# Experimental Testing of Passive Linear TMD for Postural Tremor Attenuation
## 4 Discussion  
The addition of two and three TMDs did not show a remarkable improvement in the system response compared with the response obtained with one TMD in Figure 7, in contrast to what is expected by [23]. This can be explained by the low modal damping ratios (in comparison with that obtained in the numerical study) provided by the manufactured TMDs (of stainless beams), which are not high enough to lessen the amplitude of critical peaks. Despite this, the TMDs improved the response of the system and cause a minimum reduction of 88%; however, a considerable value of 5.7% minimum mass ratio was used for the testing. To find a compromise between the patient's comfort due to the addition of masses to the hand and the reduction in the amplitude of the tremor caused by these TMDs, a study with a lower mass ratio can be performed while achieving a satisfying reduction. The optimal damping ratios determined numerically are not reached in this study due to a low damping ratio provided by the strain rate of the stainless steel beam material, air damping provided by the beam and the screw, and frictional damping provided by the clamped end and the surface of contact with the attached screw, without the addition of an external damper. Due to this, the optimization of TMDs parameters obtained from the numerical study was not very useful for reflecting the best position of the TMD in the experimental study. Since the manufactured TMDs have low modal damping ratios, tuning these absorbers may be a good choice to obtain a better reduction for the system with three TMDs (Figure 7). The operating frequency of the three TMDs is chosen to be close to the critical frequency (6.64 Hz), and within the best frequency range (6.44-6.66 Hz) of the one TMD deduced from Figure 6. The three TMDs placed at positions '0', '1', and '2' (Figure 4a) are adjusted to 6.61 Hz, 6.61 Hz, and 6.52 Hz, respectively, and referred to as Set#2. The responses of the experimental arm (without IMU) due to the addition of the three TMDs of Set#1 (Figure 7) and Set#2 are shown in Figure 10 and compared with that obtained for one TMD corresponding to the numerical study (Figure 7). The three TMDs of Set#2 improved the response at the critical frequency in comparison with the other responses. It causes also a slight amplification in comparison with Set#1 at the frequency of 9.57 Hz, which is a frequency higher than the frequency of the critical peak, thus the 9.57 Hz will not lead to a critical effect on the signal of the system. However, a slightly higher level of damping is still interesting to further reduce the amplitudes at all peaks within the range of PT. Figure 9: PSD obtained from IMU measurements for the system with three TMDs (Set#1). Encouraging results are obtained in this study, which motivates the development in the design of the passive type of tremor controllers, to be competitive to the work found in the literature. The 120 g controller used by [PERSON] et al. [6] represents a PID controller which provides a 20-60% reduction in the displacement amplitude, although a higher level of reduction could be expected by an active type of controller. A TMD of 200-400 g (representing 18.3-36.7% mass ratio) was used by [PERSON] et al. [7] and adjusted by the water level entering or leaving the piezoelectric micro-pump. It provided a 57% reduction in the amplitude of acceleration. The system was loaded with a high mass ratio that did not cause a high reduction. An efficient 280 g TMD used by [PERSON] et al. [8] causes an 83% reduction in the pronation-supination amplitude of a system modeled as an inertial rod excited at resonance. An interesting design of the bracelet was provided in the study of [PERSON] et al. [8] which can be comfortable and easily wearable by the patient. The 530 g passive TMDs (representing 31.4% mass ratio) manufactured by [PERSON] and [PERSON] [9] cause a good reduction of 70-80% in the tremor amplitude.