VIBRATION SUPPRESSION DRAFTING ARM FOR TREMOR PATIENTS
A Thesis
Presented to the faculty of the Department of Mechanical Engineering
California State University, Sacramento
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
Mechanical Engineering
(Manufacturing)
by
Jose Wilson Mojica
SPRING
2014
VIBRATION SUPRESSION DRAFTING ARM FOR TREMOR PATIENTS
A Thesis
by
Jose Wilson Mojica
Approved by:
__________________________________, Committee Chair
Dr. Akihiko Kumagai
__________________________________, Second Reader
Dr. Jose Granda
____________________________
Date
ii
Student: Jose Wilson Mojica
I certify that this student has met the requirements for format contained in the University format
manual, and that this thesis is suitable for shelving in the Library and credit is to be awarded for
the thesis.
__________________________, Graduate Coordinator ___________________
Dr. Akihiko Kumagai
Date
Department of Mechanical Engineering
iii
Abstract
of
VIBRATION SUPPRESSION DRAFTING ARM FOR TREMOR PATIENTS
by
Jose Wilson Mojica
Essential Tremor (ET) is a progressive neurological condition that affects over 10 million
Americans. It causes a rhythmic trembling of the body that is most pronounced in the hands.
Many ET patients lose the ability to perform simple yet vital tasks, such as writing. Current
writing assisting devices are not able to efficiently cancel or restrict the trembling experienced by
these patients when they write. A drafting arm has been developed that diminishes the arm and
hand vibrations of ET patients by dampening the motion of the pen. The design incorporates a
two-segment arm with variable dampers at its joints. One end of the arm attaches to any table
while the other holds a writing device. The two dampers resist the rotation at each joint. ET
patients using this tool have shown significant improvement in their writing ability in comparison
to using other consumer devices available today.
_______________________, Committee Chair
Dr. Akihiko Kumagai
_______________________
Date
iv
ACKNOWLEDGEMENTS
I appreciate the support that University Enterprises, Inc. (UEI) of California State University,
Sacramento has given me. I also would like to thank International Essential Tremor Foundation
(IETF) support groups in California and Arizona for participating in my study.
v
TABLE OF CONTENTS
Page
Acknowledgements ................................................................................................................... v
List of Figures ........................................................................................................................ vii
Chapter
1. INTRODUCTION ……………. ………………………………………….…………….. 1
2. PRELIMINARY DESIGN / PROOF OF CONCEPT ........................................................ 5
3. FINAL DESIGN ................................................................................................................. 8
3. TEST RESULTS............................................................................................................... 16
3. DISCUSSION ................................................................................................................... 19
3. FUTURE WORK .............................................................................................................. 21
3. CONCLUSION ................................................................................................................. 23
Appendix A. MATLAB® PROGRAM FOR HORIZONTAL CONTOUR MAP.................. 24
Appendix B. MATLAB® PROGRAM FOR VERTICAL CONTOUR MAP........................ 25
Appendix C. MATLAB® FUNCTION FOR CONTOUR MAPS ......................................... 26
Appendix D. ARDUINO PROGRAM FOR ACCELEROMETER DATA .......................... 28
Appendix E. DRAWING SET FOR VIBRATION SUPPRESSION DRAFTING ARM …. 29
Appendix F. BILL OF MATERIALS FOR PURCHASED PARTS ……............................. 40
References ............................................................................................................................... 41
vi
LIST OF FIGURES
Figures
Page
1.
First design used as a proof of concept…………… ... .………………………………. 7
2.
Optimal writing angle for each link………………….… ……………………………. 9
3.
Simplified representation of the system as a two force member……………….…….11
4.
Writing effectiveness in the horizontal direction………… ... ………………………. 13
5.
Writing effectiveness in the vertical direction..............................................................13
6.
Accelerometer circuit attached to vibration suppression drafting arm.........................14
7.
Wiring schematic for accelerometer circuit..................................................................15
8.
Writing sample of person with hand tremor using a regular pen..................................16
9.
Writing sample of person with hand tremor using the vibration suppression
drafting arm.................................................................................................................. 17
10.
