1
Introduction
Essential tremors are a condition where a person develops a semi regular shaking
in one of their limbs or other muscles. It is common for this tremor to develop in the arm,
wrist or hand, which is used for writing. Even a minor tremor will make such writing
unreadable. A pen has been developed which isolates the limb vibration from the actual
pen, facilitating legible writing. The legibility will depend on the severity of the tremor
and the extent that the pen is adjusted to cancel the tremor vibration. The input, due to
the tremor of the user will be referred to, in this paper, as “noise”.
Problem Description
In order to cancel the vibration of a person writing with a tremor, the actual
marking component of the pen needs to be isolated from the tremor motion input. The
principal is for the pen tip to maintain a fixed position on the page, and not change
direction or position due to the person’s vibration but only when deliberately pushed by
the user in writing. This is accomplished by isolating the actual marking component of
the pen from the handle by a spring system. The second will be selecting the springs and
weight of the writing component such that the inertia of the writing component resists
movement due to the user’s vibration and inertia can only be overcome when pushed by
the user, in writing.
Previous Research
Working with Dr. Ahkiko Kumagai (AK), Kosuke Naritomi (KN) of Kyushu
Sangyo University, as well as Tyron Tracy (TT), both graduate students at California
State University Sacramento, have performed research on a vibration isolation pen as
the
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topics. Improvement on the design of the KN, AK and TT concepts forms the basis of
this
thesis. The KN pens features three design concepts. One consists of a shell where the
penholder is suspended with leaf or helical springs that are attached to the inertial
weights. The second replaces the springs with a resilient sponge material, and the third
consists of ring magnets to replace the springs. The TT design is similar to that of KN but
features enclosed helical springs in place of the leaf springs. A common feature of these
researchers’ models is that the writing component of the pen are held in a tube shaped
penholder, on which weights are mounted, i.e. an “inner assembly”. Springs are mounted
to the weights as well as attached to the inside of an outer shell, which acts as the grip for
the pen user.
Forms were designed for this research to evaluate the pen performance, when
tested by essential tremors patients as well as forms for collecting feedback from the
patients with regard to the performance of the pen. These forms , were carried over for
use in this thesis study. Additional forms were also used in the pen performance
evaluation. All forms are in Appendix1.
Design Concepts
The models of Dr. Kumagai, Tyrone Tracy, and Kosuke Naritomi served as
springboard for this new concept which is a modification of theirs. In place of the leaf or
helical, springs, elastic rubber springs are substituted, first trying a membrane spring,
then switching to rubber bands in two directions and finally in one direction. These
springs offer six, rather than one degree of freedom, i.e. Linier and rotational movement
3
in the x, y, and z directions. This study assumes a tremor amplitude in one direction with
minute amounts of movement in the other 3 direction degrees, and minute rotations in 3
degrees. Despite small movements in these additional degrees, in the analysis section, the
system was treated as a one-degree system. Another change in the design is a shell design
that prevents the weighted inner assembly from contacting the inside of the shell. This
prevents “noise” or feedback in the form of the inner assembly impacting the shell and
transmitting vibration to the pen and canceling benefits resulting from the shell-inner
assembly isolation. A second design features a narrow shell with the weights positioned
outside the shell entirely, being both above and below the shell. This design produces the
same result as the window in the wider shell.
Theoretical
The spring (k) is on top, damper (B) is on the bottom, and the black square (m), to
the right, is the mass. The equation, modeling the behavior of these parameters is below.
F is the input force which, in this case, is the person’s tremor.
Figure 1 Mass Spring System(from Wikicommons , public domain)
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For a user whose tremor consists of a horizontal vibration parallel to a line passing
through both shoulders, this will be called the x direction. A tremor consisting of
movement toward and away from the user, perpendicular to the x-axis, will be designated
in the y direction etc. Movement of the mass spring system along an axis passing through
the length of the shell will be the z direction, not necessarily orthogonal with the x/y axis.
Since the pen spring mass system has six degrees of freedom, a multi degree vibration
analysis can be used. In this paper, it was decided to model the system in one degree
since the motion of the system is primarily in one direction which mirrors that of the
user’s tremor. There may be some minor rotation of the system, perpendicular to the
tremor direction, but movement for the other degrees seems negligible. The International
Essential Tremor Foundation considers a tremor of 4 to 7 Hz to be typical [3].
