Proceedings of Eurohaptics 2008, LNCS 5024, Springer-Verlag, pp. 229–237
http://www.disam.upm.es/~eurohaptics2008/

Tactile Illusion Caused by Tangential Skin Srain
and Analysis In Terms of Skin Deformation
Masashi Nakatani1 , Akihiro Sato2 , Susumu Tachi1 , and Vincent Hayward2
1

Graduate School of Information Science and Technology,
The University of Tokyo, Japan{nakatani,tachi}@star.t.u-tokyo.ac.jp
2
Haptics Laboratory, Center for Intelligent Machines,
McGill University, Montréal, Canada{aki,hayward}@cim.mcgill.ca

Abstract. We describe a new tactile illusion of surface geometry thatcan be easily produced with simple materials. When the fingertip skinis strained by loading it in traction along a narrow band surrounded by
two fixed traction surfaces, the sensation of a raised surface is typicallyexperienced. This and other analogous cases are discussed in terms oftissue deformation created at a short distance inside the skin where thetarget mechanoreceptors are presumably located. A finite element analysis allowed us to propose that the basis of this illusion is connected withthe observation that normal loading and tangential loading can create
similar strain distribution, thereby creating an instance of an ambiguous stimulus. In the discussion we relate this stimulus to several otherambiguous tactile stimuli.
Key words: tactile illusions, tactile perception, tangential skin stretch,ambiguous stimuli

1

Introduction

Not a small part of the tactile perception mechanisms remains mysterious. A
most interesting question is the manner in which the attributes of objects andsurfaces generate cues that eventually give rise to perception. Studies have shownthat many aspects of the physics of an object contribute to tactile perception. To
name a few, surface roughness, thermal properties, and compliance all contributeto the unified subjective experience of an object [1, 2]. Humans experience theworld outside using these properties. Surface flatness, and deviation from it,
could one of these attributes since the tactile sense excels at detecting suchdeviations as local features of high curvature [3], or shapes of low curvature [4].
The perception of the geometric attributes of surfaces makes it possible tograsp and manipulate objects, to appreciate the finish of surfaces, or even toread Braille. Several studies have shown that the experience of flatness can be
modified when the fingerpad is actively stimulated using certain geometric patterns or vibration [5, 6]. Other studies indicate that deforming the skin laterallyProceedings of Eurohaptics 2008, LNCS 5024, Springer-Verlag, pp. 229–237
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Nakatani, Sato, Tachi, Hayward

can produce the sensation of objects indenting the skin due to the inherently
ambiguous nature of mechanical stimulation [7], a phenomenon that has been
applied to the development of high-performance tactile transducers [8, 9].
In this paper, we describe a new stimulus that produces the sensation ofa narrow band being raised or lowered relatively to the side regions although
all the surfaces remain geometrically flush. This effect is caused by applying a
shearing load to the skin via the central band or via the neighboring surfaces.
Interestingly, this illusion is also effective in quasi-static conditions. The effectcould presumably be explained by mechanical factors, neurophysiological factors
at the periphery and centrally, as well as by higher level perceptual mechanisms.
Here, we focus on mechanical factors which, once understood, could provide
a basis on which a more complete account of why the conscious experience offlatness is modified by this stimulation. To this end, a detailed finite element
analysis of a three-layered skin model loaded as described was conducted. The
results indicate that, indeed, this loading pattern of traction creates at a shortdistance inside the skin, where the targeted mechanoreceptors would be located,a strain distribution that resembles the distribution caused by a geometricallyraised or indented narrow band, thereby creating an ambiguous stimulus.

2

Description Of The Stimulus

A schematic of the stimulus is shown in Fig. 1a. The stimulus consists of twoparts. The central plate has a narrow band extending from it. The other plate
has a matching slot. Combining the two plates together results in a flat plate.

a

center stripb
lateral plate
central plate

c

!

d

!

Fig. 1. Schematic of the stimulus. a, drawing of the stimulus. b, one hand manipulates
the plate, the other gounds it. The index finger is stimulated. c,d, a raised, respectively
recessed, surface is experienced.