Accelerometer data of person with hand tremor tracing shapes with a regular pen.....18
11.
Accelerometer data of person with hand tremor tracing shapes with the vibration
suppression drafting arm .............................................................................................. 18
vii
1
INTRODUCTION
Essential Tremor (ET) is a progressive neurological condition similar to Parkinson’s Disease
(PD). It is sometimes referred to as benign essential tremor, familial tremor, or senile tremor
[1,2]. The effects of ET are easily identified in the involuntary shaking of the upper limbs,
although it can also affect other parts of the body such as the head, voice, legs, and trunk. It is
often mistaken for Parkinson’s Disease but can be loosely differentiated by its lower amplitude,
higher frequency as well as whether or not the symptom is present at rest or during the execution
of a gesture [1].
ET is not as well known or thoroughly studied as PD, partly because ET is not considered as life
threatening as PD, so it is not given the same importance. Despite its lower severity, it still
greatly diminishes the quality of life for an estimated 10 million people in the U.S. alone. Despite
the number of people it affects, and the high demand for assistive technologies, the development
of mechanical aids for everyday life is only recently starting to gain traction.
The few
innovations that have become available for consumers break down into two categories, passive
and active systems. Passive systems consist of mechanical devices which resist body movement
and have no electrical components or feedback control. Active systems on the other hand are
more reactive and may have circuitry with feedback control to better respond to unique
movement. In addition to mechanical aids, there have been advances in drugs that are meant to
relax the body, aswell as more invasive procedures such as thalamotomy where a portion of the
thalamus is destroyed, and deep brain stimulation which involves an implant that sends an
electronic signal to parts of the brain, much like a pace maker does for the heart [3]. Although
drugs and surgical procedures have been known to be effective, this paper will focus only on
mechanical aids and solutions.
2
The passive systems for writing that are available on the market today are mainly a variety of
weighted or ergonomic implements. Weighted implements are regular pens and pencils that are
equipped with a dense metal casing that increases their weight to approximately 7 ounces. These
pens and pencils come in many shapes and styles but perform similarly to one another. Their
effectiveness is limited by their total weight. Other designs rely on ergonomic shapes. These
pens are intended to relax the person’s grip and thus diminish the tremor. Overall these devices
are primarily effective for people with mild tremor.
The more complex solutions are the use of active devices. There are currently no active devices
available for public consumption, but there are several ideas and patents that hold promise. One
such device is proposed in a U.S. patent issued to H.J. Reinsma in 2001 [4]. Reinsma presents
the idea of a pen that is equipped with a servo motor at the back end which pivots the writing end
of the pen about a central point in order to counteract the tremor movement. The design suggests
two motors, one for each of the main directions perpendicular to the length of the pen. No
response is considered for the direction along the length of the pen. The actual mechanics or
software controlling the servo motors is not discussed in detail, but the patent does go on to
prescribe ideal motor frequencies of between 60 and 80 Hz.
This is an interesting
recommendation because most research suggests that typical tremor frequencies are close to 4 Hz,
an order of magnitude lower [1]. This idea has recently been implemented in a spoon that
behaves in the exact manner. The spoon became available to consumers in recent months. Video
demonstrations of this spoon show that like the weighted pens, it is mostly effective for people
with mild tremor. Both the spoon and pen designs have limited effectiveness cancelling severe
tremor due to the small width of their bodies. As tremor amplitude increases the amplitude of the
3
counter action must also increase. However, in order to be practical the pen and spoon bodies can
only be a few centimeters in diameter.
This means that the full range of motion for the
counteracting levers within their bodies are also limited to a few centimeters. People with
medium to sever tremor experience larger amplitudes which require implements of impractical
diameters in order to be effective.
Another active device which is being developed is a gyroscopic stabilizing brace described in a
U.S. patent [5]. This brace is equipped with a rigid exterior case that cradles the user’s forearm
and hand while leaving the finger tips exposed so that they are able to grip a normal pen or pencil.