Since the springs are rubber bands, the behavior of the system, in the 5 degrees other
than the one featuring the tremor direction, may be more complex, even, than that of one
using six conventional spiral springs, and may be chaotic.
The equation that models one degree of freedom [4] is well known and is
𝑚𝑥̈ + 𝑐𝑥̇ + 𝑘𝑥 = (𝐴)𝑐𝑜𝑠(𝑤𝑡)
𝑥̈ (𝑡) + 2𝜉𝜔𝑛 𝑥̇ (𝑡) + 𝜔𝑛2 𝑥(𝑡) = 𝜔𝑛2 𝐴𝑒 𝑖𝜔𝑡
(1)
(2)
𝜔 = working frequency or the input frequency of the user. 𝜔𝑛 is the natural response of
the system.
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𝑘
𝜔𝑛 = √
(3)
𝑚
𝜉
=
𝑐
2𝑚𝜔𝑛
.
(4)
The steady state response is:
Z(iω)X(iω) e𝑖𝜔𝑡 = 𝜔𝑛2 A𝑒 𝑖𝜔𝑡
(5)
The impedance function representing the contribution of the sinusoidal input is. [4]
Z(iω)= 𝜔𝑛2 − 𝜔2 + 𝑖2𝜉𝜔𝜔𝑛
(6)
When a person’s tremor is known, it is convenient, for the sake of argument, to be
able to select a spring tension that optimizes the pen performance, i.e. there is no
resonance in the system, when in use. Full resonance is when:
𝜔
𝜔𝑛
=1
(7)
With full resonance there will be violent vibration making the pen unusable. If
𝜔
𝜔𝑛
greater, or less than or equal to 0.5, the system is not in resonance and the pen tip,
= 3 or
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theoretically, will be still, when the shell is vibrating. Estimating the user’s tremor
frequency, 𝜔, and inserting this in the equation
𝜔
0.5
= ωn will give a value for the natural
frequency which can be used to solve for a value of k, or spring constant using
𝜔𝑛
𝑘
= √𝑚 .
Inspection of the pens natural frequency, by eye, without the formal analysis
with an oscilloscope, suggests that equation 10 has a value of approximately 0.5, and is
on the left side of Figure 2.
Figure 1A Spring Constant Determination (Author’s Photograph)
An assumption is made that a stretched rubber band is stiff enough to obey
Hook’s law since in rest position, the rubber bands are stretched and fastened to both
sides of the shell. See Figure 5. The mass of the penholder assembly is known so m is
known. The pen tip does not vibrate on the paper when the shell is vibrating when the
inner assembly is weighted with 8 oz. or 0.2268 kg. Note that this figure was taken from
Wikicommons and the symbol δ in the figure corresponds to ξ in this paper, ωA = ω ,
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and ω0 = ωn are also nomenclature differences between the chart and this paper. In this
way, a user’s tremor frequency can be used to select an appropriate k, thereby selecting a
spring tension to optimize the performance of the pen. A rubber band can then be
selected to satisfy k by hanging a known weight from the rubber band and using this
to determine k with the equation s= - km, where s is the distance traveled by the
weight.
A spreadsheet can be used to solve for a range of k values given mass inputs or
vice-versa.
Spring Constant Table
m (kg)
0.23
0.23
0.23
0.23
ω(Hz)
4
5
6
7
ωn(Hz)
8
10
12
14
K
14.72
23
33.12
45.08
Table 1
A rubber band can be selected to satisfy k by hanging a known weight from
the rubber band and using this to determine k with the equation s= - km, where s is
the distance traveled by the weight. See the illustration of the spring constant
testing device, Figure1A.
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Figure 2 Resonance (From Wikicommons public domain)
Figure 2, above shows that ξ (δ) is semi-independent of
values of ξ share the characteristic that
𝜔
ωn
𝜔
ωn
. Since many
= 0.5, is not resonant, it would be ideal if 𝜉
were chosen such that the pen had optimum response, i. e., a relatively small value such
as 0.1. Inserting equation (9), below, into equation (8) and solving for 𝜉can be used to
determine the viscous damping coefficient.
