Tremor Reduction at the Palm of a Parkinson’s Patient Using Dynamic Vibration Absorber
Abstract
:1. Introduction
2. System Design
2.1. Hand Model
2.2. Equations of Motion
- Kinetic Energy
- Potential Energy
- Rayleigh dissipation function
2.3. Absorber Design
3. Results and Discussions
3.1. Complex Transfer Function
3.2. Numerical Simulations
3.2.1. Behavior in Frequency Domain
- For the four DOF system with “absorber 1”:
- For the four DOF system with “absorber 2”:
- For the five DOF system with the “dual DVA”:
3.2.2. Behavior in Time Domain
3.3. Absorber’s Lifetime
4. Conclusions
Author Contributions
Conflicts of Interest
Appendix A
Abbreviations and Symbols
Distance between centroid of the upper arm, forearm and the palm to its corresponding proximal joint (m) | |
Position from the attached mass to the fixed joint of “absorber 1” and “absorber 2” (m) | |
Base of absorber’s cantilevered beam and the attached mass (m) | |
Damping coefficient matrix of the system (Nms/rd) | |
Load, reliability, size, surface and temperature correction factors | |
Bending damping coefficient of absorber’s beam and shoulder, elbow, biceps brachii and wrist muscles (Nms/rd) | |
Linear damping coefficients of “absorber 1” and “absorber 2” (Ns/m) | |
DBS | Deep brain stimulation |
DOF | Degree of freedom |
DVA | Dynamic vibration absorber |
Modulus of elasticity of absorber’s beam material (GPa) | |
Generalized conservative and frictional moments (Nm) | |
Input moment at shoulder and wrist joints (Nm) | |
Vector of bending moment functions (Nm) | |
Height of absorber’s cantilevered beam and the attached mass (m) | |
Complex transfer function (rd/Nm) | |
Area moment of inertia of the beam (m4) | |
Mass moment of inertia of the upper arm, forearm and the palm (kgm2/rd) | |
Stiffness coefficient matric of the system (Nm/rd) | |
Bending damping coefficient of absorber’s beam and shoulder, elbow, biceps brachii and wrist muscles (Nm/rd) | |
Linear stiffness coefficients of “absorber 1” and “absorber 2” (N/m) | |
Fatigue stress concentration factor | |
Length of absorber’s cantilevered beam and the attached mass (m) | |
Distance between absorber’s joint and controller device to the elbow joint (m) | |
Distance from the location of concentrated masses of the upper arm, forearm and the palm to its corresponding proximal joint (m) | |
Mass matrix of the system (kgm2/rd) | |
Effective proof mass of “absorber 1” and “absorber 2” (kg) | |
Mass attached to absorber’s beam (kg) | |
Masses of the upper arm, forearm, controller device and the palm (kg) | |
Total mass of the absorber (kg) | |
Fatigue and yielding safety factors | |
PD | Parkinson’s disease |
Generalized coordinates of angular displacement and velocity (rd) and (rd/s) | |
Raleigh dissipation function (J) | |
Corrected and uncorrected endurance limit of the absorber’s beam (MPa) | |
Ultimate and yielding strength of absorber’s beam (MPa) | |
Proportional constant relating stiffness and damping coefficients | |
Kinetic and potential energy of the system (J) | |
Bending reaction moment on absorber’s beam (Nm) | |
Receptance transfer function (rd/Nm) | |