Gyroscopes encased in a rigid cell can be attached at different places along the brace in response
to the specific directions of the tremor for each individual. The unavoidable problem with this
design is that gyroscopes tend to stop sudden acceleration but they can also be difficult to
maneuver in an intended way. This can be problematic during writing because of the intended
directions that the pen has to move. In addition, this device is bulky and becomes even more so
with multiple gyroscopes if several are needed for multidirectional tremor.
Although the amount of interest in designing assisting devices for tremor patients is increasing,
the supply of effective devices is still in its infancy. Most devices available for consumers today
are limited to one severity of tremor which can be a problem because of the progressive nature of
the disease. In this paper I discuss the development of a passive system which combines the
concept of a simple drafting arm with variable rotary dampers in order to diminish the vibration
of a pen for various amplitudes while writing. The design incorporates a two-segment arm,
similar to a drafting arm, with variable dampers at each joint. The arm attaches to the writing
4
table at one end and holds a writing device such as a pen at the other. Testing has shown
significant improvement in patient’s writing ability, compared to standard devices.
5
PRELIMINARY DESIGN / PROOF OF CONCEPT
The initial design originated with the intent of dampening the high frequency vibrations from the
writing implement while preserving the low frequency motions of intentional writing. Thus far
most passive methods that have been explored have added weight to a pen in order to increase its
mass. The increase in mass decreases the acceleration experienced due to the force applied by the
hand. This relationship is described by Newton’s second law Eq. (1).
𝐹 = 𝑚𝑎
(1)
𝐹 is the force applied to the pen by the hand, 𝑚 is the mass of the pen, and 𝑎 is the acceleration
experienced by the pen. The weighted pen does seem to improve some people’s writing ability
but it is most effective on people with mild tremor.
Equation (1). shows that as the tremor becomes more severe and the force on the pen increases,
the mass of the pen must also increase to keep the acceleration low. Therefore the mass required
to decrease the vibration for a moderate tremor would need to be increasingly large and thus
would also become unmanageable.
In order to overcome this obstacle I decided to incorporate dampers into a multi-link mechanism
that would allow for two degrees of freedom on a writing surface. Rotary dampers were chosen
over linear ones due to their compact size and availability.
described by a first order differential relationship Eq. (2).
The damper’s performance is
6
𝐹𝑐 = −𝐶
𝑑𝜑
𝑑𝑡
(2)
𝐹𝑐 is the dampening force, 𝐶 is the viscous dampening coefficient of the fluid used in the rotary
damper, and 𝑑𝜑/𝑑𝑡 is the rate of change in angular displacement over time or in other words, the
velocity of the oscillations.
Equation (2). states that the force exerted by the damper is directly proportional to the angular
velocity. This means that fast movements caused by tremor will cause the damper to exert a
stronger force than the slow writing motions would. The overall effect is that the dampers are
able to act as a motion filter, cancelling out fast movements caused by tremor and allowing slow
movements cause by writing actions.
The use of rotary dampers resolved the weight challenge limiting the weighted pen, but they also
introduced a design restriction of their own. It meant that the system needed to be anchored to a
fixed location independent of the user’s arm. The resulting design was a two member mechanism
with adjustable link lengths Fig. 1. The system has two degrees of freedom on the x-y plane
(parallel to the writing surface). The writing range was adjusted by manipulating the length of
each link. The final arrangement for this design allowed coverage of a writing area equal to that
of a standard sheet of paper (8.5” x 11.0”). The rotary dampers used for this design were of fixed
resistance so the only way to adjust the resistance felt at the pen was by adjusting the link lengths.
7
Figure 1. First design used as a proof of concept.
8
FINAL DESIGN
The initial design provided a proof of concept, and illuminated a few areas that needed
refinement. The first and most important feature that needed improvement was the system’s
resistance adjustment. The original design required that the damper resistance be adjusted by
lengthening the links, thus coupling the damping effectiveness with the size of the writing area.
Furthermore, the length adjustment was a labor intensive and slow process given the way that the
links were secured to each other. A second needed improvement was better performing dampers.
