Exercise methods of human therapists in CPM exercise were analyzed in prior to the design of the device. The exercise sessions were observed at a university hospital. The session usually took about 45 min, including 15 min of hot pack treatment prior to the session.

Exercise principles of human therapists could be classified into three stages: sensing, actuation, and decision. First, sensing stages are conducted by putting hands on the patients. As can be seen from (Figure 1), human therapists put their hands on two spots of the patient, one on the trapezius muscle and the other on the arm being elevated. The hand on the trapezium detects whether the patient has proper scapulohumeral rhythm (25), while the hand on the arm checks the stiffness of the shoulder. Second, the actuation stage is mainly carried out by the hand on the moving arm with rotating the shoulder joint. Human therapists have the ability to move their hands freely to rotate shoulder joints in three main directions: forward flexion (FF), abduction (Abd), and external rotation (ER). The hand on the trapezium acts as preventing excessive movements of the scapula and maintaining the scapulohumeral rhythm. Third, in the decision stage, the therapist decides whether to move the joint further or not by integrating whole senses acquired from the patient.

Based on the human-therapist analysis, requirements for developing a robotic CPM device could be derived from both a hardware and software point of view. For the hardware, the device should provide passive motion in three different motions with the full ROM. For the software, the device should detect the end-range of the shoulder joint in each direction and determine when to release the passive motion.

The device (Figure 2) is an aluminum-frame-based, cable-driven system with a handle attached to a linear guide on which the arm of the patient is held using a wrist brace (Formfit®, Össur, Reykjavik, Iceland). The geared motor (9DCW24, DKM Motors Co. Ltd., Incheon, Korea) is mounted at the bottom of the device and moves the handle via cable-pulley system. The position of the handle is measured using a rotary encoder attached to the device. The rotary encoder and the motor were separated in order to measure the movement of the handle when the motor is not moving, which enabled easier position calibration.

When using the device, patients sit on a chair where a shoulder pad is attached. The pad covers the shoulder being lifted and prevents excessive elevation of the scapula, thereby controlling scapular compensation during passive shoulder movements. By adjusting the sitting position, patients can perform three degrees of freedom exercises. When conducting external rotation exercise (Figure 2e), an additional module is added to the device in order to fix the elbow of the patient and make a linear up-and-down motion of the handle into the rotating motion of the shoulder joint. The device operates without being constrained by the alignment of the elbow and shoulder joints. Additionally, the device does not require customization for joint alignment, even for patients of varying heights.

The device utilizes two load cells (333FDX, Ktoyo Co. Ltd., Gyeonggi-do, South Korea) to mimic the sensing part of human therapists. The load cell embedded in the handle Figure 2 measures the vertical force during the CPM exercise and is further used for calculating torque applied to the shoulder joint. The other load cell attached to the shoulder pad measures the force exerted by the scapula and could be used to monitor the muscle synergy during shoulder movements.

The device is operated using a controller with a Teensy 3.2 board inside. Load cell data is accumulated using an Arduino board and transmitted to the controller through serial communication. Overall operation is monitored with a computer program developed with Processing, on which control parameters including force threshold, motor speed, and number of repetitions can be adjusted.

During the rehabilitation exercises with the device, IMU data of the patients were collected for the reference data of the shoulder joint angle. We attached 5 IMU sensors (MTw Awinda, Xsens Inc., Culver City, USA) onto the limbs of the patient and 1 IMU sensor on the motor pulley to synchronize the movement of the human joint with the motor actuation.

To calculate the shoulder angle with the IMU data, the patient takes the initial calibration posture (standing tall with a straight back and arms relaxed at the sides) with one IMU attached on the back, two IMUs on the upper arm, and two IMUs on the lower arm. The directional vector of each segment is estimated using the rotation matrix. Shoulder angle during flexion and abduction exercise is calculated based on the rotation angle of the upper arm vector from the chest vector, while the rotation angle of the lower arm vector from the chest vector is used for the external rotation exercise.

