds the pre-set values Threshold _grasp and Threshold _release , respectively (Figure 2B). To calculate Threshold _grasp and Threshold _release , the voluntary force of the user is first calculated during voluntary grasping in a setup procedure. The user applies the maximal flexion force for a grasping task while wearing the orthosis. The FSR_f measures the peak value for five attempts, and the values are then recorded. The baseline force, which corresponds to the force at rest, is measured before the voluntary grasping. The minimum difference between the peak and baseline forces is defined as the voluntary force. Threshold _grasp and Threshold _release were defined as the sum of the calculated voluntary force and baseline force. These values are updated at the end of every grasping and releasing task because the baseline force varies with spastic contractions over time. At the end of a grasping and releasing task, a waiting period of 2–4 s is implemented until the spastic response settles down, and the force measured after the waiting period is set as the baseline force for the next tasks. The waiting period is determined as per the time required for the force to settle down to 110% of the baseline force that is measured before the voluntary grasping during the setup procedure.

The grasping and releasing tasks are initiated when the user applies a flexion force (F _f ) that exceeds the pre-set values (Threshold _grasp , Threshold _release ). In the initial state, the fingers are passively extended (open-hand posture) at the initial angle of the motor, which is set when the cable is completely untwisted. Active flexion of the beam is initiated once the user applies a force that exceeds Threshold _grasp . The active flexion is driven by rotating the motor to twist the cable under a nominal step input current. The motor rotates until the angle limit, which is set to when the end of the beam makes contact with the thumb module. Once the rotation angle reaches the angle limit, a proportional–integral–derivative (PID) controller maintains the angle limit for safety. When the grip strength (F _g ) reaches 15 N (Yurkewich et al., 2019) before the motor rotates to the angle limit, the PID controller holds the rotation angle to maintain the holding angle that grasps objects at a 15-N grip strength. The minimally required grip strength of 15 N for grasping (Yurkewich et al., 2019) is used to increase the life cycle of the cable, which can break because of abrasion during twisting. To release an object, the user should flex the fingers to apply a force over Threshold _release . Passive extension is achieved by reversely rotating the motor under a nominal input current, which untwists the cable. Once the rotation angle reaches the initial angle, the PID controller holds the initial angle. For false activation (i.e., unintended grasping and releasing) caused by physical perturbation, the user must reapply a force to return their hand to the desired posture.

The beam geometry was designed to satisfy two conditions: it should passively extend the fingers in the pre-grasping phase, and it must be bendable to allow finger flexion under the action of the assistive force in the grasping phase. To achieve these conditions, the geometric constraints of the beam were determined based on the kinematics of the finger movement. The kinematics varies depending on the anthropometric dimensions of an individual hand. The positions of hand landmarks were used as a reference to measure the anthropometric dimensions and determine the geometric constraints on the beam design. The finger joints and following skin creases were selected as hand landmarks (Figure 3A): the palmar digital crease (PDC) and proximal palmar crease (PPC). Note that the PPC is where the proximal phalanx is folded toward the palm to achieve 90° metacarpophalangeal (MCP) flexion. To satisfy the first condition, the beam was designed to cover the proximal and middle phalanges of index and middle fingers (Figure 3B). This design allows the MCP and proximal interphalangeal (PIP) joints to be passively extended while sensory feedback is obtained via the fingertips.

To meet the second condition, the stiffness of the beam was designed as follows. Active flexion requires that the beam deflection along the MCP and PIP joints be significantly larger than in other regions; thus, stiffness close to the MCP and PIP joints should be less than that in other regions. The beam comprises two soft regions (Soft ₁ and Soft ₂ ) and two hard regions (Hard ₁ and Hard ₂ ) (Figure 3B). Because the beam is at the palmar aspect of the fingers, the proximal edge of soft regions was constrained to be more proximal than the corresponding joint by at least the radius of the joint to allow finger flexion (Figure 3C). The proximal edge of Soft ₁ was assigned to the PPC, which is more proximal than the MCP joint by the radius of the MCP joint (r _M ) for all users. The position of Soft ₂ was determined by considering the slip occurrence between the beam and fingers during MCP flexion. The beam slips with respect to the fingers (Figure 3D) during MCP flexion. Thus, the proximal edge of Soft ₂ was set to be more proximal than the PIP joint by a length that is greater than the sum (L _const2 ) of the slip distance (L _slip ) and radius of the PIP joint (r _p ). Because 35° of MCP flexion has been reported to occur during tripod grasping (Park et al., 2014), L _const2 that occurs during MCP flexion was used as a geometric constraint for Soft ₂ , and it can be calculated as follows: L c o n s t 2 = L s l i p + r p ≈ A + r M ⁡ tan 35 ∘ 2 − A − r M ⁡ tan 35 ∘ 2 + r p = 2 r M ⁡ tan 35 ∘ 2 + r p (1)

