## 4 Discussion
### From a Single-Linked Model to Multi-Segmental Model  
Quiet standing tends to approximate a single-link inverted pendulum. Recent studies have pointed out that hip joints play an important role in maintaining balance even in quiet standing [20; 33; 34; 35; 36], as well as in dynamic tasks, which show more ankle-hip joints characteristics [36] and which we can consider as a multi-segmental model. In this paper, the sigmoid model has shown that there was an upper and lower distribution of CCF coefficient data of COM-COP and ankle-hip, which revealed that there was a sudden transition from low to high frequency and vice versa at a certain frequency. These pattern changes are consistent with the results from [PERSON] et al. [24]. The joint degree of freedom was regulated by a small amplitude as the motion from the moving platform was at a low frequency. However, as the motion was increased, the joint degree of freedom motion showed a large amplitude and forced the postural strategy to re-organize and dissipate the large force; i.e., the head fixed pattern and transition from ankle to hip strategy and vice versa. The means of transition frequency for COM-COP and ankle-hip transitions were 0.44 Hz and 0.42 Hz for increasing frequency and 0.55 Hz and 0.56 Hz for decreasing frequency, respectively. This finding was parallel with [PERSON] and [PERSON], who obtained a coordination change around of0.4 Hz-0.6 Hz for the COM-COP transition frequency [11]. The transitions frequencies in both increasing and decreasing frequency were almost in the same frequency for both COM-COP and ankle-hip. Even though the transition occurred almost at the same frequency, a slightly difference was observed where the ankle-hip transition frequency was earlier than that of COM-COP. This finding was consistent with [PERSON] et al., who stated that the COM-COP coordination is relatively robust and on a slower time scale of change compared to the coordination of joint components and their individual motions [24]. As the perturbation applied originated from the lower extremities, the perturbation moved to the sole then regulated muscle activation, which increased joint stiffness and moment at the ankle joint. Then, as the physiological limit was reached, the hip movement was involved. Within this process, the COM and COP positions were also moved from the origin. The transition happened when the initial pattern was undergoing a state of instability. The differences of transition frequency were observed between increasing and decreasing frequency, where the mean transition frequency for increasing frequency condition occurred at the lower frequency than decreasing frequency condition. These different values for the transitions indicated that the coordination mode observed is dependent upon the direction of the changes in the control parameter (platform frequency) [37; 38]. These results exhibit a hysteresis phenomenon when the frequency transition value is varied at different conditions of perturbation frequency. Hysteresis in this study means that the tendency for the postural control systems itself to remain in the current behavior state as the control parameter moves through the transition region, provides different frequency transition values depending on the direction of the control parameter [39]. Furthermore, the coordination of the postural control strategy was more stable when moving from anti-phase to in-phase (decreasing frequency) compared to in-phase to anti-phase (increasing frequency) [11]. In decreasing frequency, the instabilities decreased as the frequency perturbation decreased, which resulted in the earlier transition frequency compared to increasing frequency. Therefore, the mean value of decreasing transition frequency occurred earlier than that of increasing transition frequency, which indicates the subjects easily coordinated the postural strategies during high frequency perturbation tasks. The differences and variability of the transition point frequency of COM-COP and ankle-hip among the subjects were also observed.