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Finite element model to understand the role of fingerprints in generating vibrations

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Finite element model to understand the role of fingerprints in generating vibrations

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FINITE ELEMENT MODEL TO UNDERSTAND THE ROLE OF FINGERPRINTS IN
GENERATING VIBRATIONS

by

Deborah Mandy Lai Chuck Choo

A Dissertation Presented to the
FACULTY OF THE USC VITERBI SCHOOL OF ENGINEERING
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(BIOMEDICAL ENGINEERING)

May 2012

Copyright 2012 Deborah Mandy Lai Chuck Choo
ii
Table of Contents

List of Figures .................................................................................................................... iii
Abstract ............................................................................................................................... v
Introduction ......................................................................................................................... 1
Methods............................................................................................................................... 5
Results ............................................................................................................................... 11
A. Stick/Slip Detection ............................................................................................ 11
B. Normal Force ..................................................................................................... 13
C. Curvature ........................................................................................................... 14
D. Skin Dimensions ................................................................................................. 18
E. Reversing Direction ............................................................................................ 20

Discussion and Conclusion ............................................................................................... 22
References ......................................................................................................................... 25
Appendix ........................................................................................................................... 27

iii
List of Figures

Figure 1: Tactile sensor design. The pressure transducer is in the core of the finger
and detects vibration from sliding transduced through the fluid[3]. ............................2

Figure 2: Vibration data for the smooth skin (blue) versus the fingerprinted skin
(green) when the finger is slid on a textured surface. There is an evident
difference in modalities and amplitude between the two signals.................................3

Figure 3: (A) Simple domain to solve physics with differential equations. (B) The
complex geometry cannot be solved without a mathematically defined shape. (C)
The shape is divided into mathematically defined geometrical shapes to build a
model. ...........................................................................................................................4

Figure 4: Geometry of the 2D fingerprinted skin cross- section. The base (grey dash)
is fixed, the sides of the skin are free to move and horizontal and vertical point
loads are applied to the tip of the ridge (red arrows). ..................................................6

Figure 5: Segment of the 20-ridges skin to illustrate the dimensions of the skin and
point load application. Sth is the skin thickness, pwd the print width and pht is
the print height. The red arrows represent the vertical and horizontal point loads
applied on the print tips to produce a set displacement on the tips. .............................7

Figure 6: Flowchart illustrating the algorithm used to implement the stick/slip
simulation where Ft is the tangential force and Fn is the normal force on the
ridge tip and μ is the coefficient of friction. .................................................................9

Figure 7: Initial downward normal force applied on each ridge tip to model curvature
of the finger (radius of curvature= 0.5cm). The outer ridges have the maximum
load and the middle ridge has the minimum vertical load. ........................................10

Figure 8: Horizontal measured displacement of ridge tips 1 to 20 versus surface
displacement (disp_u). The slip “wavelength” is the surface displacement
between two “cascades” of slip. There is a transition period during which the
vertical compressive force dominates the horizontal displacement. The initial
downward displacement on the middle ridge was 2 um and the coefficient of
friction, μ was 0.2. .....................................................................................................11

Figure 9: Ratio of tangential force to surface displacement (disp_u). The “cascade” of
slip can be more easily identified here, at the point where Ft/Fn for all the 20
ridges falls to zero. .....................................................................................................12

Figure 10: Normal force generated in each ridge versus initial applied normal
displacement. Some of the tips were omitted for the sake of clarity. ........................13
iv
Figure 11: Sum of vertical forces developed across all the 20 tips versus vertical
displacement. The range vertical displacement used to detect texture is 1- 3 um. ....14

Figure 12: The slip wavelength of a 20-ridges curved skin is compared to a flat skin
with varying slip coefficient. The curved skin has a lower slip wavelength at low
slip coefficient than the flat skin. However, at high slip coefficient (> 0.3)
curvature has no effect on slip wavelength. ...............................................................16

Figure 13: The slip wavelength of a 20-ridges curved skin is compared to a flat skin
with varying vertical displacement. The curved skin has a lower slip wavelength
than the flat skin for all applied normal displacements. Coefficient of friction
was set at 0.2. .............................................................................................................16

Figure 14: The sum of vertical forces over 20 ridge tips in a curved (black) and a flat
(red) skin over 200 iterations. The slip coefficient was 0.2 and the middle tip
initial vertical displacement was 2 um. ......................................................................16

Figure 15: Slip wavelength versus skin thickness. Skin thickness has no effect on rate
of slip of the ridge tip. There is also no significant difference between the 8-
ridges model and the 20-ridges model.The thickness used in the actual model is
1/16 inch. ....................................................................................................................18

Figure 16: Horizontal Displacement of tip before it settles into a regular slip pattern
versus skin thickness. For thin skins (<1/8 inches), the thinner the skin the longer
it takes for the ridges to settle in a regular slip pattern (longer transition pattern).
For thin skins (<1/8), the 20-ridge model has a much longer transition period. ........18

Figure 17: Slip wavelength versus print width (pwd). Original print width used in the
model is 1/64 in and varying the print width has very little effect on the slip
wavelength (2.4- 2.8 um). The vertical displacement (at middle ridge) was 2 um
down and the slip coefficient was 0.2. .......................................................................20