Torque applied to the shoulder joint is calculated using the shoulder angle acquired from the IMU data, force measured by the device, statistically estimated anthropometric values, and additional distance measured on-site. In cases of flexion and abduction, the estimated torque is as follows:τ=Floadcell∗l^−meq∗g∗r^ (1) where l¯ is the horizontal distance of the shoulder joint from the device, meq is the equivalent mass of the whole arm, r¯ is the horizontal distance of meq from the shoulder joint, and g is the gravitational acceleration constant.

Torque during the external rotation movement is estimated as follows: As the elbow support module is applied for the external rotation movement, elements used in the formula were modified. m^eq is the equivalent mass of only the lower arm and hand; r^ is the horizontal distance of m^eq; l is the distance from the elbow to the strap; θ is the angle between the strap of the wrist brace and the device; and ϕ is the angle of the lower arm from the horizontal axis calculated from the IMU data.τ=Floadcellcos⁡(θ)∗l∗cos⁡(θ−ϕ)−m^eq∗g∗r^ (2) The torque Equations 1, 2 used in the calculation are illustrated in the free body diagram Figure 3.

At the first visit, patient demographics and baseline clinical data were collected, including age, height, weight, ROM in flexion, abduction, and external rotation, as well as VAS and SPADI scores. During each robotic exercise session in the intervention group, biomechanical data were acquired via IMU sensors and load cells embedded in the robotic device.

ROM was measured using IMU sensors attached to the upper and lower arms, and shoulder angles were derived from relative orientation changes. For flexion and external rotation, limited shoulder mobility due to device-chair distance was mitigated by placing a cushion on the participant’s lap to allow slight torso inclination and expand rotational freedom. Among the 20 repetitions performed per session, the last five were selected for analysis to minimize adaptation effects.

To quantify passive stiffness, torque-angle data were obtained by synchronizing load cell and IMU measurements. Stiffness was calculated by fitting a first-order linear regression to the torque-RoM curve between 50% and 100% of the motion range in each direction (26, 27). The resulting stiffness indices served as objective indicators of joint resistance and rehabilitation progress Figure 4.

12 frozen shoulder patients from the Seoul National University Hospital were recruited Table 1. Patients diagnosed with adhesive capsulitis of shoulder or suffering from shoulder pain with decreased ROM for more than 3 months were invited. Exclusion criteria were those who has rotator cuff tear, glenohumeral osteoarthritis, systematic rheumatic disease, neurological diseases including strokes which affect shoulder ROM or those who had any kind of surgery on the affected side shoulder. All subjects provided informed consent to a protocol approved by Seoul National University Hospital Institutional Review Board (IRB No. 2206-161-1335).

This study was designed as an exploratory pilot trial to evaluate the feasibility, safety, and preliminary efficacy of the robotic CPM device in patients with frozen shoulder. A 3-armed clinical trial was conducted in which participants were randomly allocated to (1) hot pack treatment: negative control, (2) exercise with human therapists: active control, and (3) exercise with the robotic device: intervention group. The primary outcomes were range of motion (ROM) in flexion, abduction, and external rotation, as well as biomechanical measures such as passive resistive torque and joint stiffness. Secondary outcomes included pain and functionality of the affected shoulder, assessed using the Visual Analogue Scale (VAS) and the Shoulder Pain and Disability Index (SPADI).

The hypothesis of this study was that the intervention group would demonstrate therapeutic effects comparable to the active control group and superior to the negative control group. After allocating each patient into one of the three arms, baseline measurements were completed, followed by a 6-week intervention (Figure 5a). The second and third assessments were conducted immediately and six weeks after the intervention. Variations in outcome measures were used for quantitative comparisons between the three groups.

This study was not double-blinded. Due to the nature of the interventions, participants were aware of their assigned groups, and outcome assessments were performed by the treating therapists and researchers involved in device operation. While assessor blinding was not feasible, objective measures (e.g., ROM and torque collected via sensors and IMUs) were prioritized to minimize subjective bias. This limitation was considered in the trial design.

Participants allocated in negative control group received hot pack treatment for 20 min once a week. Negative control group was designed based on the current therapeutic protocol conducted by general university hospitals. Active control group participants received both the hot pack treatment followed by PROM exercise by therapists for 20 min a week. The exercise was comprised of flexion, abduction, and external rotation, 20 times each.