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Tactile Illusion Caused by Tangential Skin Traction

3

The plates must have the same thickness, and the clearance should be tightso that the upper surface feels flush when stationary. The width of the central
band is preferably 3.0 mm. This width was determined from the study of a
related effect, the “fishbone illusion” [5], which provided the inspiration for thisreport. The plates were made of Delrin R plastic, but other materials could be
used. Sandpaper is glued on the upper surfaces to enhance tangential traction.
Variants of this stimulus can also be prepared with PostIt R notes as for the“ridge/trough illusion” [10], or cardboard of a cereal box, for instance. For thosevariants, glue or absence of it is used to vary adhesion. In the present instance,
the side regions or the central band are actively moved by an external agent
while the sensing finger remains passive.
To experience the illusion, place the two combined pieces of the stimulus ona flat surface. Then, hold down the sides of one piece with the thumb and middle
finger of one hand, and touch the center of the stimulus with the index finger ofthe same hand as shown in Fig. 1b. Hold the other piece with the other handand manually move it back and forth along the band direction (i.e. one piece is
moved and the other is fixed). An assistant can be called upon to apply the load.
The illusion may be experienced whether or not the moved section slips on thefinger, albeit with different intensity. In any event, the plates should not movevertically. Then, attend to the surface geometry under the index fingerpad, andevaluate whether it feels raised, indented, or flat during movement. Now, switch
roles of the two hands (or switch two plates) and evaluate it again. In either
case, the sensing index finger is stationary with respect to the fixed plate.
The apparatus and method above gave the authors illusory shape sensations.
Although the touched surface is geometrically flat, when one plate of the twoplates is moved, the central strip part felt higher or lower than the lateral regions.
The sensation of the surface no longer being flat is strong that it is easy to decide
which case creates the sensation of a raised band or of an indented band. The
central band feels raised when it is moved and indented when the lateral regions
are moved, see Fig. 1c,d.

3

Beginning Of An Explanation

What causes this illusion?, and why do these cases result in the sensation of araised or indented central band? An intuitive answer to the first question caneasily be imagined. The flat surface geometry of the two plates is the same,but the skin deformation is nonuniform and highly characterized, due to thetraction pattern created by the moving plate. The moving part pulls the skin in
one direction while the stationary part holds the skin. The skin stretch causedby the moving plate produces much more strain than the skin compression on
the flat surface at rest does. The uneven strain distribution in the finger padtissue may resemble that caused by a raised or depressed band. The association
between skin stretch and shape sensations has already been noted [9, 11].
As for the second question, one can easily imagine that a geometrically raised
band will cause more stimulation in the central region than in the sides. The

Proceedings of Eurohaptics 2008, LNCS 5024, Springer-Verlag, pp. 229–237
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Nakatani, Sato, Tachi, Haywardsame is true when pulling the central band sideways. A mirror situation occurs
when pressing the finger on a depressed band or when pulling the side regions
tangentially. While this sounds reasonable, it provides motivation for a morein-depth analysis.
Could it be that, inside the skin tissue regions where the mechanoreceptors
are located, the strain distribution caused by a geometrically raised or indented
band is similar to the distribution caused by partial surface traction of our
stimulus? If it is true, then the sensation should be similar, i.e., one cannot
distinguish the geometic surface caused by the normal load and the tangential
traction.
In order to pursue this explanation, a finite element analysis can be used toassess the strain distribution in the skin quantitatively. Although the results ofsuch simulation should be treated with the greatest caution, they can provide
valuable insight. Such models, to be reliable, particularly to predict the behaviorof living tissues, even more so at a small scale, should be extensively validatedby measurements, which is exceedingly difficult to do in our case.
Several other possibilities for analysis exist. One approach would be to record
the response of peripheral nerves. From the neural response of multiple fibers,
it would be possible — in principle — to evaluate the similarity of the ensemble
neural response to different physical stimuli. However, as discussed by Goodwin
et al. [12], current technology does not allow us to measure a large number ofmultiple neuron responses simultaneously.
Another complementary approach is to adopt a psychophysical method. Measuring human behavior to a stimulus can help us discover the input-output relation of the human tactile system. This is useful to model the relationship between
physical stimuli and perception but would not contribute directly to clarifying
the underlying mechanisms of the illusion. It would give little insight regarding
the mechanics of the strain distribution mentioned in the previous section.
With all its limitations, we must resort to a finite element analysis. Several
studies related to the tactile response using finite element methods have beenreported. These studies using 2D models [13, 14] and 3D models [15] provide
some insight regarding the relation of mechanical stimulation with mechanicaldeformation, and even with neural responses. In most physiology textbooks,
tactile perception of surface geometry is thought to result from normal pressure.
But here, normal pressure is uniform; a 2D-section model would not be sufficient
for analysis. In our study, the analysis of the strain tensor field in tissue volume
caused by tangential load requires a 3D model. In the following section, a finite
element model of skin deformation patterns in question is described.