Figure 18: Applied horizontal displacement profile over iteration/index number to
illustrate reversal of direction of horizontal displacement halfway through the
simulation (at index 100). ..........................................................................................21

Figure 19: Horizontal tip displacement measured versus iteration number. Reversal of
direction occurred at index 100. The vertical downward displacement was 2 um
and the slip coefficient was 0.2. .................................................................................21

Figure 20: Sum of vertical forces across the 20 ridge tips. Reversal of direction
occurred at step 100 at which point the pattern of normal force is inverted about
the horizontal axis, corresponding to a change in direction of horizontal
displacement. .............................................................................................................21
v
Abstract

In the human finger, specialized transducers capable of detecting micro-vibrations in the
skin as it slides over a surface make it possible to discriminate textures and identify slip
events. Robotic fingertips modeled after biological designs have been proposed to
perform this sensing function as well. In artificial sensors, it has been found that ridges
on the finger skin that mimic the shape and structure of fingerprints greatly increase the
amplitude and spectral richness of the vibrations that are sensed as the finger slides over
various textured surfaces. We speculate that such a behavior is the result of division of
the skin surface into "stick/slip" regions, amplifying the vibrations in the skin and
increasing tactile sensitivity. Finite Element models have been built to model the partial
incipient slippage of fingerprint ridges during grip control, but none for texture
discrimination. This thesis presents a finite element model of skin ridges with individual
friction that simulates the pattern of stick and release of ridges that could give an insight
into the mechanism behind their role in generating vibrations.
1
Introduction

In the human finger, specialized transducers capable of detecting micro-vibrations in the
skin as it slides over a surface make it possible to discriminate textures and identify slip
events. When texture perception was studied, evidence pointed that texture perception
relied on two distinct mechanisms, one for the detection of coarse surfaces (spatial
periods above 200 μm) and one for fine surfaces. Hollins and Risner [5] successfully
demonstrated this difference in mechanism when coarse texture discrimination was
equivalent in a stationary finger and a moving finger, while with fine textures
discrimination is only possible in a scanning finger. Hollins and Risner[5] attributed the
poor performance for fine texture discrimination in the stationary condition to the
absence of vibrations due to the lack of motion of the finger with respect to the surface.
In contrast, the ability to discriminate coarse textures was not affected by the lack of
movement because the perception of coarse textures does not rely on vibrations but rather
on static patterns of skin deformation[1].

Such a complex behavior requires finely tuned sensory neurons capable of detecting the
different spatial and temporal modalities of a textured surface. Based on further
biophysical, physiological, and psychophysical evidence, it wasdetermined that coarse
surfaces are coded in terms of their spatial properties [2]and mediated by slowly adapting
type-I (SA-I) afferents[6]. On the other hand, Bensmaia and Hollins[1]observed that finer
surfaces are perceived primarily on the basis of the vibrations they produce in the skin
2
through the Pacinian corpuscles. Pacinian corpuscles have frequency responses of 60-500
Hz [9]and are capable of measuring vibrations associated with fine texture during
exploratory methods[6].

Robotic fingertips modeled after biological designs have been proposed to perform this
sensingfunction of the human finger by detecting two categories of events: static forces
(normal and tangential to the surface) and dynamics (sliding across a surface). Fishel et
al. [3] developed an easily repaired, durable, yet sensitive and precise tactile sensing
device (Figure 1). It has a replaceable compliant skin with sensing element or electronic
connection. The rigid core, to which the skin is attached, contains a biomimetic tactile
array of sensing electrodes that can detect deformation of a fluid-filled space [14]. The
fluid used in the finger pulp is incompressible, has a low viscosity and is an efficient
conductor of acoustic frequencies such that vibrations in the skin and in the fluid can be
detected using a pressure transducer inside the protective core of the finger[3].

Figure 1: Tactile sensor design. The pressure transducer is in the core of the finger and detects vibration from sliding
transduced through the fluid[3].

3
While characterizing the vibration-sensing characteristic of the tactile sensor, it was
observed that adding ridges on the finger skin that mimic the shape and structure of
fingerprints greatly increase the amplitude and spectral richness of the vibrations that are
sensed as the finger slides over variously textured surfaces (Figure 2)(unpublished
results).Other studies have indeedobserved that fingerprints amplify pressure modulation
signals induced by a texture by up to a 100 times and with frequencies of 200-300 Hz,
which is well within the range Pacinian corpuscle sensitivity [12]. It was also observed
that the relative orientation of scanning axis and fingerprints in contact with surface
determines to a large extent the spectrum of skin vibration [10].We speculate that this
occurs as a result of storage of energy in the strained elastic fingerprint ridges and
coherent release of mechanical energy as slip of one ridge affects the distribution of stress
in the others. This could divide the skin surface into “stick/slip” regions, amplifying the
vibrations in the skin and increasing tactile sensitivity.

Figure 2: Vibration data for the smooth skin (blue) versus the fingerprinted skin (green) when the finger is slid on a
textured surface. There is an evident difference in modalities and amplitude between the two signals.