Participants in the intervention group received the hot pack treatment and robotic exercise therapy twice a week, which reflects easier accessibility to the robotic device compared with human therapists. For the patients in the intervention group, the overview of the measurement protocol is shown in (Figure 5b). The robotic device was positioned on a square grid sheet so that the sitting position of a participant is fixed for every visit. To minimize scapular compensation during shoulder movements, patients were seated with a shoulder pad designed to restrict excessive scapular elevation and promote proper scapulohumeral rhythm. After fixing the participant’s wrist on the wrist brace of the device, the handle was elevated with the controller until the patient felt high enough stretching strength while measuring the corresponding force with the robotic device so that the force threshold was set. After setting the force threshold, the handle was lowered to the initial position, where shoulder angles were set to 60∘,45∘, and 100∘ for flexion, abduction, and external rotation direction. During the exercise, motor speed was fixed to manipulate the handle to move 0.15 m/s. While elevating the handle, once the force value on the handle exceeded the force threshold, the motor stopped for 10 s to ensure enough time for stress relaxation and then lowered to the initial position.

On the first visit, the patients in all groups were handed out with self-exercise manuals and encouraged to follow the guidelines but were not checked from then on.

Statistical analyses were conducted to evaluate both intra-group and inter-group rehabilitation effects. The primary outcomes were range of motion (ROM) in flexion, abduction, and external rotation, as well as biomechanical measures such as passive resistive torque and joint stiffness. Secondary outcomes included the Shoulder Pain and Disability Index (SPADI) and Visual Analog Scale (VAS) scores for pain.

For within-group analysis in the intervention group, a two-sample t-test (MATLAB R2023a, ttest2 function; MathWorks Inc., Natick, MA) was used to compare passive resistive torque between the first and last sessions.

To compare treatment effects across groups, a linear mixed model was applied to account for repeated measures at three time points: baseline, interim, and post-intervention. Fixed effects were defined as group, time, and baseline values; the random effect was participant identity. An interaction term between group and time was initially included but excluded from the final model due to lack of significance. All mixed model analyses were performed using SAS software (version 9.4; SAS Institute Inc., Cary, NC).

The participants were divided into three groups: negative control (3 participants), active control (4 participants), and the intervention group (5 participants), with average ages of 58.0, 61.3 and 59.6 years respectively Table 1. There were no statistically significant differences between the groups in terms of age, weight, duration of symptoms, or other relevant indicators. Similarly, the initial assessment showed no significant differences between the three groups.

When comparing the ROM evaluation results across the three groups Table 2, a gradual increase in all directions of ROM was observed as the treatment sessions progressed, except for abduction in the thermo-therapy group. However, there were differences in the degree of improvement between the groups, with the most notable difference seen in external rotation Figure 6. Compared to the negative control group, the intervention group showed a faster recovery in external rotation ROM (p-value = 0.022). The difference between the negative control and the intervention group became more pronounced during the interim assessment. Although the external rotation ROM in the negative control group showed some recovery during the follow-up assessment, the extent of improvement was still smaller compared to the intervention group. The SPADI test also showed a gradual decrease in pain levels, although statistical significance was not achieved (p-value = 0.642).

When examining the average ROM in each exercise direction of participants in the intervention group, a gradual increase in ROM was observed with each session Figure 7. Compared to the first session, by the 12th session, the ROM increased by an average of 14.52∘ in the flexion, 16.72∘ in the abduction, and 14.19∘ in the external rotation. Since the ROM is determined by the force threshold set by the participant for the robot, it can be inferred that the participant’s stretch tolerance increased with each session.

Passive stiffness values in the intervention group significantly decreased from the first visit to the 12th (last) visit, particularly in abduction and external rotation Figure 8. Specifically, passive stiffness in abduction decreased from 0.17 to 0.10 (p-value = 0.010), and in external rotation, from 1.29 to 0.46 (p-value < 0.001). In flexion, passive stiffness showed a decrease from 0.27 to 0.21; however, this change was not statistically significant (p-value = 0.590).