The original dampers had a plastic shaft that allowed for too much play in their rotation. This
meant that when a force was applied to the pen in any direction, it was able to move unaffected
by the dampers for the first few millimeters of travel. For those few millimeters the dampers
were not resisting motion thus not cancelling unwanted vibrations. In addition to the mechanical
refinements I also wanted to determine the link positions that would be optimal for writing.
The first two improvements were addressed with the incorporation of more sophisticated rotary
dampers. The new dampers had an adjustable resistance knob. This allowed the links to be fixed
at an ideal length while the resistance was adjusted independently. The new dampers were also
entirely made of aluminum parts and exhibited less play which helped cancel more of the low
amplitude tremor. Their only drawback was that they had a limited 60° range of travel. The
limited rotation reduced the total writing area which made the optimization of the link position
even more important.
The initial positioning of the two links was based on the maximization of the writing area. Figure
2. shows the final design with all of its major components labeled. D1, D2 are the damper joints,
and L1, L2 are the links.
9
Figure 2. Optimal writing angle for each link.
It was determined that in order to maximize the pen’s travel in the x-direction, L1 had to be
placed vertically (perpendicular to the x-axis) when D1 was at the middle of its rotational range
Eq. (3).
𝐿1𝑥 = 𝐿1𝑙 cos 𝜃
(3)
𝐿1𝑥 is the x-component of L1’s range at its top end, 𝐿1𝑙 is its length, and 𝜃 is the angle it makes
with the positive x-axis. This placement restricted L1 to operate between 60° and 120° from the
positive x-axis. L2 was placed perpendicular to L1 when D2 was at its middle position. This not
10
only allowed adequate travel in the vertical direction, but it also maximized the force
transmission angle for D2. This meant that the force transmitted through L2 is most effective in
turning D2 when the angle between the two links is at 90°.
At this stage in the design, preliminary testing showed that ET patients found some areas easier
and some harder to write in. In order to further investigate this observation I generated a contour
map of the writing effectiveness throughout the writing area. Writing effectiveness was defined
as the amount of effort required to move the pen in both the x and y-directions.
For
simplification of the problem the following assumptions were made.
1. All fast movements caused by involuntary tremor are filtered out by the dampers, thus the
only movements left to consider are those from intentional writing.
2. The system can be treated as a simple two force member with no friction, or any dynamic
effects like inertial torques.
3. All external torques on the pen are negligible.
4. There is no friction between the writing surface and the pen.
These assumptions allowed me to consider the system as a simple two-force member. Figure 3.
below shows the same components described in Fig. 2. with the addition of angles α, β x, βy and
forces Fx and Fy.
11
Figure 3. Simplified representation of the system as a two force member.
α is the angle between L1 and L2. βx is the angle between L2 and the horizontal component of
the force exerted on the pen (Fx). βy is the angle between L2 and the vertical component of the
force exerted on the pen (Fy). The writing effectiveness was greatest when most of the forces
from writing went into the rotation of the two dampers. For D1 this is achieved when α is 90º
because none of the force transmitted by L2 is transmitted along the L1 link where it would
become useless given that D1 is a fixed point. For D2 the effectiveness is broken down into two
parts. The first is effectiveness in the x-direction which is greatest when βx is 90º and decreases
as βx approaches 0º or 180º. The second is effectiveness in the y-direction which is greatest when
βy is 90º and decreases as βy approaches 0º or 180º. Effectiveness in both the horizontal and
vertical directions can be represented by a sine function Eq. (4) and (5).
12
𝐸𝑥 = sin 𝛼 + sin 𝛽𝑥
(4)
𝐸𝑦 = sin 𝛼 + sin 𝛽𝑦
(5)
The next step in generating the contour maps was to calculate 𝐸𝑥 and 𝐸𝑦 for any x-y coordinate
on a two dimensional writing surface. This was achieved by using a method described in
Kinematics Analysis of a Two-Link Robot [6]. The difference in effectiveness between one point
from the next was very minimal for both directions and therefore showed little variance in color
on the original maps. The highest any of the values could be was two because sine of any angle
cannot exceed one. In order to magnify the variations across the writing surface bot 𝐸𝑥 and 𝐸𝑦
were raised to the power of seven for the final plots, bringing the potential maximum to 128.