4
Finite element modeling has been previously used to solve complex friction problems;
especially when instantaneous observations during a simulation are needed for every step.
Finite element methodis the division of a given domain into a set of simple subdomains,
called finite elements, and an approximate solution to the problem is developed over each
of these. It has the advantages of allowing analytical representation of complex
geometries and accurate representation of the solution within each element, to bring out
local effects [11].

Figure 3: (A) Simple domain to solve physics with differential equations. (B) The complex geometry cannot be solved
without a mathematically defined shape. (C) The shape is divided into mathematically defined geometrical shapes to
build a model.
Finite element modeling has been previously used to detect partial incipient slip in
fingertip systems, but none have implemented a model to study the effect of fingerprints
on texture discrimination. Yamada et al. [15]designed a model of the artificial finger
having ridges and distributed tactile sensors in an attempt to detect stick and slip for grip
control. While slip was successfully detected, the model had oversized dimensions and
stopped the simulation once the first slip was detected, without observing the sequence of
slip of ridges with respect to each other or the re-sticking ridges. Ho and Hirai [4]also
came up with a dynamic sliding motion of a 2-D model of a soft fingertip using finite
virtual cantilevers, which are compressible, tensile and bendable. However, they failed to
(A) Simple domain to
solve physics with
differential equations
(B) Cannot be solved
without mathematically
defined shape
(C) Shape divided into
mathematically defined
geometrical shapes to build a
model

5
specify any interaction between the cantilevers, which is an important part of simulating a
“redistribution” of stresses in the ridges when one of them slip. The aim of this study is to
build a finite element model of a finger skin to understand the role of fingerprints in
generating vibrations. This may provide a useful basis for designing algorithms whereby
such vibratory information could be processed in order to perceive and discriminate
various textures by a human finger with a nervous system or a robotic finger with a
digital processor.
Methods

The skin model is built as a 2D cross-section of the skin in COMSOL 4.2 with COMSOL
MatlabLiveLink as shown in figure 4. The geometry and meshing of the 20-ridges skin
was built in COMSOL. Each ridge has a skin thickness of 1.58 mm (1/16 in) and a print
width of 0.397 mm (1/64 in) for the rectangular 8-nodes quadratic rectangular element
(Q8). The ridges are made up of quadratic 6-nodes triangles (T6) with print height of
0.198 mm (1/128 in).The base is fixed and the rest of the segments are completely free to
move (figure 6). The above dimensions and units were selected according to the BioTac
manufacturer’s specifications [14].
At the tip of each ridge (red arrows), a point load is applied using a stiff spring:

_

_

6
Where kstiff is 1E10 N/m(the spring coefficient of a very stiff spring), disp_u is the
assigned displacement and u is the displacement calculated by COMSOL due to the point
load. Noslipstate is a coefficient that is 1 when the node sticks and 0 when the node slips.
A stiff spring is used here in order to assign known horizontal and vertical displacements
(disp_u and disp_v) to a ridge through the application of a point load.

Figure 4: Geometry of the 2D fingerprinted skin cross- section. The base (grey dash) is fixed, the sides of the skin are
free to move and horizontal and vertical point loads are applied to the tip of the ridge (red arrows).
7

Figure 5: Segment of the 20-ridges skin to illustrate the dimensions of the skin and point load application. Sth is the
skin thickness, pwd the print width and pht is the print height. The red arrows represent the vertical and horizontal point
loads applied on the print tips to produce a set displacement on the tips.
The stick/slip boundary conditions were applied using MATLAB LiveLink. The
algorithm is illustrated in Figure 6.

The ridges are initially compressed a distance of disp_v. Initial horizontal displacement
disp_u is zero and advanced by a displacement defined by the resolution of the simulation
(step-size and final disp_u). At every loop, ratio of tangential force (Ft) and normal force
(Fn) are calculated at each ridge tip so that the ridge tip with the maximum Ft/Fn can be
determined. The ridge tip with the maximum Ft/Fn is the first one to slip. If the
maximum Ft/Fn exceeds a set coefficient of friction μ, the ridge is considered to “slip” by
setting noslipstate=0, consequently making horizontal point load zero. The vertical point
pht
sth
pwd
8
load is maintained during slip. The ratios of Ft/Fn in the remaining ridge tips that resulted
from the slippage of the first ridge are calculated and the maximum Ft/Fn calculated
again. The loop is set up so that the disp_u is only advanced to the next step if the
previous iteration found no slip in any of the ridges. This creates a slippage "cascade"
effect through the whole skin, triggered by the first ridge slipping.

9

Calculate Ft/Fn in
other ridges
Calculate max
Ft/Fn
Yes
SLIP

Calculate max
Ft/Fn

?
Yes
SLIP
Apply Load
Advance
Displacement
Calculate Ft/Fn
No
No

?
Figure 6: Flowchart illustrating the algorithm used to implement the stick/slip
simulation where Ft is the tangential force and Fn is the normal force on the ridge
tip and μ is the coefficient of friction.
10
Curvature was also an important aspect of the geometry of a finger. To model the
curvature of the straight skin in figure 4, the initial vertical displacement disp_v was
varied from ridge tip 1 to ridge tip 20, with the outer ridges having the maximum
downward vertical load and the middle ridge having the minimum downward vertical
load as shown in figure 7. The radius of curvature of the skin was set at 0.5 cm.