Ftr = 𝐴𝑘[1 + (
2𝜔𝜉 2 0.5
) ] |𝐺(i𝜔)|
ωn
|𝐺(𝑖𝜔)| = [{(1-(
𝜔 2 2
))
ωn
+ (2 𝜉 (
(8)
𝜔
ωn
))2}0.5]-1.
(9)
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A rubber band can then be selected to satisfy k by hanging a known weight from the
rubber band and using this to determine k with the equation s= - km, where s is the
distance traveled by the weight. See the illustration of the spring constant testing
device,
Fabrication
Initially, rolled paper tubing was to be the design concept for the shells. The
advantages are that the materials are inexpensive; ease of fabrication and the fact the any
tube diameter and wall thickness is possible. The disadvantages are an inability to get a
precisely circular shell, strength of the shell against normal point forces arising from the
grip of the user, as well as difficulty in attachment of the springs to the body. Paper
tubing was abandoned if favor of readily available PVC pipe, notwithstanding the
limitations in wall thicknesses and diameters to work with.
The 1st model utilized membrane springs which consisted of a thin sheet of rubber
which covered the end of the shell like a drumhead. It was thought that the rubber would
flex in response to input vibration in the x, y, and z directions similar to the intent of the
foam springs in the KN model. However, in testing the model, the membrane spring was
unresponsive, and these springs were abandoned.
Rubber band springs, stretched between the penholder and screws on the outside of
the shell, were the next choice. Like the membrane springs, they offer three degrees of
movement. At first, rubber bands at 90-degree angles were used, but the lack of response
was similar to the membrane springs. When rubber bands were reduced to a 180-degree
alignment, good results were obtained. The photographs of the pen, Figure 5, clarifies the
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orientation of the rubber bands with the pen assembly and shell. The dimensions settled
on for the most successful models were a 35mm internal diameter for the shell, 147.5
mm shell length, 42.5 mm external shell diameter, and a slightly longer length for the Al
penholder. See the drawings in Appendix 2,
Figure 3 Paper Shell, Al penholder with small lead weight (Author’s Photograph)
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Figure 4 Membrane Spring (Author’s Photograph)
Progress in the design occurred when PVC pipe was selected for the shell, with
the rubber band springs anchored to the shell on the outside by looping around brass
screws. Four variations on the models were made. All are notched on the ends to retain
the rubber bands and keep the penholder centered in the shell while in use. All feature a
penholder, consisting of a four mm wide Al tube which is 0.5 mm in thickness. The
penholder is suspended by the springs in the center of the shell and protrudes at both
ends. Bushings that retain the rubber bands are made from rolled paper, or are store
bought plastic, depending on the variation.
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Figure 5 Cutout Shell. Shell is the medium grey external object in which the yellow screws are inserted to anchor the rubber band
springs , penholder is the grey thin object in the center of the assembly, the black disk weights are on the penholder. The cutaway is
simplified for ease in drawing.
The weights are adapted lead fishing weights. Numerous overall weights were
adapted and trial and error showed that about 8 ounces (0.226 kilograms) overall has
provided the best performance. The ideal weight is not a result of calculation. The inertia
of the weight assembly combined with the static and dynamic friction of a standard ball
point pen tip on the paper are the components that prevent the pen from shaking in
response to the tremor input from the user. The frequency ration discussed above follows
from the choice of weights. The pen tip is a store bought medium point.
Washers or bushings that retain the weights and springs in the proper positions on
the penholder can be Teflon washers, rolled and glued paper, metal sleeves with
setscrews, or of many other designs. In the prototypes developed here, rolled paper was
mostly used.
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As the prototypes evolved, many spring materials evolved. The initial, all over
membrane types (unsatisfactory) were made from the rubber, stretched of the ends of the
shell like a drumhead. Rubber bands, anchored to the outside of the shell by brass screws
were next tried. Best results were obtained when the rubber band springs were acting on
the penholder at a 180° angle. Initially, a 90° orientation was tried. For the successful
180° orientation, the bands are normal to the shell openings and the direction of the
tremor. See Figure 5.