Effectiveness in the horizontal direction showed little variance over the entire area Fig. 4. On the
other hand, the effectiveness in the vertical direction showed a distinct gradient Fig. 5. A copy of
the program used to generate the contour maps is presented in Appendices A-B.
13
Figure 4. Writing effectiveness in the horizontal direction.
Figure 5. Writing effectiveness in the vertical direction.
14
In addition to the improvements described, I designed a method to quantify the total effect the
system had on patient’s writing by using an accelerometer circuit to measure the acceleration of
the x-y motion of the pen with and without the vibration suppression arm Fig. 6.
Figure 6. Accelerometer circuit attached to vibration suppression drafting arm.
The accelerometer circuit consisted of a 3-axis analog accelerometer, model number MMA7361
made by Freescale Semiconductor. The accelerometer was coupled with an Arduino Uno Rev 3
microcontroller made by Arduino. The Arduino was then connected to a lap top computer via
USB. The wiring of the MMA7361 to the microcontroller required a total of 6 wires as shown in
Fig. 7.
15
Figure 7. Wiring schematic for accelerometer circuit.
The MMA7361 requires 5 volts for its power which in this case was supplied by the Arduino,
and 3 analog inputs, one for each of the axes. The SL pin is used to turn the MMA7361’s outputs
either on or off. Setting this pin low turns off all of the outputs and allows the MMA7361 to sit
idle with considerable lower power consumption. This option is important when running on a
limited power supply, but in this case, the lap top supplied the system abundant power so the pin
was permanently set high.
The final program collected data for all three axes and recorded them on a laptop computer at a
rate of 5Hz. The data was first written by the software on the computer’s serial monitor and later
cut and pasted into a basic text editor. A copy of the final program is presented in Appendix C.
16
TEST RESULTS
The results shown below are writing samples from a volunteer with Essential Tremor. The
objective for the volunteer was to write the sentence printed on the sample page, and trace a
vertical, horizontal, and spiral line. Figure 8. shows the volunteer’s writing while using a normal
pen. Figure 9. on the other hand shows a writing sample of the same person using the vibration
suppression arm.
Figure 8. Writing sample of person with hand tremor using a regular pen.
17
Figure 9. Writing sample of person with hand tremor using the vibration suppression
drafting arm.
Comparing the two writing samples, it is clear that the volunteer experienced major tremor while
tracing the shapes with a regular pen. These fast movements were almost entirely cancelled by
the vibration suppression arm. The clearest example can be seen when comparing the two
horizontal lines, or the spiral shapes. Figures 10-11. show the accelerometer data for the same
tracing exercise without and with the vibration suppression arm respectively. The x and y axes
indicated in these two figures were set parallel to edges of a desk where the writing device was
mounted. While using a regular pen, the accelerations spike up to 20 m/s 2, while when using the
arm the highest acceleration experienced is 2.5 m/s2.
18
Figure 10. Accelerometer data of person with hand tremor tracing shapes with a regular
pen.
Figure 11.
Accelerometer data of person with hand tremor tracing shapes with the
vibration suppression drafting arm.
19
DISCUSSION
From the writing samples in Fig. 8-9. it is clear that the patient’s penmanship becomes more
legible and they are better able to follow a simple pattern on the page. The acceleration data
presented in Fig. 10-11. quantifies the improvement, and shows that the acceleration felt by the
pen decreases by approximately 10 times when using the drafting arm. Although a more direct
metric would have been to measure velocity directly, by keeping a constant sampling interval
during all cases, changes in acceleration directly relate to changes in velocity Eq. (6).
𝑎=
𝑑𝑣
𝑑𝑡
(6)
Overall, the combined data shows that the design effectively suppresses hand tremor while
allowing the slow intentional movement of writing.