Figure 7: Initial downward normal force applied on each ridge tip to model curvature of the finger (radius of curvature=
0.5cm). The outer ridges have the maximum load and the middle ridge has the minimum vertical load.
Most humans instinctively use a V-shaped velocity profile (velocity vs. lateral position)
[13]. While many studies investigate the effect of scanning speed on perceived roughness
[7, 8], none of them addressed the V-shaped profile that is the lateral to-and-fro
movement of the finger. In order to investigate the effect of change in direction of
scanning motion on the fingerprints, disp_u is set to reverse signs (from positive to
negative) at an arbitrary iteration in the simulation. For example, disp_u is switched to –
disp_u at index 100 if the scanning direction needs to be reversed in the middle of a 200-
step simulation.
‐0.05
‐0.045
‐0.04
‐0.035
‐0.03
‐0.025
‐0.02
‐0.015
‐0.01
‐0.005
0
12345678 9 1011121314151617181920
Initial Vertical Force (N)
Ridge Number
11
Results
The simulations were performed with different slip ratios, initial vertical displacements,
print widths and skin thicknesses. The simulation was also performed with a flat skin,
curved skin of radius 0.5cm.
A. Stick/Slip Detection
For each simulation, the horizontal tip displacement (u), normal force (Fn), horizontal
force (Ft) and sum of vertical forces over all the ridges ( ΣFn) were calculated and plotted
against either assigned horizontal displacement (disp_u) or iteration number.A “cascade”
of slip is defined as all 20 ridges slipping at the same value of disp_u (but not necessarily
at the same iteration in the loop). The rate of slip (or slip wavelength) is the horizontal
displacement of the tip (disp_u) between two “cascades” of slip, as shown in figure 8.

Figure 8: Horizontal measured displacement of ridge tips 1 to 20 versus surface displacement (disp_u). The slip
“wavelength” is the surface displacement between two “cascades” of slip. There is a transition period during which the
vertical compressive force dominates the horizontal displacement. The initial downward displacement on the middle
ridge was 2 um and the coefficient of friction, μ was 0.2.
λ
Transition period
12
The horizontal tip displacement plot shows an initial “transition” period (Figure 8), where
the vertical point load due to the initial compression is dominating the horizontal
displacement. The ridges are compressed down and as they all move horizontally in a
positive direction they stabilize in a regular slip pattern.

Assuming a mean scanning velocity of 20 mm/s previously reported by Vega-Bermudez
et al. (1991) and a slip wavelength of 2.8 um/s for a vertical displacement of 2 um and a
slip coefficient of 0.2, the frequency is calculated to be 7143 Hz, which is much higher
than the Pacinian corpuscles sensitivity frequency[12].

Figure 9: Ratio of tangential force to surface displacement (disp_u). The “cascade” of slip can be more easily identified
here, at the point where Ft/Fn for all the 20 ridges falls to zero.

λ
13
B. Normal Force
Initial vertical force generated in the ridge tips is plotted against different vertical
displacements in the middle ridge of the curved finger (disp_v) in figure 10.

Figure 10: Normal force generated in each ridge versus initial applied normal displacement. Some of the tips were
omitted for the sake of clarity.
Figure 10 shows that the normal force generated in each tip is proportional to the normal
applied displacement. The overlapping of opposite ridges (for example tip 1 overlapping
tip 20) shows that the physics of the model is behaving well with respect to the symmetry
of the skin.

-0.12
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.E+00 1.E-06 2.E-06 3.E-06 4.E-06 5.E-06 6.E-06
Normal Force (N)
Normal Displacement (m)
Tip 1
Tip 2
Tip 4
Tip 6
Tip 8
Tip 10
Tip 12
Tip 20
14

Figure 11: Sum of vertical forces developed across all the 20 tips versus vertical displacement. The range vertical
displacement used to detect texture is 1- 3 um.
The vertical forces over the 20 ridges are summed and plotted against normal applied
displacement at the middle ridge. Experiments where a human subject freely scanned a
surface mounted on a force plate determined that the force applied on a surface by a
finger during texture discrimination ranged between 0.26 N and 1.29 N[8]. According to
the model above, this range of force would correspond to a vertical downward
displacement between 1 and 2.5 um. Therefore, a vertical displacement of 2 um was used
throughout the rest of the simulations.

