Parkinson’s patients suffer from severe tremor due to an abnormality in their central oscillator. Medications used to decrease involuntary antagonistic muscles contraction can threaten their life. However, mechanical vibration absorbers can be used as an alternative treatment. The objective of this study is to provide a dynamic modeling of the human hand that describes the biodynamic response of Parkinson’s patients and to design an effective tuned vibration absorber able to suppress their pathological tremor. The hand is modeled as a three degrees-of-freedom (DOF) system describing the flexion motion at the proximal joints on the horizontal plane. Resting tremor is modeled as dual harmonic excitation due to shoulder and elbow muscle activation operating at resonance frequencies. The performance of the single dynamic vibration absorber (DVA) is studied when attached to the forearm and compared with the dual DVA tuned at both excitation frequencies. Equations of motion are derived and solved using the complex transfer function of the non-Lagrangian system. The absorber’s systems are designed as a stainless steel alloy cantilevered beam with an attached copper mass. The dual DVA was the most efficient absorber which reduces 98.3%–99.5%, 97.0%–97.3% and 97.4%–97.5% of the Parkinson’s tremor amplitude at the shoulder, elbow and wrist joint.

Active and semi-active control devices can be used as advanced and accurate controllers to reduce the undesired vibration of a structure. However, some of these controllers may have a complex design, especially for systems excited with multi-degree-of-freedom frequencies, which demand the use of high anti-fatigue material properties, and others that may require a large power source. So, improvements in the design of passive controllers are of high interest for researchers. These controllers have a very simple design and aim to counteract vibration with no power requirements. In this paper, six different passive controllers were designed to analyze and compare their performance. The performance is considered in terms of the percentage of reduction in the primary system’s displacement amplitude and the bandwidth of each designed passive controller. The system of interest is taken as the three-degree-of-freedom dynamic hand system reflecting the behavior of Parkinsonian patients. Four joint muscles operating at two resonance harmonic excitation frequencies are considered to produce movements. Each controller was attached to the forearm of the hand set in the horizontal plane to analyze their capability in reducing the rest tremor (3–7 Hz) at the proximal joint. The dual series elastic–viscous absorber is shown to be a very effective controller. It is formed from a series connection between an elastic absorber (mass–spring) and a viscous absorber (mass–dashpot). It causes about 80% reduction in tremor amplitude with 4 Hz wide frequency band at the shoulder, elbow and wrist joints. This range of operational frequency is close to that of healthy cases, 4.5 Hz.

Parkinson's disease is characterized by involuntary movement of body parts resulting from antagonistic muscle contractions. In this paper, an effective passive vibration absorber is modeled to control the involuntary pathological rest tremor in the right hand of Parkinson's disease patient. The three-degree-of-freedom dynamic hand model capable to describe the flexion-extension planar motion at shoulder, elbow, and wrist joints in horizontal plane is designed. The passive tuned vibration absorber is modeled to suppress flexion motion of shoulder, elbow and wrist joints. Active inputs producing motion are considered at shoulder and elbow joints, and driven at resonance frequencies. The equations of motion for the dynamically coupled modeled hand system are derived. The responses are represented in time and frequency domains using the complex transfer function method. Optimum position of the absorber on the forearm is determined in terms of its effectiveness in reducing tremor's amplitude.

Tuned mass dampers (TMDs) are proposed as a solution to reduce the involuntary tremor at the upper limb of a patient with postural tremor. The upper limb is modeled as a three-degrees-of-freedom rotating system in the vertical plane, with a flexion-extension motion at the joints. The measured extensor carpi radialis signal of a patient is used to excite the dynamic model. We propose a numerical methodology to optimize the parameters of the TMDs in the frequency domain combined with the response in the time domain. The objective function for the optimization of the dynamic problem is the maximum angular displacement of the wrist joint. The optimal stiffness and damping of the TMDs are obtained by satisfying the minimization of the selected objective function. The considered passive absorber is a cantilever beam–like TMD, whose length, beam cross-sectional diameter, and mass position reflect its stiffness for a chosen additional mass. A parametric study of the TMD is conducted to evaluate the effect of the TMD position along the hand segment, the number of TMDs, and the total mass of TMDs. The sensitivity of the TMD to a decrease of its modal damping ratio is studied to meet the range of stainless steel. TMDs are manufactured using stainless steel beams of the same length (9.1 cm) and cross-sectional diameter (0.79 mm), for which the mass (14.13 g) position is adjusted to match the optimal frequency. Three TMDs holding a mass of 14.13 g each cause 89% reduction in the wrist joint angular displacement.

Vibration absorbers are effective devices used to reduce the unwanted motion of a vibrating system. It is recently used to reduce the involuntary tremor of a Parkinson's patient. The absorber can be attached to the forearm of the patient hand. Such system can be excited at resonance frequencies reflecting the resting tremor due to the shoulder and elbow muscles activation. Two single absorbers are designed and tested numerically in reducing the involuntary tremor: the conventional absorber having its spring and damper connected in parallel and the elastic-damper absorber having its spring and damper connected in series. Both absorbers are designed to satisfy the tuning conditions at the fundamental frequency of the primary system with the same total mass. The conventional absorber causes 75.5-97.4%, 11.1-48.0% and 41.2-49.7% reduction at the shoulder, elbow and the wrist joints, respectively. However, the elastic-damper absorber causes 74.0-78.7%, 5.0-35.0% and 29.3- 45.8% at the same positions, respectively. The elastic-damper absorber can cause this reduction with a device of shorter length.