## 4 Discussion
We reviewed the mobilization protocols from previous related studies and our force 80 N and frequency 5 Hz parameters of the joint mobilization were within regular range of manual mobilization [37; 38]. [PERSON] et al. measured the force of the experienced therapist when they were performing posterior glenohumeral mobilizations on the participants and they found that the range of the manual force was between 41.7 and 209.4 N [37]. [PERSON] et al. measured the force of the experienced therapist when they were performing inferior glenohumeral mobilizations on the participants and they found that the range of the manual force was between 37.4 N and 140 N [38]. The force output of the joint mobilization apparatus when performing shoulder posterior and inferior glide joint mobilization was in line with the force output range of the experienced therapist. Our study showed that the joint mobilization apparatus with shoulder posterior and inferior glide via 80 N force was able to help patients with FS to improve shoulder joint ROM. The oscillation frequency of the performing manual joint mobilization presented and recommended in the previous research is 1-3 per second, i.e., 1-3 Hz [15; 29; 31]. However, some studies have shown that a higher oscillation frequency of joint mobilization can produce greater neurophysiological mechanism stimulation to the human body [39, 40]. The oscillation frequency of the joint mobilization apparatus in this study stably maintained 5 Hz for 30 min, which was slightly higher than the manual mobilization. Our study showed that 80 N force and 5 Hz oscillation frequency had efficacy in reducing shoulder pain and improving shoulder ROM in patients with FS. Although manual mobilization was beneficial to patients with FS, the execution of these manual mobilization techniques required a professional therapist, which consumed a lot of professional manpower. In our study, the joint mobilization apparatus was operated easily by the very small amount of professional manpower for 30 min in patients with FS and further improve shoulder ROM and pain than regular physical therapy. In a clinical application, the device can not only help patients with FS to relieve symptoms, but also partially solve the problem of shortage of professional manpower of a manual physical therapist. Some limitations also existed in this research. We needed a controlled study with two groups of patients who had similar conditions to understand the preliminary efficacy of the apparatus. Therefore, we distributed all patients to three strata by shoulder flexion ROMs baseline assessment data, and then performed a stratified and randomized controlled study to make the two groups of patients as similar as possible in the beginning of this research. Although a stratified randomization method was used to divide all patients with FS into a control group and an experimental group in this study, some allocation bias within the same stratified ROM may still occur. The joint mobilization apparatus with certain force, certain frequency, and certain duration applied in the current study is the first reported and cannot be found in previous research, so no relevant information of the mobilization apparatus can be compared. The best efficacy, best force, best frequency, or best duration of the joint mobilization apparatus is still unclear and is still in the phase of exploration. This experiment cannot be executed in a blind study because the researcher and the patients must know whether the apparatus is working when receiving the mechanical mobilization treatment. Regarding the other limitation, the control group received regular physical therapy only and no placebo treatment was designed in the current study. Therefore, we have no idea about placebo effects of the joint mobilization apparatus. Because our inclusion criteria are patients with FS who are older than 50 years old, the average ages of the control group and the experimental group are 59.2 \(\pm\) 1.7 and 58.8 \(\pm\) 1.3, respectively.