# Experimental Testing of Passive Linear TMD for Postural Tremor Attenuation
## 2 Materials and Methods  
### Experimental Arm  
A 77-year-old patient, suffering from ET, participated in this work. The patient performed a postural clinical task to study the PT of the hand. Measurements of the ECR tremor signals were conducted by the department of neurology at Pitie-Salpetriere Hospital (Paris), following appropriate informed consent. An experimental arm, excited by tremor signals measured for the patient, is used to study the ability of a passive TMD in reducing the amplitude of its response. This work aims to design a prototype to be modeled as a wearable anti-vibration bracelet if the passive absorbers reveal their effectiveness.  
The experimental arm, shown in Figure 1a, is fabricated as a steel beam of dimensions 330.0 mm \(\times\) 18.0 mm \(\times\) 50.0 mm and mass of 242.30 g. The experimental arm is modeled as a rigid link, representing a hand segment situated in a postural position with a flexion-extension angular motion at the wrist joint. A mechanical shaker is used to excite the experimental arm by a measured signal for the ECR muscle of the patient. The connection of the mechanical shaker to the experimental arm is made in the way shown in Figure 1b. This connection is made to avoid the introduction of stiffness, between the shaker and the steel beam, which may induce a resonance frequency in the range of interest of this study. A force sensor is placed between the experimental arm and the vibrometer, as shown in Figure 1b, to provide the applied excitation signal.  
The raw ECR signal (Figure 2a) is implemented on the LabVIEW interface and amplified to obtain the same range as the patient for the response signal. The excitation force is applied to the experimental arm at a distance of 48.0 mm from the clamped end (Figure 1a). A rectangular piece is attached to the end of the experimental arm and used to hold the TMD(s). A vibrometer (PDV-100 from Polytec) is used to measure the response of the experimental arm, before and after the addition of the TMDs. The measurement full-scale range of the vibrometer is 500 mm/s with a corresponding resolution of \(<\)0.1 \(\mu m/s/(\sqrt{Hz})\). The measurement point of the vibrometer is at a distance of 20.0 mm from the free end of  
Figure 1: (**a**) Experimental setup used to test the behavior of the TMD system with realistic tremor signal; (**b**) connection between the mechanical shaker and the experimental arm.  
the experimental arm. All measurements are performed for 60 s. A LabVIEW program is also used for data acquisition with a sampling rate of 1707 Hz. The measured signal is downsampled to obtain a sampling frequency of 50.00 Hz, which is higher than twice the frequencies of biological tremors [15]. Responses in the frequency domain are analyzed in terms of the PSD, obtained in this study using [PERSON]'s method with a Hamming window of 256 points and 80% overlap.  
A comparison between the PSD of the input and output signals of the mechanical shaker, corresponding to the measured ECR signal of the patient, is shown in Figure 2b. The plots of PSD are normalized to the amplitude of the first peak. The ECR muscle of the patient operates at two frequencies, 6.64 Hz and 13.28 Hz. Figure 2b shows that the input and output signals of the mechanical shaker fit well, especially at the first critical frequency (the frequency of concern in this study).