4

Finite Element Analysis

Figure 2 shows the 3D finite element model used in our simulation.The model isa rectangular solid shape (10 × 20 × 6.75 mm in width, length and height). Thissolid is divided into three material regions having a uniform Young’s modulus
in each. These regions simulate the epidermis, the dermis, and the subcutaneousProceedings of Eurohaptics 2008, LNCS 5024, Springer-Verlag, pp. 229–237
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Tactile Illusion Caused by Tangential Skin Traction

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tissues. The thicknesses are 1.0, 0.75, and 5.0 mm respectively, and the Young’s
moduli are 0.136, 0.08, and 0.034 MPa, respectively. These data are taken from
Maeno et al. [14]. The number of tetrahedrons in the mesh is 8 637.
dermis E = 0.080 MPa

6.75 mmepidermis E = 0.136 MPa

1.00 mm0.75 mm20

5.00 mm

mm

m

10 m

subcutaneous tissues E = 0.034 MPa

Fig. 2. Three-dimensional finite element model used in the simulation.

The simulation was carried out in two steps with a view to tune the parameters to realistic values. In a first step, standard loads of 1 N were applied
to the six conditions shown in Table 1, top row. In these condition the block
is clamped on all sides but the upper surface and the loads are applied at theupper surface. The first and second conditions correspond to the case of a simple
normal and tangential loads. The third and fourth conditions are designed toevaluate the putative similarity of mechanical deformation between the normal
and tangential load applied in the central area. The fifth and sixth conditions
are mirror cases.
In a second step, the displacements observed in the first simulation wereapplied as boundary conditions in a second simulation. This time, however, thesubcutaneous tissues were not clamped to replicate more closely the natural
condition, except for the bottom surface to represent the bone anchor. This gave
another set of six conditions listed in Table 1, bottom row.
The strain of each component is calculated in the region between the epidermis and the dermis, where the mechanoreceptor cells are located [16].
Table 1. Six loading and displacement conditions examined in the analyses.
1: uniform 2: uniform 3: central
normaltangential
normal4: central 5: lateraltangential
normal6: lateraltangential

To analyze the data generated by the finite element model, we made theassumption that the receptor cells respond to the maximum strain, which is notProceedings of Eurohaptics 2008, LNCS 5024, Springer-Verlag, pp. 229–237
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Nakatani, Sato, Tachi, Hayward

3rd principal strain x10 -5 2nd principal strain x10 -5 1st principal strain x10 -5

specific to a particular direction. Moreover, the choice of coordinates selected toperform the simulation is arbitrary and is selected for convenience. Evaluating
the results in terms of principal strains eliminates the dependence of the resultson this choice.
The results of the two simulations are seen in Figs. 3 and 4. The principal
strain distribution in the tissue is different between conditions 1 and 2 (Fig. 3
and 4, left). On the other hand, the region where the surface load applied has apositive value in the center for both conditions 3 and 4 (Figs. 3 and 4, center).
Similarly, for conditions 5 and 6 (Figs. 3 and 4, right), the central area has only asmall strain value (almost zero) and the lateral areas have a positive value. The
maximum shear strain is also calculated based on the components of principal
strain by using the relationship between principal strain and principal shear
strain [17]. The results are similar to the top row of Figs. 3 or 4, and therefore
the plot is not shown here. This indicates that a similar pattern of strain andshear strain is applied in the area where the receptor cells would be located.

uniform load

central load1

lateral load

1 normal

0.5

tangential

0

normal

1

0.5
0

-0.5

0

tangential

-0.5

-1
2 4 6 8location (mm)

10

-1
0

2

4

6

8

10

0

1

1

1

0.5

0.5

0.5

normal0

normal0tangential

-0.5
2

4

6

8

10
1

0.5

0.5

0
-0.5

2

4

6

8

10

normaltangential-0.5
tangential

-1
0

2

4

6

10

10

8

10

tangential

0

2

4

6

0.5

normal0tangential

-0.5

-1
8

8

1

0

normal

6

-1
0

1

4

normal

-0.5

-1
0

2

0

tangential

-0.5

-1

normal-0.5-10tangential

0.5

-1
0

2

4

6

8

10

0

2

4

6

8

10

Fig. 3. Plot of the principal strain for each experimental condition when loading theskin. Uniform surface load (left), surface load in the central area (center) and in thelateral area (right) are shown. Areas shaded in grey indicate the regions where the load
is applied.