C. Curvature
The effect of curvature on the stick/slip behavior of the model is shown in Figure 12. A
curved skin has lower slip wavelength than a flat skin at low coefficient of friction (<0.3).
However, at high coefficient of friction, there is no difference between the two skins. The
slip wavelength of curved skin was also compared to the flat skin with varying initial
vertical displacements, while the coefficient of friction was kept constant at 0.2. The
‐2
‐1.8
‐1.6
‐1.4
‐1.2
‐1
‐0.8
‐0.6
‐0.4
‐0.2
0
0.E+00 1.E-06 2.E-06 3.E-06 4.E-06 5.E-06 6.E-06
Force (N)
Normal Displacement, disp_v (m)
15
curved skin had lower slip wavelength than the flat skin for all initial vertical
displacements. They both followed the same trend that is as vertical displacement
increases, so does the slip wavelength (figure 13). The lower slip wavelength in the
curved skin might be due to a lower vertical force at the outer tips that will cause Ft/Fn to
reach the slip coefficient threshold faster at outer tips and induce slip in the rest of the
tips more frequently. At high coefficients, the effect of friction dominates that of vertical
force and the two slip wavelengths remain very similar.

16

0
1
2
3
4
5
6
0.1 0.2 0.3 0.4 0.5
Slip Wavelength (um)
Slip coefficient
Curve No Curve
0
1
2
3
4
5
6
12 34 5
Slip Wavelength (um)
Normal Applied displacement (um)
Curve No Curve
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0 50 100 150 200
Force (N)
Step number
Curve NoCurve
Figure 12: The slip wavelength of a 20-
ridges curved skin is compared to a flat
skin with varying slip coefficient. The
curved skin has a lower slip wavelength
at low slip coefficient than the flat skin.
However, at high slip coefficient (> 0.3)
curvature has no effect on slip
wavelength.

Figure 13: The slip wavelength of a 20-
ridges curved skin is compared to a flat
skin with varying vertical displacement.
The curved skin has a lower slip
wavelength than the flat skin for all
applied normal displacements.
Coefficient of friction was set at 0.2.

Figure 14: The sum of vertical forces
over 20 ridge tips in a curved (black)
and a flat (red) skin over 200 iterations.
The slip coefficient was 0.2 and the
middle tip initial vertical displacement
was 2 um.

17
The net force across the 20 nodes was also calculated in both the curved skin and the flat
skin over 200 iterations. The flat skin (red) does have a slightly higher net normal force
than the flat skin (black) although the difference is barely noticeable. This might further
contribute to the lower slip wavelength observed in the curved skin, although the outer
ridges slipping first and provoking the slip “cascade” might be a bigger factor in the slip
wavelength difference.

18
D. Skin Dimensions

Figure 15: Slip wavelength versus skin thickness. Skin thickness has no effect on rate of slip of the ridge tip. There is
also no significant difference between the 8-ridges model and the 20-ridges model.The thickness used in the actual
model is 1/16 inch.

Figure 16: Horizontal Displacement of tip before it settles into a regular slip pattern versus skin thickness. For thin
skins (<1/8 inches), the thinner the skin the longer it takes for the ridges to settle in a regular slip pattern (longer
transition pattern). For thin skins (<1/8), the 20-ridge model has a much longer transition period.
The effect of skin thickness and the number of ridges on slip wavelength and the
transition period (see figure 8) was also observed. While it is certain that a 20-ridge
model would be a better representation of reality, it was important to see if the model
could be reduced to fewer ridge tips for computational efficiency reasons. As shown in
1/4
1/8 1/16
1/32
0
0.5
1
1.5
2
2.5
3
0 1/20 1/10 3/20 1/5 1/4 3/10
Slip Wavelength (um)
Thickness (in)
20 ridges 8 ridges
1/4 1/8
1/16
1/32
0
5
10
15
20
25
0 1/20 1/10 3/20 1/5 1/4 3/10
Horizontal Displacement disp_u(um)
Thickness (in)
20 ridges 8 ridges
19
figure 15, skin thickness has no effect on rate of slip of the ridge tip. There is also no
significant difference between the 8-ridges model and the 20-ridges model unless the skin
becomes very thick (>1/8 in). Since the model has a skin thickness of 1/16 inch, the
model is not very sensitive to changes in thickness.

From figure 16, it is observed that the thinner the skin the longer it takes for the ridges to
settle in a regular slip pattern (longer transition period), so long as the skin is thinner than
1/8 inch. The 20-ridges model also has a higher transition period in the same thickness
range and highlights the need for a 20-ridges curved model versus a reduced 8-ridges
model.

Print width (pwd- see figure 8) was also varied from 1/150 inch to 1/50 inch with a
downward vertical displacement of 2 um, with the original pwd in the model to be 1/64
inch. The slip wavelengths ranged from 2.4 um to 2.8 um, which indicates that the slip
wavelength is not very sensitive to changes in print widths.

20

Figure 17: Slip wavelength versus print width (pwd). Original print width used in the model is 1/64 in and varying the
print width has very little effect on the slip wavelength (2.4- 2.8 um). The vertical displacement (at middle ridge) was
2 um down and the slip coefficient was 0.2.
E. Reversing Direction
The effect of reversing the direction of the horizontal applied displacement (disp_u) on
the stick/slip pattern was included in the simulation by switching disp_u to a negative
value halfway through the simulation.

1/50
1/64
1/80
1/128
1/150
0
0.5
1
1.5
2
2.5
3
0 1/200 1/100 3/200 1/50 1/40
Slip wal=velength (um)
Ridge width (in)
21

-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0 50 100 150 200
Force (N)
Step number
Curve Curve Reverse
(m)
Index
Figure 18: Applied horizontal displacement
profile over iteration/index number to
illustrate reversal of direction of horizontal
displacement halfway through the simulation
(at index 100).