Initially the shell was solid, but even the wide diameter resulted in collisions
between the inner assembly weights and the shell, resulting in noise input into the inner
assembly and resulting vibration and rough writing. One of the key improvements in this
pen design was the introduction of a cutaway shell, allowing the weights to swing outside
the body, thus avoiding the unwelcome input from shell, weight collisions.
An improvement attempt in pen design featured a 26.5 mm outer diameter shell,
with two 4 oz. weights mounted both above and below, and completely external to the
shell. The weight, action on the inner assembly is the same as for the cutout shell model.
This model comes closer to a more normal pen diameter for the user. The performance,
so far, for this model has been inferior to the cutout model. This model is shown in
Figure 6. The suspected reason is that the bottom weight is too close to the writing
surface and is therefore over damped, transferring too much energy to the upper weight,
resulting it a pendulum action by the upper weight, and resulting vibration to the pen tip.
Critical selection of values for k at both the top and bottom springs may improve
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the performance of this model. Also, a design with a shorter shell and the bottom weight
located further up from the pen tip may be an improvement.
Figure 6
External weight model
Another concept involves a movable or anchored plunger, which is a smaller
diameter piece of pipe that fits inside the shell. This plunger can be slid inside the shell to
apply tension to the lower spring, thus making it possible to adjust the spring tension.
This model also features the cutout, even though the figure shows a solid shell. A
variation of this consists of the plunger fixable in position using a wing nut assembly in
place of the spring-loaded plunger. A model with the wing nut assembly was constructed.
See Figure 7.
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Figure 7 Plunger Model
Initial Testing
On creation of the models, the pens were tested by Paul Dessau, Dr. Kumagai, and
Jose Mojica, a researcher working on a drafting arm restraint to assist tremor patients in
writing. It was found that since the pen tip constrains the bottom of the inner assembly,
use sends undue vibration to the top springs, where the tip is acting as a pivot, the
penholder as a moment arm, and undue vibration occurs at the top of the assembly. This
resulted in noise, in the form of feedback occurring in the pen tip, adding vibration at the
point where none is desired. Improvement in this defect occurred when additional springs
(rubber band) were added to the top part of the assembly. The increased stiffness reduced
the pendulum – moment arm effect. Like all parameters of the pen, the amount of
constraint at the top is best adapted to the tremor and writing behavior of the individual
user.
Additional sets of tests with the cutaway shell and narrow shell models were
conducted with members of the International Essential Tremors Foundation at Kaiser
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Permanente in Roseville California, as well as with the organization in Phoenix
Arizona.The writing results by persons with tremors of varying degrees of severity were
collected on forms and compared. A standard test form, see Appendix 1, was used
allowing the patients to draw a horizontal, vertical, and spiral line, using both a regular,
ergonomic, weighted, previous tremor, the drafting arm, and current tremor pen, enabled
the patient perform the tests with some improvement. The ergonomic pen, and the
weighted pen used in the tests are designs already available on the market. The
ergonomic pen has a wishbone shape that facilitates a different grip while the weight
pen resembles a standard writing instrument, but has several times the weight due to a
lead or tungsten core. The drafting arm, designed by Jose Mojica, has two articulated
arms with joints, adjustable for friction, that anchors to the edge of a table, and provided
resistance to the tremor with a result similar to the weighted pen. The results were highly
variable, depending on the person performing the test.
It became obvious from testing that there is a learning curve to becoming proficient
with the pen. It would be preferable if a person could write with it with no learning but
some inventions require mastery of their users, the violin being a good example. While
the straight strokes in standard handwriting are easy to execute, the curves in letters like
a, o, etc, are where a lot of learning is required. The pen tip encounters to most static
friction during these maneuvers and tends to release, uncontrollably while negotiating the
curve. Persons with tremors were tested, using the form in Appendix 1, page 21, and
tabulated on the table below tables 3 and 4. LOC is location, Roseville, Phoenix.
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User Feedback Table, Tremor Detail Questions.
Table 2.
18
User Feedback Table, Pen Model Effectiveness Questions.
Table 3.
19
User Feedback Table, Pen Model Effectiveness Questions.
Table 4.