A (Figure 3D) is the length between the distal interphalangeal (DIP) and MCP joints at full extension. r _M and r _P are the radii of the MCP and PIP joints, respectively. The proximal edge of Soft ₂ was set to the PDC considered to be more proximal than the PIP joint by length greater than the L _const2 (An et al., 1983; Buryanov and Kotiuk, 2010). Thus, the determined beam geometry comprises two soft regions (Soft ₁ and Soft ₂ ) and two hard regions (Hard ₁ and Hard ₂ ) at predefined locations to allow bidirectional finger movement.

The stiffness can be adjusted by changing the thickness along the beam (Figure 4). The stiffness of Soft ₁ and Soft ₂ is determined by design variables ( λ 1 , λ 2 , h 1 , h 2 ), where λ 1 , λ 2 and h 1 , h 2 are the longitudinal length and thickness of the soft regions, respectively, and are determined via stiffness optimization to achieve sufficient grip aperture in the pre-grasping phase and minimal assistive force in the grasping phase. The other variables (L ₁ , L ₂ , L ₃ , W, and H) are determined as per the measured anthropometric dimensions of an individual hand. In particular, L ₁ , L ₂ , and L ₃ are the lengths between the PPC and PDC, PDC and PIP, and PIP and DIP, respectively. W is the width of the index and middle fingers. H is the thickness of the hard regions. To ensure high stiffness in the hard regions and the applicability of the Euler–Bernoulli theory, H is set so that the aspect ratio of the entire beam slightly exceeds 10. As geometric constraints, the distal edge of Soft ₁ should be more proximal than PDC ( λ 1 < L ₁ ), and the distal edge of Soft ₂ should be more proximal than PIP joint ( λ 2 < L ₂ ). The routing structures are positioned along the PPC, PDC, and PIP joint to deflect each of Soft ₁ and Soft ₂ under the assistive force.

There exists a tradeoff between an achievable grip aperture and grip strength because an increase in the spatial stiffness leads to an increase in the grip aperture and required assistive force for grasping. The stiffness optimization enables the orthosis to achieve a target grip aperture in the pre-grasping phase while minimizing the required assistive force in the grasping phase. It would enable the orthosis to grasp common objects with increased grip strength by a given small-sized motor. Because stroke survivors have different joint characteristics (Kim et al., 2019) such as degree of spasticity, the stiffness should be optimized as per the measurements of individual hand parameters. Otherwise, the spatial stiffness distribution that is equally designed for all stroke survivors may result in a limited grip aperture for users with a severe degree of spasticity and or require an unnecessarily large amount of assistive force for users with flaccid hands. The stiffness optimization process has two steps: obtaining stiffness solutions that can achieve the target grip aperture and identifying the optimal solution that requires a minimal assistive force.

The beam deflection was less than the target deflection, thereby yielding a grip aperture larger than the target grip aperture of 80 mm. The distal end of the beam deflected by 12.17 ± 10.00 mm immediately after donning, generating the grip aperture of 94.26 ± 10.73 mm. This measured deflection was less than the target deflection of 40.08 ± 7.37 mm primarily owing to viscosity of the TPU. Because of creep occurred after donning and plastic deformation by active flexion, the beam deflection increased by 9.38 ± 5.48 mm after four repetitions of active flexion, which corresponded to an average decrease of 6.74 mm for the grip aperture. Non-etheless, the measured beam deflection of 21.54 ± 9.36 mm still did not equal to the target deflection of 40.08 ± 7.37 mm, yielding a grip aperture of 87.52 ± 6.40 mm. The error for the beam deflection would be because of the safety factor considered in designing the stiffness of the beam. The beam stiffness was set to yield the target grip aperture against the maximal joint resistive force; however, fingers would apply force less than the maximal joint resistive force on the beam. This would primarily make the measured deflection be less than the target deflection, which led to increase in the grip aperture.