Figure 19: Horizontal tip displacement
measured versus iteration number. Reversal
of direction occurred at index 100. The
vertical downward displacement was 2 um
and the slip coefficient was 0.2.

Figure 20: Sum of vertical forces across
the 20 ridge tips. Reversal of direction
occurred at step 100 at which point the
pattern of normal force is inverted about
the horizontal axis, corresponding to a
change in direction of horizontal
displacement.

22
The results above (figure 18 to 20)show that when the horizontal displacement is
reversed, both the horizontal tip displacement and the sum of normal force are inverted
about the horizontal axis with no change in slip wavelength.
Discussion and Conclusion
This thesis has described initial research on finite element model of a finger skin to
understand the role of fingerprints in generating vibrations during tactile exploration. The
quasi-static model was successful in modeling the stick and slip that occurs when two
surfaces are in contact with each other. A robust algorithm was develop to link the
fingerprint ridges together, so that the slippage of one ridge would affect the next one and
cause a “cascade” of slip throughout the skin. Detecting stick and slip patterns of each
ridge on the skin can help us better understand the vibrations that arise due to the release
of mechanical energy when a region of the skin ridge slips.

The geometry and material properties of the model were validated as the downward
displacement applied on the ridges produced similar forces previously reported in
literature[8]. As expected, the model was symmetrical about the central ridge, showing
that the geometry built in COMSOL was behaving correctly.

A vertical displacement and a horizontal displacement were applied on each tip ridge as
point loads to induce a stick/slip behavior at the tips similar to two surfaces in contact. It
was found that modeling 20 ridges instead of just 8 ridges and curvature played an
23
important role in the rate of slippage of the ridge tips. On the other hand, variations in
skin thickness and print width had very little effect on slip wavelength for the dimensions
of our model.

A vertical displacement and a horizontal displacement were applied on each tip ridge as
point loads to induce a stick/slip behavior at the tips similar to two surfaces in contact. It
was found that modeling 20 ridges instead of just 8 ridges and curvature played an
important role in the rate of slippage of the ridge tips. On the other hand, variations in
skin thickness and print width had very little effect on slip wavelength for the dimensions
of our model. When considering the average scanning velocity of the human finger when
judging texture, the frequency of slip was much higher than expected or reported in
literature [12].Furthermore, when the horizontal displacement direction was reversed,
there was no additional disturbance in slip pattern or change in the rate of slip except for
a change in horizontal displacement from positive to negative. The model is a quasi-static
model, where dynamics such as a time domain, inertia, velocity and accelerations of the
ridges with respect to each other have not been implemented. Adding dynamics to the
model could contribute to “damping” the high frequencies so that the lower frequency
modulations can be observed. Dynamics can also provide more accurate insight on how
the ridges slipping interact with each other, especially when the scanning direction is
reversed. Vertical downward displacements (disp_v) were also kept constant from the
initial value, which would represent scanning the finger over a perfectly flat surface. In
order to correctly model texture discrimination, the vertical displacement should be
24
varied, similar to scanning over a "bumpy" surface. Vertical displacement could be varied
throughout the simulation as a sinusoid to keep it simple, or randomly with some
maximum amplitude for more complex surfaces.
The current model has successfully simulated the stick and slip behavior of fingerprint
ridges during friction with accurate geometry. It has implemented a robust algorithm to
help us understand how the slip of one ridge affects its neighboring ridge and the finger
skin as a whole. The next step of for the project is to add dynamics to the model to give
us insight about the role of fingerprints in detecting textures, and what the modalities in
the skin vibrations really mean.

25
References

[1] Bensmaia, S. and Hollins, M., "Pacinian representations of fine surface texture,"
Perception & Psychophysics, vol. 67, pp. 842-854, 2005.

[2] Connor, C. E. and Johnson, K. O., "Neural coding of tactile texture: comparison
of spatial and temporal mechanisms for roughness perception," The Journal of
Neuroscience, vol. 12, pp. 3414-3426, 1992.

[3] Fishel, J. A., Santos, V. J., and Loeb, G. E., "A Robust Micro-Vibration Sensor
for Biomimetic Fingertips," IEEE, vol. In press, 2008.

[4] Ho, V. A. and Hirai, S., "Two-dimensional dynamic modeling of a sliding motion
of a soft fingertip focusing on stick-to-slip transition," in Robotics and
Automation (ICRA), 2010 IEEE International Conference on, 2010, pp. 4315-
4321.

[5] Hollins, M. and Risner, S., "Evidence for the duplex theory of tactile texture
perception," Attention, Perception, & Psychophysics, vol. 62, pp. 695-705, 2000.

[6] Johnson, K. O., Hsiao, S. S., and Yoshioka, T., "Book Review: Neural Coding
and the Basic Law of Psychophysics," The Neuroscientist, vol. 8, pp. 111-121,
April 1, 2002.

[7] Klatzky, R. L. and Lederman, S. J., "Touch," in Handbook of Psychology, ed:
John Wiley & Sons, Inc., 2003.