The data from the trials can be summarized as follows. Of the 15 who participated in
the trials, but one of the persons had Essential Tremors (ET). One had neither Parkinson’s
nor ET. Most were right handed. A majority of the participants had tremors in their
dominant hand. A majority stated that their tremor is predominantly in one direction.
As for the various pen tests, the ergonomic and weighted pens produced the most
positive results, indicating that they have the advantage that there is a smaller or
nonexistent learning curve, in using them. The designer’s practice sessions with the pen
have made it apparent that a change to lighter pen pressure on the paper when the small
curve strokes are made creates an improvement. Each individual user will need to
practice and determine the details such as pen angle pressure, etc that will best work for
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them. Also, changes during the learning process, with respect to spring tension, may need
to be made. The suggested pen practice sheet is in Appendix 1.
Improvement Suggestions
Once the prototype is finalized for manufacture, the components can be made in a
method more becoming for a consumer product. The rubber bands need to be replaced
with a product made from a synthetic polymer since common rubber bands are made
from natural rubber and become brittle after a few months, eventually losing their
elasticity. Progress toward a narrow-bodied pen that uses to window design could
incorporate tungsten (W) rather than lead weights since W is almost twice as dense as
lead. Lead was used in the prototype design, as it is readily available and inexpensive.
Another
A thinner shell wall would be an improvement as the shell could be made narrower
and more like conventional writing instruments. The plastic used in the prototypes was
common PVC pipe since this was inexpensive and easy to work. Many other plastics can
be used as well as metal, to control the width of the shell. Design changes to ballpoint
such as more efficient ink release with the same amount of friction as well as a design
that permits less length for the pen protruding from the penholder.
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Appendix A
Test Forms
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Testing Form – Writing Instruments
Date: Oct. 20 (Sat.) 2012
Place: Sun Lakes, AZ
Sheet #
Please answer the following questions by putting a check mark over a box of
your answer.

Are you an ET or Parkinson patient? ET  Parkinson  Neither ET nor
Parkinson 
 Are you right-handed (RH) or left-handed (LH)?
RH 
LH 
 Is one directional dominant vibration a correct assumption?
Yes 
No 
(Please contact one of presenters if you don’t understand this question.)
 Please rate their effectiveness by circling below
a. “Regular ball-point pen” | Effectiveness: 0% 
25%  50% 
75% 
100%
b. "Ergonomic pen" | Effectiveness: 0%  25%  50% 
75% 
100%
c. "Weight pen" | Effectiveness: 0% 
25% 
50%  75% 
100%
d. “Our first prototype pen”
| Effectiveness: 0% 
25%  50%  75%  100%
e. “Prototype pen” by Paul Dessau
| Effectiveness: 0% 
25%  50%  75%  100%
f. “Vibration suppression drafting arm” by Jose Mojica
| Effectiveness: 0% 
25%  50%  75%  100%
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Please provide your sample hand writings using the instruments mentioned above
on the following pages.Sheet #
Select the writing instrument used. Please see the list of writing instruments on
Page 1.
a
b
c
d
e
f
Write the following sentence: “This is a sample of my handwriting.”
Draw the following patterns as closely as possible over the given paths.
The start point is indicated by “ “
Select the writing instrument used.
Please see the list of writing instruments on Page 1.
a
b
c
d
e
Write the following sentence: “This is a sample of my handwriting.”
Draw the following patterns as closely as possible over the given paths.
The start point is indicated by “ “
f
24
25
26
27
28
29
30
31
32
33
34
Appendix B
Pen Drawings
35
Cut out shell, Dimensions are in mm
36
Pen Holder, Dimensions are in mm
37
Lead Weight and Brass Screw, Dimensions are in mm
38
Narrow shell, Dimensions are in mm
39
Plunger, Dimensions are in mm
40
Works Cited
[1] Naritomi, K, 2005, “Vibration Reducing Pen for People With Tremors”, California
State University Sacramento
[2] Tyrone Tracy, 2009, “Vibration reducing pen for people with tremors”, California
State University Sacramento
[3] ITT website, http://www.essentialtremor.org/read.asp?docid=846 , 2012, webinar,
[4] Meirovitch, L, 1986, Elements of Vibration Analysis, McGraw-Hill Book Company,
New York pp. 1-67