The orthosis effectively assisted the finger joints for all participants (Figures 8A, B). All participants demonstrated a limited voluntary ROM of 20.7° on an average because of spastic finger joints. They were only able to flex their fingers from a neutral posture to a closed-hand posture. Although the orthosis-enabled finger flexion was limited by the thumb module, the orthosis increased the joint ROM by 31.7° ± 26.6°. Note that the finger flexion was not restricted by the thumb when the voluntary ROM was measured. The ROMs of the MCP and PIP joints were increased by 9.0° ± 12.1° and 22.8° ± 18.2°, respectively. Moreover, the orthosis provided passive assistance to yield a maximal assisted extension angle of 33.2° ± 12.0°; the fingers were significantly more extended compared to the maximal voluntary extension (maximal unassisted extension angle of 118.2° ± 25.8°).

The finger joint angles increase in accordance with the inter-joint coordination pattern obtained by the individual hand–beam model. The “Measured joint angles” in Figure 8C was obtained based on the measurement results during active flexion. The “Predicted joint angle path” in Figure 8C was obtained by increasing joint angles from the maximal assisted extension posture according to the inter-joint coordination pattern. It was confirmed that the joint angles increase in accordance with the inter-joint coordination pattern. The error between the joint angles at maximal flexed posture and predicted joint angles were 4.9° ± 2.9° which were respectively 4.3° ± 2.6° in the MCP joint and 2.2° ± 1.4° in the PIP joint. The joint resistive force was not considered in the hand-beam model to obtain the inter-joint coordination pattern, and it would result in the error which was only 9.3% of assisted joint ROM on average. The inter-joint coordination of the MCP and PIP joints during assistance can be controlled by spatial stiffness distribution design.

All participants could grasp each object with the orthosis. Furthermore, they were able to establish contact between their fingertips and large-size objects (i.e., the glass cup and baseball). However, the large slip between the fingers and beam prevented the fingertips from contacting the small-size objects (i.e., banana, stapler, golf ball, and battery). The maximum grip strength was measured as 26.27 ± 3.90 N, and the orthosis showed a high grip strength-to-weight ratio (Table 2).

The results of the CAHAI-9 tasks (Table 3) demonstrated that all participants had difficulty without the orthosis owing to contracture and low grip strength. The score of one or two was assigned for all tasks because participants do not voluntarily show any manipulation of the affected hand. With orthosis, all participants were able to complete the tasks except for tasks 2, 6, and 9 with only arm support and cueing (Figure 9). The orthosis increased the grip aperture and grip strength of participants to improve their performance of most tasks (score increase: 14.40 ± 1.78). To precisely locate targeted objects along the beam for grasping, the unaffected hand was used for positioning because the orthosis cannot assist with in-hand and upper-limb manipulations. Non-etheless, with only the passive assistance of the arm, the orthosis enabled the participants to independently accomplish bimanual tasks by stably holding targeted objects with the affected hand. Specifically, for task 1, they could open a lid of the jar using the unaffected hand because the affected hand could hold a jar. For task 3, they could draw a line by grasping a pen with the affected hand while the unaffected hand is fixing the ruler. For task 4, participants held a glass cup using the affected hand while pouring water with the unaffected hand. For task 5, one side of a washcloth was held by the affected hand, and the unaffected hand wrung out a wash cloth. For task 7, one side of a towel was held by the affected hand, and the unaffected hand dried the back with a towel. Thus, stroke survivors were assigned score of four for these tasks because they can accomplish 100% of tasks with arm support. For task 8, although it was possible to hold a toothpaste using the affected hand to make the unaffected hand unscrew a lid, squeezing the toothpaste using only the affected hand was impossible with the control algorithm used for the orthosis. Thus, a score of three was assigned for task eight by considering that 50% of the task is accomplished. The orthosis could not provide adequate assistance in tasks 6 and 9 because the tripod grasp type was insufficient to manipulate the object. Task two was not completed because the participants were unable to prevent their ring and little fingers from pushing non-targeted buttons.

The participants answered that the device is sufficiently lightweight (score: 4.3 ± 0.7) and comfortable (score: 4.2 ± 0.5). Moreover, they were satisfied with the assistance of the orthosis (score: 4.3 ± 0.48).