An interesting observation is the writing effectiveness throughout the writing area. Fig. 4-5.
show that while writing in the vertical direction is most effective in the upper middle of the area,
that same area is not ideal for writing in the horizontal direction. This is explained by the
rotational range of each damper. For the vertical direction, the ideal link positions are when both
α and βy are close to 90º which is precisely in the upper middle of the page. However, this same
area places L2 such that it minimizes βx. βx is closest to 90º only at the upper and lower extremes
of the writing area, and even then it never exceeds 60º. Figure 4. shows the effectiveness starting
to increase near the bottom edge of the plot. This effectiveness pattern was observed during the
testing for most patients. The majority of the patients reported having very little trouble moving
the pen in the vertical direction while they had more difficulty moving it in the horizontal
20
direction. Specifically, patients spent more effort moving the pen towards their backhand. That
is, right handed patients easily pushed the pen towards their left while straining when pulling it
towards their right. The difference in the two directions may be due to the individual’s arm
strength in each direction. One potential solution to this problem would be to add an additional
link and damper to the system. The added articulation may increase the writing effectiveness in
the horizontal direction but in turn would increase the cost of the design by a significant amount.
21
FUTURE WORK
The drafting arm is currently functional, but can use several refinements. One of the more useful
improvements would be to increase the accelerometer’s resolution by at least ten fold. The
current circuit does provide clear evidence that the drafting arm reduces spikes in velocity, but
higher resolution could provide more subtle data such as vibration frequency. This data will help
quantify effectiveness, and help further the understanding of how other modifications may affect
the overall performance of the system.
The most common criticism that patients had was that they were not able to see the tip of the pen
as well as they would have liked. This is because for right-handed individuals the arm sat to their
left. This caused L2 to partially obscure the pen’s lower half. Some patients had to position their
heads in an un-natural posture in order to see the pen tip as they were writing. A good solution to
this problem would be to position the arm to the outside of the writing hand. Left-handed people
would then have it on the left and right-handed people on the right of their writing hand. This
modification will require redesigning the pen holder. As it is now the pen holder is positioned too
low and would not allow the gipping of the pen. It would have to sit above the writing hand.
Another important objective would be to lower the cost of materials. The biggest challenge in
reducing cost will be finding alternative variable rotary dampers that will not compromise
performance. This is a substantial challenge because after testing a few versions I found that the
performance of these dampers was directly related to their cost. One of the most important
qualities that cannot be compromised is mechanical play or slip of the shaft and base. Any
significant play in the dampers will render their dampening effect useless.
22
Aside from improvements in functionality and cost, an equally as important challenge is to
streamline the drafting arm and make it as user friendly and as aesthetically pleasing as possible.
In its current state, the vibration suppression arm is bulky and unattractive as a writing implement
for the general public. The majority of the patients who tested the design stated that they would
consider using it if it was more streamlined and less bulky.
23
CONCLUSION
A person’s ability to write legibly is very clearly not essential to their survival, but it is however
one facet of a group of things that affect that person’s quality of life. My design has shown to
improve the penmanship of people suffering from Essential Tremor. The device diminishes hand
tremor while writing by dampening the high frequency vibrations transferred by the hand. Tests
using the final design show significant improvement in writing samples.
Recommended
improvements for future system improvements are increasing its ease of use, specifically its pen
attachment mechanism, and refining its overall appearance.
24
APPENDIX A. MATLAB® PROGRAM FOR HORIZONTAL CONTOUR MAP
% Main Program
% This script generates a horizontal direction efficiency chart
% while writing with the vibration suppression drafting arm.
clc % clear display
clear % Clearing all parameters before executing this program
effiaray = zeros(280, 350); % creates empty array
for x = 1:1:350
for y = 1:1:280
XB = x;
YB = y;
[alpha, betaX, betaY] = Transmission(XB, YB); %Calls Transmission function
betaX = abs(betaX);
betaY = abs(betaY);
EfficiencyX = abs(sin(alpha)) + abs(sin(betaX));
gama = pi - alpha - betaX;
if alpha > 120*(pi/180)
effiaray(y,x) = 0;
elseif alpha < 60*(pi/180)
effiaray(y,x) = 0;
elseif betaX > 60*(pi/180)
effiaray(y,x) = 0;
elseif gama < 60*(pi/180)
effiaray(y,x) = 0;
else
effiaray(y,x) = EfficiencyX^7;
end
end
end
surf(effiaray)
% End Main Program
25
APPENDIX B. MATLAB® PROGRAM FOR VERTICAL CONTOUR MAP
% Main Program
% This script generates a vertical direction efficiency chart
% while writing with the vibration suppression drafting arm.