Angular displacement, velocity and acceleration functions (rd), (rd/s) and (rd/s2) | |
Angular displacement magnitude (rd) | |
Angular displacement magnitude of the controlled and uncontrolled systems (rd) | |
Driving frequency (rd/s) | |
Fundamental frequency of absorber’s system and its beam alone (rd/s) | |
Natural frequency of the attached mass (rd) | |
Natural frequency of the system (rd/s) | |
Phase angle of the response () | |
Bending stress (MPa) | |
Damping ratio | |
Density of the cantilevered beam of the absorber and the attached mass (kg/m3) |
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Muscle | Shoulder | Elbow | Biceps | Wrist |
---|---|---|---|---|
k (Nm/rd) | 180 | 70 | 40 | 10 |
c (Nms/rd) | 0.002 | 0.002 | 0.002 | 0.001 |
Dimensions | L (cm) | H (cm) | B (cm) | |
---|---|---|---|---|
Absorber 1 | Beam 1 | 9 | 2.4 | 0.03 |
Attached Mass 1 | 2.24 | 2.3 | 2.3 | |
Absorber 2 | Beam 2 | 7.5 | 1.8 | 0.03 |
Attached Mass 2 | 2.4 | 2 | 2 |
Parameters | (g) | (Nm/rd) | (Nms/rd) |
---|---|---|---|
Absorber 1 | 105.239 | 0.3184 | 0.0002 |
Absorber 2 | 85.044 | 0.2662 | 0.0002 |
Parameters | (g) | (N/m) | (Ns/m) |
---|---|---|---|
Absorber 1 | 105.239 | 52.78 | 0.0002 |
Absorber 2 | 85.044 | 94.11 | 0.0002 |
% Reduction | Absorber 1 | Absorber 2 | Dual DVA |
---|---|---|---|
Shoulder | 69.1%–79.7% | 12.6%–47.2% | 98.3%–99.5% |
Elbow | 4.05%–32.12% | 72.6%–76.3% | 97.0%–97.3% |
Wrist | 6.4%–44.2% | 40.2%–62.9% | 97.4%–97.5% |
% Reduction | = 0.0002 | = 0.002 | = 0.02 |
---|---|---|---|
Shoulder | 98.3%–99.5% | 90.9%–93.9% | 65.24%–68.2% |
Elbow | 97.0%–97.3% | 80.8%–85.4% | 49.7%–57.1% |
Wrist | 97.4%–97.5% | 85.6%–85.9% | 54.1%–60.52% |
Flexion Angle | Absorber 1 | Absorber 2 | Dual DVA | |
---|---|---|---|---|
Absorber 1 | Absorber 2 | |||
42.97 | 23.83 | 49.43 | 43.00 | |
61.45 | 61.81 | 49.96 | 43.53 |
Safety Factor | Absorber 1 | Absorber 2 | Dual DVA | |
---|---|---|---|---|
Absorber 1 | Absorber 2 | |||
1.07 | 0.69 | 1.77 | 1.64 | |
1.20 | 1.07 | 1.47 | 1.54 |
Safety Factor | Absorber 1 | Absorber 2 | |
---|---|---|---|
= 0.0002 | 42.97 | 23.83 | |
61.45 | 61.81 | ||
= 0.002 | 40.81 | 18.69 | |
58.61 | 54.60 | ||
= 0.02 | 14.78 | 5.64 | |
36.16 | 28.40 |
Safety Factor | Absorber 1 | Absorber 2 | |
---|---|---|---|
= 0.0002 | 1.07 | 0.69 | |
1.20 | 1.07 | ||
= 0.002 | 1.21 | 0.73 | |
1.25 | 1.21 | ||
= 0.02 | 1.42 | 1.31 | |
2.00 | 2.43 |
© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).
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Gebai, S.; Hammoud, M.; Hallal, A.; Khachfe, H. Tremor Reduction at the Palm of a Parkinson’s Patient Using Dynamic Vibration Absorber. Bioengineering 2016, 3, 18. https://doi.org/10.3390/bioengineering3030018
Gebai S, Hammoud M, Hallal A, Khachfe H. Tremor Reduction at the Palm of a Parkinson’s Patient Using Dynamic Vibration Absorber. Bioengineering. 2016; 3(3):18. https://doi.org/10.3390/bioengineering3030018
Chicago/Turabian StyleGebai, Sarah, Mohammad Hammoud, Ali Hallal, and Hassan Khachfe. 2016. "Tremor Reduction at the Palm of a Parkinson’s Patient Using Dynamic Vibration Absorber" Bioengineering 3, no. 3: 18. https://doi.org/10.3390/bioengineering3030018