[8] Lederman, S. J., Howe, R. D., Klatzky, R. L., and Hamilton, C., "Force variability
during surface contact with bare finger or rigid probe," in Haptic Interfaces for
Virtual Environment and Teleoperator Systems, 2004. HAPTICS '04.
Proceedings. 12th International Symposium on, 2004, pp. 154-160.

[9] Mountcastle, V. B., LaMotte, R. H., and Carli, G., "Detection thresholds for
stimuli in humans and monkeys: comparison with threshold events in
mechanoreceptive afferent nerve fibers innervating the monkey hand," Journal of
Neurophysiology, vol. 35, pp. 122-36, 1972.

[10] Prevost, A., Scheibert, J., and Debrégeas, G., "Effect of fingerprints orientation on
skin vibrations during tactile exploration of textured surfaces," Communicative &
Integrative Biology, vol. 2, pp. 422-424, 2009.

26
[11] Reddy, J. N., An Introduction to The Finite Element Method, 3rd Edition ed. New
York: McGraw Hill, 2006.

[12] Scheibert, J., Leurent, S., Prevost, A., and Debrégeas, G., "The Role of
Fingerprints in the Coding of Tactile Information Probed with a Biomimetic
Sensor," Science, vol. 323, pp. 1503-1506, 2009.

[13] Vega-Bermudez, F., Johnson, K. O., and Hsiao, S. S., "Human tactile pattern
recognition: active versus passive touch, velocity effects, and patterns of
confusion," Journal of Neurophysiology, vol. 65, pp. 531-546, March 1, 1991
1991.

[14] Wettels, N., Santos, V. J., Johansson, R. S., and Loeb, G. E., "Biomimetic Tactile
Sensor Array," Advanced Robotics, vol. 22, pp. 829-849, 2008.

[15] Yamada, Y., Fujimoto, I., Morizono, T., Umetani, Y., Maeno, T., and Yamada,
D., "Development of artificial skin surface ridges with vibrotactile sensing
elements for incipient slip detection," in Multisensor Fusion and Integration for
Intelligent Systems, 2001. MFI 2001. International Conference on, 2001, pp. 251-
257.

27
Appendix

The following is a print out of the MATLAB .m file used to simulate the stick/slip
transition in the COMSOL model.

%% Load model1 trial1_matlab
clear all, clc
model1=mphload('curve_20nodes_rev.mph');

Num=20;
% Retrieve coordinates
tip{Num} = [0 0];
for n = 1:Num
tip{n}=mphgetcoords(model1,'geom1','point',3*n);

end

%% Set Parameters

SlipRatio=0.4;
numsteps = 200;
step= 80e-6/numsteps;
Frac=1; % Fraction of total index at which reversal occurs
%model1.param.set('disp_v',2e-6);
middle_v= 4e-6; % displacement at center of the finger

%% Set curvature of ridges

for n = 1:Num, ni = int2str(n);
pwd=mphinterp(model1, 'p_wd','coord',tip{n});
sth=mphinterp(model1, 's_th','coord',tip{n});
radcurve=1; % RADIUS of curvature of finger

ax=(Num/2)*pwd; % x coord of circle
by=0;%-1*(radcurve-sth); %y coord of circle
dispv(n)=sqrt((radcurve^2)-(tip{n}(1)-ax)^2)+by; % curvature of
finger
%model1.param.set(['disp_v' ni],sqrt((radcurve^2)-(tip{n}(1)-
ax)^2)+by);

model1.param.set(['disp_v' ni],dispv(n)*middle_v);
fv(n)=dispv(n)*middle_v;
end

%% Initialize
uSurf=zeros(numsteps,1);
uNs = zeros(numsteps,Num);
FxNs = zeros(numsteps,Num);
28
FyNs = zeros(numsteps,Num);
FrNs = zeros(numsteps,Num);
slipNs = zeros(numsteps,Num);

%% Compression Step
index1 = 1;

uSurf(1) = 0;
for n = 1:Num, ni = int2str(n);
model1.param.set(['disp_u' ni],0);
end

% Compute the solution and save Vars
model1.sol('sol1').run
fprintf('\n%i/%i : uSurf = %i : ',index1, numsteps, uSurf(index1)*10e6)
for n = 1:Num, ni = int2str(n);
uNs(index1,n) = mphinterp(model1,'u','coord',tip{n});
FxNs(index1,n) = mphinterp(model1, ['kstiff*(disp_u' ni '-
u)*noslipstate' ni],'coord',tip{n});
FyNs(index1,n) = mphinterp(model1,['kstiff*(-disp_v' ni '-
v)'],'coord',tip{n});
FrNs(index1,n) = -FxNs(index1,n)./FyNs(index1,n);
fprintf('%i - %f : ',n,FrNs(index1,n))
end