clc % clear display
clear % Clearing all parameters before executing this program
effiaray = zeros(280, 350); % creates empty array
for x = 1:1:350
for y = 1:1:280
XB = x;
YB = y;
[alpha, betaX, betaY] = Transmission(XB, YB); %Calls Transmission function
betaX = abs(betaX);
betaY = abs(betaY);
EfficiencyY = abs(sin(alpha)) + abs(sin(betaY));
gama = pi - alpha - betaX;
if alpha > 120*(pi/180)
effiaray(y,x) = 0;
elseif alpha < 60*(pi/180)
effiaray(y,x) = 0;
elseif betaX > 60*(pi/180)
effiaray(y,x) = 0;
elseif gama < 60*(pi/180)
effiaray(y,x) = 0;
else
effiaray(y,x) = EfficiencyY^7;
end
end
end
surf(effiaray)
26
APPENDIX C. MATLAB® FUNCTION FOR CONTOUR MAPS
% Transmission function
% Transmission function receives the x,y coordinate of pen and returns
% the transmission angles alpha, beta-x, and beta-y for the drafting arm.
function [alp1, betaX1, betaY1] = Transmission(XB, YB)
L1=194; % length of arm attached to table base (mm)
L2=251; % length of arm attached to pen (mm)
% Output
dXB=0;
dYB=0;
ddXB=0;
ddYB=0;
% initial setting of vectors
th1=[];
th2=[];
dth1=[];
dth2=[];
ddth1=[];
ddth2=[];
E=(L2^2-L1^2-XB^2-YB^2)/(-2*L1);
double(E);
p=[(E+XB) -2*YB (E-XB)];
s=roots(p);
s1=s(1);
s2=s(2);
% theta 11 and theta 12
th11=2*atan(s1);
th12=2*atan(s2);
phi11=th11;
phi12=th12;
% finding theta 21
th21a=acos((XB-L1*cos(th11))/L2);
th21a=[th21a; -th21a];
th21b=asin((YB-L1*sin(th11))/L2);
if th21b>0
th21b=[th21b; pi-th21b];
end;
27
if th21b==0
th21b=[th21b; pi-th21b];
end;
if th21b<0
th21b=[th21b; -pi-th21b];
end;
if abs(th21a(1)-th21b(1)) < 0.01
th21=th21a(1);
end;
if abs(th21a(1)-th21b(2)) < 0.01
th21=th21a(1);
end;
if abs(th21a(2)-th21b(1)) < 0.01
th21=th21a(2);
end;
if abs(th21a(2)-th21b(2)) < 0.01
th21=th21a(2);
end;
phi21=th21-th11;
if phi21>pi
phi21=phi21-2*pi;
end;
if phi21<-pi
phi21=phi21+2*pi;
end;
% transmission angles Branch 1
alp1=pi-phi21;
if alp1>=pi
alp1=2*pi-alp1;
end
alp1=alp1;
betaX1=th21;
betaY1=pi/2-th21;
end
% End Transmission function
28
APPENDIX D. ARDUINO PROGRAM FOR ACCELEROMETER DATA
// Main Program
// This program turns on outputs from MMA7361 IC and records data from all three axes
// 5 times per second. The frequency can be adjusted by changing the delay
int _sleepPin = 4;
int _GS = 5;
int _xpin = A0;
int _ypin = A1;
int _zpin = A2;
void setup()
{
Serial.begin(9600);
pinMode(_sleepPin,OUTPUT);//output mode
pinMode(_GS,OUTPUT);
//output mode
pinMode(_xpin, INPUT);
//input mode
pinMode(_ypin, INPUT);
//input mode
pinMode(_zpin, INPUT);
//input mode
digitalWrite(_GS,LOW);
//sets GS mode
digitalWrite(_sleepPin, HIGH); //turns off sleep mode and activates device
digitalWrite(_xpin, HIGH);
//turn on pull up resistor
digitalWrite(_ypin, HIGH);
//turn on pull up resistor
digitalWrite(_zpin, HIGH);
//turn on pull up resistor
}
void loop()
{
delay(200);
//Delay for readability, 200 = 5Hz sampling rate
//Write XYZ data to Serial Monitor
Serial.print("X Reading: ");
Serial.println(analogRead(_xpin), DEC);
Serial.print("Y Reading: ");
Serial.println(analogRead(_ypin), DEC);
Serial.print("Z Reading: ");
Serial.println(analogRead(_zpin), DEC);
Serial.println(" ");
}
// End Main Program
29
APPENDIX E. DRAWING SET FOR VIBRATION SUPPRESSION DRAFTING ARM
30
31
32
33
34
35
36
37
38
39
40
APPENDIX F. BILL OF MATERIALS FOR PURCHASED PARTS
ITEM #
PART NAME
VENDOR
MODEL #
1
Variable Rotary Damper
EFDYN INC.
KD-A2 DD
2
¼” – 20 Screw x 1.125”
McMASTER-CARR
92949A835
3
10-32 Captive Nut
McMASTER-CARR
96439A540
5
¼” – 20 Captive Nut
McMASTER-CARR
96439A630
7
Pen Holder
McMASTER-CARR
90654A311
8
Pen Retainer Screw
McMASTER-CARR
92949A192
9
Pen Swivel Head
B&H Foto & Electronics Corp.
Giottos MH 1004
11
C-Clamp Screw
McMASTER-CARR
1705A11
12
C-Clamp Top
McMASTER-CARR
1705A11
13
C-Clamp Bottom
McMASTER-CARR
1705A11
14
C-Clamp Handle
McMASTER-CARR
1705A11
16
¼” – 20 Nut
McMASTER-CARR
90473A029
18
10-32 Screw x ½”
McMASTER-CARR
92949A265
20
Variable Damper Lever
EFDYN INC.
KD-SRS
21
10-32 Screw x 1.5”
McMASTER-CARR
92949A273
41
REFERENCES
[1] Ondo, W., and Jankovic, J., 1996, “Essential Tremor,” CNS Drugs, 6(3), pp. 178-191
[2] Wang, S., Bain, P.G., Aziz, T.Z., & Liu, X., 2005, "The direction of oscillation in spiral
drawings can be used to differentiate distal and proximal tremor," Neuroscience Letters,
384, pp. 188-192.
[3] Ushe M, Mink JW, Revilla FJ, Wernle A, Schneider Gibson P,McGee-Minnich L, Hong M,
Rich KM, Lyons KE, Pahwa R, Perlmutter JS. Effect of stimulation frequency on tremor
suppression in essential tremor. Mov Disord. 2004; 19:1163-8.
[4] H.J. Reinsma, “IMPLEMENT HOLDER FOR USE BY MOTOR DISABLED PATIENTS,”
U.S. Patent 6 213 961 B1, April 10, 2001.
[5] M.A. Kalvert, “ADJUSTABLE AND TUNABLE HAND TREMOR STABILIZER,” U.S.
Patent 6 730 049 B2, May 4, 2004.
[6] Kumagai, A, 2013, “Kinematics Analysis of a Two-Link Robot,” pp. 14-20, California State
Univ., Sacramento.
[7] Chwaleba, A., Jakubowski, J., and Kwiatos, K., 2003, “The measuring set and signal
processing method for the characterization of human hand tremor,” CAD Systems in
Mechatronics, Proc. 7th International Conference, Lviv-Slasko, Ukraine, pp. 149-154
[8] Riviere, C.N., and Thakor, N.V., 1997, “ADAPTIVE HUMAN-MACHINE INTERFACE
FOR PERSONS WITH TREMOR,” IEEE-EMBC, 5, pp. 1193