Proceedings of Eurohaptics 2008, LNCS 5024, Springer-Verlag, pp. 229–237
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3rd principal strain x10 -5 2nd principal strain x10 -5 1st principal strain x10 -5

Tactile Illusion Caused by Tangential Skin Traction
central displacement

uniform displacement
1

1 tangential

tangential

0.5
normal00normal-0.5-1
2 4 6 8location (mm)

10

-1
0

2

4

6

8

10

0

1

1

1

0.5

0.5

0.5

normal0-0.5

normal0tangential

2

4

6

8

10
1

0.5

0.5

0
-0.5

tangential

-1
0

2

4

6

8

10

8

10

8

10

8

10

normal

2

4

6

8

10

0

2

4

6

1
normal0

normal

6

-1
0

1

4

tangential

-0.5

-1
0

2

0

tangential

-0.5

-1

tangential

-0.5

-1
0

normal

0.5

0

-0.5

lateral displacement
1

0.5

7

tangential

0.5

-0.5

-0.5

-1

-1
0

2

4

6

8

10

tangential

0

normal0

2

4

6

Fig. 4. Same layout as in Fig. 3. Here the skin is displaced instead of being loaded.

5

General discussion

The results presented in the previous section show that we might be in thepresence of an interesting phenomenon. They indicate that the illusion could be
explained by the patterns of the resultant principal strains in the skin tissue.
From the finite element analysis, it can be speculated that:
1. At least for certain components the strain between normal surface load andtangential surface load are comparable.
2. If the tactile stimulus can be interpreted in multiple ways, i.e., the stimulus isambiguous, and if there are only two possible solutions, i.e., relative elevationof the central band with respect to the sides, the stimulus may be associatedwith the prior assumptions that cause the brain to confuse the shear loadwith the normal load.
To appreciate the surface geometry of contact, presumably, the only possible
cue given by the physical stimulus is the deformation of the skin tissue. Recently,
Wang and Hayward [7] suggested that mechanoreceptors are likely to respond tostrain caused by the deformation in the tissues in which they are embedded. They

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8

Nakatani, Sato, Tachi, Haywardalso exhibited another possible instance of different load condition where tactile
stimulus yields similar strain fields at a short distance inside the skin tissue,
using the results of Kikuuwe et al. [18]. These results indicate that different
deformation conditions can be perceptually equivalent when the strain fields are
similar. In other words, if a pair of resultant strain fields from two different
physical stimuli would be indistinguishable for the sensory system, they are also
perceptually indistinguishable. This may explain the phenomenon in part.
It is probably the case that the peripheral input from our physical stimuli issimilar to that from other stimuli, but is not exactly the same. Inexact replication
might confuse the nervous system. This is seen in Fig. 3 and 4, in which a pair ofprincipal strain components are similar to each other but not exactly the same.
However, even in this case, the sensory nervous system is forced to determine it
as one of the two possibilities: the central strip is raised or recessed; and use thisprior constraint to solve the problem. This follows from the observation thatmost adjacent regions of common surfaces that give non-uniform stimulation
are not at the same height. If the ensemble neural responses are monotonicallyrelated to the strain distribution, then the elevation of the central strip may be
determined from the relative activity of adjacent regions, yielding an experienceof height variation.
In the simulation we only evaluated the magnitude of the principal strains.
Whether the mechanoreceptors respond to preferred directions or not is an open
question. In fact, when the strain magnitude is large, it is quite likely thatreceptors respond to all components of normal and shear strains. With this taken
into consideration, the magnitude of the maximum component of the principal
strain would determine the intensity of the response. The phenomenon that we
found supports this view.
We found yet another instance where tactile stimuli can be as ambiguous asvisual stimuli can be. The central nervous system must make the best possible
judgement given available sensory input, analogously to what is observed in thevisual domain and which is at the origin of many illusions, such as the Necker
cube, the Mach card illusion, the hollow mask illusion and so on.
The ability of human tactile perception to overcome the lack of sensory information also indicates the necessity to develop design criteria for tactile sensors
and displays. Robotic researchers concerned with the design of artificial tactile
sensors already noticed the ambiguous nature of the tactile input mediated byelastic materials [19–22]. Efforts devoted to making artificial tactile sensors could
prove fruitful for helping us comprehend the human tactile mechanisms.

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