%% Start Loop
for index1 = 2:numsteps
if max(abs(FrNs(index1-1,:))) <= SlipRatio
if index1 >= 2 && index1<=(numsteps/Frac)
% Advance Loop in positive direction
uSurf(index1) = uSurf(index1-1) + step;
for n = 1:Num, ni = int2str(n);
if slipNs(index1-1,n) == 0
model1.param.set(['disp_u'
ni],mphinterp(model1,['disp_u' ni],'coord',tip{n})+step);
else
model1.param.set(['disp_u'
ni],mphinterp(model1,'u','coord',tip{n}));
end
model1.param.set(['noslipstate' ni],1);
end
else
% Advance Loop in negative direction
uSurf(index1) = uSurf(index1-1) - step;
for n = 1:Num, ni = int2str(n);
if slipNs(index1-1,n) == 0
model1.param.set(['disp_u'
ni],mphinterp(model1,['disp_u' ni],'coord',tip{n})-step);
else
model1.param.set(['disp_u'
ni],mphinterp(model1,'u','coord',tip{n}));
end
model1.param.set(['noslipstate' ni],1);
29
end
end

else
% Slipping Loop
uSurf(index1) = uSurf(index1-1);
slipNs(index1,:) = slipNs(index1-1,:);
for n = 1:Num, ni = int2str(n);
if abs(FrNs(index1-1,n)) >= SlipRatio
model1.param.set(['noslipstate' ni],0);
slipNs(index1,n) = 1;
fprintf('\nNode %i slipped',n)
end
end
end
% Compute the solution and save Vars
model1.sol('sol1').run

fprintf('\n%i/%i : uSurf = %.0f : ',index1, numsteps,
uSurf(index1)*10e6)
for n = 1:Num, ni = int2str(n);
uNs(index1,n) = mphinterp(model1,'u','coord',tip{n});
FxNs(index1,n) = mphinterp(model1, ['kstiff*(disp_u' ni '-
u)*noslipstate' ni],'coord',tip{n});
FyNs(index1,n) = mphinterp(model1,['kstiff*(-disp_v' ni '-
v)'],'coord',tip{n});
FrNs(index1,n) = -FxNs(index1,n)./FyNs(index1,n);
FyNs_sum(index1)=sum(FyNs(index1,:));

fprintf('%i - %f : ',n,FrNs(index1,n))
end
end

FyNs_sum=FyNs_sum';

%% PLOT RESULTS

leg= {};
for n=1:Num
leg{n}=['Tip' int2str(n)];
end
legend(leg)

% ForceRatio
figure(1)
plot(uSurf, FrNs)
title('ForceRatio F_t/F_n')
ylabel('F_t/F_n')
xlabel('Surface Displacement')
legend(leg)
axis tight
30
grid on
saveas(gcf,'4umCurveRatio','jpg')

% TipDisp
figure(2)
plot(uSurf, uNs)
title('Horizontal Tip Displacement (m)')
ylabel('Tip Displacement (m)')
xlabel('Surface Displacement')
legend(leg)
axis tight
grid on
saveas(gcf,'4umCurveDisp','jpg')

% Vertical force
figure(3)
plot(uSurf,FyNs)
title('Normal Force developed at the Tip')
ylabel('Force(N)')
xlabel ('Tip Displacement (m)')
legend(leg)
axis tight
grid on
saveas(gcf,'4umCurveFy','jpg')

% Sum Vertical force
figure(4)
plot(1:index1,FyNs_sum)
title('Sum of Normal Force developed at the Tip')
ylabel('Sum Force(N)')
xlabel ('Tip Displacement (m)')
legend(leg)
axis tight
grid on
saveas(gcf,'4umFySumRev','jpg')

Abstract (if available)

Abstract In the human finger, specialized transducers capable of detecting micro-vibrations in the skin as it slides over a surface make it possible to discriminate textures and identify slip events. Robotic fingertips modeled after biological designs have been proposed to perform this sensing function as well. In artificial sensors, it has been found that ridges on the finger skin that mimic the shape and structure of fingerprints greatly increase the amplitude and spectral richness of the vibrations that are sensed as the finger slides over various textured surfaces. We speculate that such a behavior is the result of division of the skin surface into ""stick/slip"" regions, amplifying the vibrations in the skin and increasing tactile sensitivity. Finite Element models have been built to model the partial incipient slippage of fingerprint ridges during grip control, but none for texture discrimination. This thesis presents a finite element model of skin ridges with individual friction that simulates the pattern of stick and release of ridges that could give an insight into the mechanism behind their role in generating vibrations.

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Asset Metadata

Creator Lai Chuck Choo, Mandy Deborah (author)

Core Title Finite element model to understand the role of fingerprints in generating vibrations

School Viterbi School of Engineering

Degree Master of Science

Degree Program Biomedical Engineering

Publication Date 05/07/2012

Defense Date 05/07/2012

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag fingerprints,finite element model,OAI-PMH Harvest,robotics,texture,vibrations

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Loeb, Gerald E. (committee chair), Khoo, Michael C.K. (committee member), Valero-Cuevas, Francisco J. (committee member)

Creator Email laich002@gmail.com,laichuck@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-33063

Unique identifier UC11288932

Identifier usctheses-c3-33063 (legacy record id)

Legacy Identifier etd-LaiChuckCh-795.pdf

Dmrecord 33063

Document Type Thesis

Rights Lai Chuck Choo, Mandy Deborah

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA