Haptical feeling of rotary switches
Haptical feeling of rotary switches
Jörg Reisinger1, Jörg Wild2
Gerhard Mauter
Heiner Bubb3
Heilbronn University
Automotive Competence Center
A u d i A G, I n g o l s t a d t
Te c h n i s c h e U n i v e r s i t ä t M ü n c h e n
Lehrstuhl für Ergonomie
ABSTRACT
It is a general standard in the description of the haptical characterization of rotary switches to plot the torque vs. angle. This
graphical description is originated in the available measurement
technology: the availability of torque and position sensors.
However, it does not consider the human perception as it cannot
describe the intuitively perceived characteristics. Therefore most
people, except those with a lot of experience, are not able to
create a realistic haptical interpretation of the torquecharacteristic. The question that should be answered by this
research project is: what feedback does the user of a rotary
switch feel intuitively?
Previously we used different ways in order to describe the
haptical characteristic. We found a main hypothesis that the
description of the used up energy plotted vs. angle shows a
much better intuitive representation than the description of plotted torque vs. angle. We stated four additional hypotheses to test
this main hypothesis. These are the rest position, the similarity
and the amplitude of sinusoidal and triangular shape and the
asymmetry of shapes.
In order to evaluate these hypotheses, tests with subjects are
made. We use a rotary haptical simulator, by which the requested parameters can be changed. The whole test runs automatically and the subject controls the duration of the single tests
by himself.
Two basic principles are used for the tests: In the first case
two haptical characteristics are compared. The applied method is
the interpretation of the yes-no answers to the question if the
characteristics are equal. In the second case the subjects have the
task to assign the haptical feeling to one of the graphic representations. The hypotheses are confirmed with 25 subjects on
80 single tests each. Clear tendencies can be found that confirm
the hypothesis in each test without any contradiction.
The test is also designed to give answers about the
just noticeable difference of haptical discrimination in connection with rotary switches. Furthermore it can be shown that the
just noticeable difference is independent of the shape of the
torque characteristics.
design of switches for an intended purpose.
Our research focuses on this question. The haptical
interpretation of the common torque vs. angle curve has hard
specific problems. These problems can only be solved with a
lot of experience and knowledge. In [1] we described these
problems in detail and showed an alternative way towards a
correct haptical interpretation. This paper describes shortly the
common problems of the torque characteristics, an alternative
description theory and their evaluation with tests in detail, as
well as we have a look at the identification of just noticeable
differences (JND) comparing rotary switches.
2
As mentioned before, the usual way to describe rotary-switch
characteristics is plotted torque vs. angle. This way to describe
switches has its roots in the availability of measurement
technologies. Torque or force sensors and also spatial sensors
for displacement are available. It requires additional
mathematical operations to get other units like speed, energy
or power. It suggests itself that the first step would be using
the given units for a characterization instead of any other. We
do the second step.
Our approach uses a plot of energy vs. angle. It can be
interpreted with a topological shape which is generating the
torque-profile idealized by differentiation. So this can be
mathematically described with an integration of the torque
against the angle as shown in (1). This energy E is necessary
to get from position ϕ1 to position ϕ2.
ϕ2
E = ∫ M dϕ
1
INTRODUCTION
For the haptical description of rotary switches the spatial plot of
torque vs. angle is the industrial standard. There is one big
question in the design of rotary switches:
How has this torque characteristic to look like to get a favored
haptical feeling? This knowledge is essential to get the haptical
1
2
3
e-mail: reisinger@hs-heilbronn.de
e-mail: wild@hs-heilbronn.de
e-mail: bubb@lfe.mw.tum.de
(1)
ϕ1
The following paragraphs describe the mentioned
problems with the torque-characteristics and their behavior
using the energy characteristics.
2.1
K e y w o r d s : Haptic, Rotary Switch, Rotary Encoder, Haptical
Description, Torque Perception, Torque Detection, Haptic Interface, Just Noticeable Difference, Psychophysics
GENERAL PROBLEMS WITH THE TORQUE
CHARACTERISTICS
Rest position
The first obvious problem is the rest position. It is usually
identified at the bottom of the characteristic curves (see
figure 1). Meanwhile the torque characteristic’s rest position is
usually in the middle of the characteristic curves when passing
the zero value as shown in figure 1.
Contrary to expectations no difference in shape is felt,
only the amplitude seems to be smaller on the triangular curve.
This could be seen as low pass behavior or a Fourier series
effect, but the rest position and the asymmetric shapes (see 2.3
below) would not fit into this theory.
The energy characteristic, as shown in figure 4, provides a
different view.
Torque characteristics
25
real
20
rest position
Torque in mNm
15
10
5
0
-5
-10
Energy characteristics
120
-15
expected
rest position
-25
0
9
18
Angle in degree
27
100
36
Figure 1: Rest position problem in the torque characteristics.
Energy in mNm
-20
80
60
40
20
This is a correct engineering description because the zero
torque is needed for a stable rest position, but it does not fit
human perception.
The energy characteristics have both expected and real rest
positions in the same position (see figure 2).
Energy in mNm
80
60
40
20
0
9
18
Angle in Degree
27
36
Figure 2: Rest position in the energy characteristics
Similarity of sinusoidal and triangular shapes
Torque in mNm
36
Energy of triangular shape
Asymmetrical shape
Torque Characteristics
25
The second problem is a strong haptical similarity of sinusoidal
and triangular torque-shapes as shown in figure 3. The haptical
perception is very similar while the graphics differ a lot.
Torque characteristics
25
27
The third problem is the use of curves which are not
symmetrical to the rest position. Applying such shapes causes,
for example, that a right turn is moving more easily than a left
turn. Subjects expected a symmetric behavior in each
direction. Figure 5 shows such an asymmetric shape.
20
15
Torque in mNm
2.2
18
Angle in Degree
Energy of sinusoidal shape
2.3
0
9
The result of the integration of the triangular shape as
shown in figure 3(b) is a parabolic energy characteristic, with
a very high similarity to a sinusoidal shape. Furthermore it can
be seen that the maximum amplitude of the triangular energy
shape is about 21 % smaller than the sine. A reduction of the
sinusoidal shapes maximum torque of about 21% can
compensate for this effect.
real = expected
rest position
100
0
Figure 4: sine and triangular shape in the energy characteristics
Energy characteristics
120
0
5
0
-5
20
-10
15
-15
10
-20
5
-25
0
Rest position
10
0
-5
9
18
Angle in degree
27
36
-10
-15
Figure 5: Asymmetric shape of the torque characteristics
-20
-25
0
9
Sinusoidal shape
18
Angle in degree
27
Triangular shape
Figure 3: Sinusoidal (a) and triangular (b) torque shape.
36
The more useful diagram is once more the energy
characteristics as shown in figure 6. Here it can be easily
imagined that a right turn is more easily performed than a left
turn. It can be interpreted as a topology with a hill and a mass
that should be moved.
Energy characteristics
50
3.2
The main hypothesis means that the energy characteristic is
more intuitive than the torque characteristic if significantly
more subjects assign the haptical perception to the energy
shape than to the torque shape. For this main hypothesis the
method of assigning haptical perception to graphical
description is suitable.
Energy in mNm
0
-50
-100
Rest
position
-150
left turn
-200
right turn
3.3
Rest position
-250
0
Main hypothesis
9
18
Angle in degree
27
36
Sub hypotheses
The main hypothesis can be split up into four sub hypotheses
that support the main hypothesis if they are all valid or not
opposite. So the main hypothesis is supported if the following
cases are fulfilled:
Figure 6: Shape of the energy characteristics
3.3.1
3
TESTING HYPOTHESES
The previously described theory is tested with a set of
hypotheses basing on the described problems. The following
paragraphs describe these hypotheses and the used testing
methods.
3.1
Used test methods
For the recent tests we are using the method of paired
comparison with the interpretation of yes-no answers and a
method of assigning haptical perception to graphical description.
3.1.1
Method of paired comparison (I)
The first test uses the method of paired comparison. Two
characteristics are applied to the haptical simulator. The focus
lies on the haptical differences, i.e. the subjects have to decide if
two applied haptical characteristics are the same or not. Their
decisions in form of ‘yes’ and ‘no’ answers are documented. The
applied characteristics change in shape and maximum torque
level.
The occurrences of the yes-no answers plotted vs. relative
differences are the basic principle for the interpretation. The
functionality of these methods is previewed in [1].
3.1.2
Method of graphical assignment (II)
The second test uses the assignment between haptical perception
and graphical description.
A haptical shape is applied to the simulator. This applied
haptical shape then has to be assigned to one out of six graphical
shapes. The selection contains both torque and energy shape. To
prevent any influences, the axes in the graphics are not labeled.
The occurrences of each graphic selection are the values for
this principle of interpretation.
3.1.3
Rest position (compare 2.1)
– If significantly more subjects locate the rest position in the
bottom of the graphical description than in the middle of it.
Principle (III) is useful for this test.
3.3.2
Similarity of sinusoidal and triangular curves (2.2)
This similarity offers three sub hypotheses.
– If significantly more subjects assign a triangular haptical
characteristic to a sinusoidal rather than to a triangular
graphical shape.
– If significantly more subjects identify sinusoidal and
triangular haptical characteristics as equal.
– If there is the significant maximum occurrences of the
relative difference of the maximum torque between sinusoidal
and triangular shapes lays shifted to the right around 21%.
For the test of these principles both the method of paired
comparison (I) and the method of graphical assignment (II) are
suitable.
3.3.3
Asymmetric curve (2.3)
– If significantly more subjects assign a falling shape
(compare the energy characteristic, similar to the main
hypothesis), the method of graphical assignment (II) is
suitable.
4
EQUIPMENT
Figure 7 shows the haptical display we used for these tests.
Drawing the stopping point in an existing graphical
description (III)
In this test the subject has to locate the rest position in a
prepared graphical shape. The occurrences of located rest
positions are the basis of this interpretation.
Figure 7: Simulator for rotary switches.
It is a single degree of freedom device, designed for haptical
research on rotary switches in our laboratory (see [1]). We use
an aluminum knob with a diameter of 35.5 mm. For this test two
characteristics can be changed via a toggle switch by the subject
himself. Actually a set of 16 different haptical characteristics can
be stored to the simulator. During the whole test different sets
are load to the simulator.
As a base for the tests we use a seat box where the simulator
is built-in and also the keypad for the recording of the answers is
mounted. The design of the seat box is oriented at the working
place of a car-driver as shown in figure 8a.
The simulator is mounted in the centre console of the seat
box obviating special haptical expectations caused by its size.
Thus only the knob is visible for the subjects. Moreover the
console is covering the simulator avoiding acoustical influence
to the subject as shown in figure 8b.
Keypad for the
subject’s answers
(a)
supervisor
Seat box with
integrated rotary simulator
(b)
Toggle switch
and LED display
Knob of the rotary
haptical simulator
Figure 8: Test setup with the seat box (a) and the integrated rotary
haptical simulator with toggle switch for changing the haptical
characteristics by the subject (b).
As shown in figure 8b the toggle switch is located next to
the simulator knob. The LED’s next to it indicate the subject if
the test can be continued.
graphics in the second test. A program based on the National
Instruments’ Labview controls the whole setup (simulator and
documentation). The tests are designed in an Excel-sheet and
the answers of each subject are documented in a separate copy
of this sheet. The summarization of all single tests is made by
a second software tool.
5
PARTICIPANTS
25 participants take part in the experiment. The group consists
of subjects with professions like economic and technical
students, employees, housewives and workers and is not
especially selected.
The subjects have to fill in a questionnaire with personal
questions about sex, handedness, age, profession, hobbies,
sports, music instruments, driven car and earlier contact with
haptical design. A presentation leads the participant to the
topic and furthermore shows him step by step the tasks he has
to fulfill. This has to be done very carefully to prevent
influence on the results. The subjects are requested to play
with the knob intensively: to turn left and right, slow and fast.
They can control the duration of the test themselves and can
switch between the two applied characteristics as often as they
like.
5.1
Order of the tests
One question that should be answered of this research project
was: what feedback does the user of a rotary switch feel
intuitively? Therefore it is important to know about previous
haptical knowledge of the subjects and rather obviate
influencing information.
Thus the order of the tests plays an important role: The
subjects are confronted with the graphical description as late
as possible.
The test starts up with the paired comparison of haptical
characteristics.
After this the participants are led to the comparison of
haptical perception with graphical description. Therefore they
are called upon drawing their haptical percept. Previous tests
have shown that this kind of test will not lead to a result, but it
is useful for getting familiar with the following tasks (see [1]).
In the following task the subjects have to do the haptical
assignment to one out of six graphs. Here the first usual
characteristics appear, but without clear definition.
In the final task the subjects see the same characteristics as
haptically applied to the simulator. Now they have to locate
the rest position in the graph.
6
EXPERIMENT 1: HAPTICAL ASSIGNMENT TO A
GRAPHICAL DESCRIPTION (3.1.2)
In this experiment the subjects have to assign the haptical
impression to one out of six graphical shapes as seen in Figure
9. The shapes have just a qualitative not a quantitative
character. In previous tests the ability of subjects was tested to
see if they were able to fulfill this task ([1]).
The test is designed to give answers about the in 3.2 and
3.3 described hypotheses: the main hypothesis, the similarity
of sinusoidal and triangular curves and the asymmetric shapes.
Figure 9: Input field for the recording of the answers.
The keypad consists of eight push buttons (see figure 9).
There are two buttons in green (yes) and red (no) color for
answering the first test. Six additional blue buttons are also
mounted on the keypad. They are used for the assignment to
6.1
Main hypothesis
Figure 10 and Table 1 show the results of testing the main
hypothesis. This summary shows the relative occurrence of
selected torque and energy shape. The remaining selections
are put together in one single group.
results of the test main hypothesis
Table 2: Results of experiment 1c:
Percentage of selections of the asymmetric shape.
13%
Torque
Shape
43%
Energy
Torque shape (asymmetric sine)
Energy shape (falling sine)
Falling saw tooth shape
Sine shape
Integrated falling saw tooth shape
44%
different
others
Figure 10: Results of experiment 1a:
Percentage of selections and ranges in the single tests.
We receive a sum of 56% for the “extended” energy and
36% for the “extended” torque characteristics. This supports
the basic trend.
6.4
Table 1: Results of experiment 1:
Percentage of selections and ranges in the single tests.
Shape
Torque shape
Energy shape
Different remaining
Percentage
of selections
13%
43%
44%
Range of
selections
(0% to 28%)
(32% to 62%)
(0% to 28%)
It can be seen clearly that the energy shape is the most
commonly selected group. The consistency of the remaining
group can be seen clearly in the range of the selections. There is
only a maximum selection of 28% while the energy shape is
selected in each single test from 32% up to 62%. Comparing the
range of the torque shape with the range of the remaining
selections shows nearly no difference: this means that other
shapes are selected as often as the torque shapes. It shows
clearly that the torque shape is selected randomly like the other
shapes.
This distribution shows a test of χ2 = 20,167 which results in
a very high statistical significance value (SPSS: 0,000%).
6.2
Similarity of sinusoidal and triangular curves
(2.2 and 3.3.2)
This test is a subset of the main hypothesis; anyway we have a
closer look at it. When a triangular torque-characteristic is
applied to the subject, most of them identify a sinusoidal or very
similar parabolic shape (56%). Only 8% of the subjects identify
the torque shape. Thereby other shapes are identified in the same
range (0% to 16%).
6.3
Asymmetric shape (2.3. and 3.3.3)
This subset needs some more interpretation because the
selections are not made so clearly.
Table 2 shows: the energy shape is once again identified in
32%. The shape of the “falling ramp” is selected in 24% and
also 28% select the “integrated falling saw tooth” shape. This
shows that it is very difficult for the subjects to fulfill this task in
this special case. The torque shape is only selected by 8% clearly the least selected.
For a more clear interpretation we determine the general
trend of the shapes: The “falling saw tooth” shape is also falling
off, similar to the energy shape. The wide bottom of the
“integrated falling saw tooth” shape has more similarity to the
torque shape for we decide to put these in another group. Even if
these values are not the real shapes they can partly explain their
huge rate in the table.
Percentage
of selections
8%
32%
24%
8%
28%
Location of the rest position (2.1 and 3.3.1)
The location of the rest position is an additional test with the
goal to find the preferred location of the rest position: at the
bottom of the shape for the energy characteristic and in the
middle of the curve for the torque characteristic (compare
figure 1). The subjects can feel a sinusoidal characteristic
(sine, because energy and torque shape are nearly the same)
and have to draw the rest position into the graph.
The result of the test shows, at 49% for the energy
characteristic, also a clear tendency supporting the main
hypothesis.
7
EXPERIMENT 2: METHOD OF PAIRED HAPTICAL
COMPARISON (3.1.1)
This test uses the method of paired haptical comparison in a
special way: The haptical perception of a rotary switch is a
multidimensional problem, i.e. changes in, for example,
‘shape’ cannot be described with one single adjective.
Therefore we limit these variations on the basic shape and in
the amplitude. In this case a comparison method (equal or
different) as described in [2], [3] or [4] is used.
The high number of possible variations requires further
restrictions: We use different basic shapes like sine, triangle,
rising and falling saw tooth and asymmetric sine. These
shapes are applied haptically to the subjects. We use two
torque amplitudes as basic values for the tests. Based on these,
percentage variations of the torque amplitude are applied.
The subjects’ task is to differentiate if the two applied
haptical characteristics are the same or not (yes-no answer).
7.1
Basic description and just noticeable difference
The following hypotheses can be evaluated with this test: (I)
sine-triangle similarity and (II) sine-triangle amplitudedifference. Additionally the just noticeable differences of
rotary switches are in focus.
For this test the relative difference of the maximum torque
of the curves is chosen for the abscissa. The maximum torque
of each pairing is the reference magnitude. The mathematical
definition to calculate the abscissa values xi is shown in (2).
The index of a single test is i.
xi =
M i ,1 − M i , 2
; M i ,1 > M i , 2
M i ,1
(2)
The relative occurrences of the ‘yes’ answers are assigned
to the ordinate. Each measuring point contains the answers of
25 subjects.
This setup generates a plot of relative occurrences vs.
relative torque difference.
To get more continuity in the graph, additional tests
focusing on the existing gaps in the abscissa are made. These
additional tests show reproducible results which are added to the
existing ones.
Finally we fit a function of a cumulated Gaussian
distribution into the measured values. The least square fit
method is used for this. The error is normalized by dividing by
the number of tests. The used equation for the cumulated
Gaussian distribution F(x) is shown in (3). The parameters we
use are the amplitude a, the average µ and the standard
deviation σ.
2
x − 1 ⎛ t −µ ⎞
⎛
⎞
⎜
⎟
1
2
⎜
⎝ σ ⎠
⋅ ∫e
F ( x ) = a ⋅ ⎜1 −
dt ⎟⎟
(3)
⎜ σ ⋅ 2π −∞
⎟
⎝
⎠
We test three different shapes: (a) a rising saw tooth shape,
(b) a sinusoidal shape and (c) a falling saw tooth shape. These
shapes show extreme differences in the haptical feeling getting a
better haptical quality from (a) to (c). Additionally we compare
the sinusoidal and the triangular shape (d). Figure 11 shows the
applied haptical shapes.
Applied haptical shapes
30
Torque in mNm
20
Rest
position
10
0
-10
-20
-30
0
9
18
Angle in degree
27
36
Rising saw tooth shape (a)
Sinusoidal shape (b)
Falling saw tooth shape (c)
Triangular shape (d)
Figure 11: Applied haptical shapes.
Figure 12 shows, as an example, the results of experiment 2
realized with the falling saw tooth shape.
Table 3 shows that the parameters of the Gaussian
distribution (amplitude a, average µ, standard deviation σ). They
are very similar for each tested shape. The changes in the
Table 3: Parameters of the
Gaussian distribution, for each tested pairing.
Generally all the basic JND functions can be described
Results of the sinusoidal shape experiment
relative ocurrency of
the 'yes'-answers
100%
a
0,86
0,85
0,83
0,83
µ
0,25
0,21
0,19
0,16
σ
0,12
0,12
0,10
0,06
Amplitude a, average µ, standard deviation σ.
parameters of (a)-(c) are negligibly small and are in the range of
measuring errors in this experiment.
60%
40%
20%
0%
0%
10%
20%
30%
40%
50%
relative difference of the maximum torques
measured values
regression function
Figure 12: Results of the test with a falling saw tooth.
with nearly the same parameters. This leads to the conclusion
that the basic shape of a haptical characteristic does not
influence the just noticeable difference.
The average value can be seen in the way that more than
half of the subjects identify differences bigger than 20% of the
maximum torque. In other words: if haptical differences have
to be felt, the amplitude of the switches will have to differ by
more than 20% to be significant for most of the subjects.
Another look at the amplitude parameter a shows that
there is an error of around 15% in the decision of the subjects.
This is of interest because only one shape is applied as a
pairing and it is not switched on the simulator during these
tests of 0% difference. This effect can be explained with the
situation the subjects are in: they concentrate on differences.
Thereby big differences will be identified clearly, while no or
even small differences cause uncertainty and thus to the
appearance of non-existing differences. This is a systematic
error. The main question is: how does this error influence the
parameters of the results. The answer could be given with the
method described in [5] and [6] where the decision has to be
made if a property of the first object is bigger or smaller than
the same property of the second one. This requires a
multidimensional analysis of the haptical differences basing
on the estimation with adjectives like ‘more’ or ‘less heavy’
for example.
7.2
Pairing
‘Rising saw tooth’ (a)
Sine (b)
‘Falling saw tooth’ (c)
sine – triangle (d)
80%
Sinusoidal compared with the triangular shape
To evaluate the sine-triangle similarity and the sinetriangle amplitude-difference the sinusoidal and the triangular
shapes are compared. Any other used combinations of
different shapes have no significant correlation.
Theoretically the results should show a high conformity to
support similarity, but with a maximum occurrence at around
21% to support the amplitude difference. It can be seen clearly
in figure 13 that there is the maximum occurrence not in the
origin of the graph, but shifted to the right.
The Gaussian distribution is used as a symmetric
regression function and identifies the maximum at around
13%. The maximum lies at around 13% and not at the
theoretically expected 21%. This difference can be influenced
by friction and other mechanical parameters and we plan to
investigate this more detailed. Regarding to this we see the
theory as supported.
8
Results of the sinusoidal-triangular shape exp.
relative ocurrency of
the 'yes'-answ ers
100%
80%
60%
Maximum
occurrence
40%
20%
Right shift
offset
0%
0,0%
10,0%
20,0%
30,0%
40,0%
50,0%
relative difference of the maximum torques
measured values
regression function
Figure 13: Results of the comparison of sinusoidal and triangular shape
with a Gaussian distribution as regression function.
For further analysis we transform the abscissa to get the
maximum to the origin of the graph. The 13% average value of
the Gaussian distribution is used for the transformation.
Background is that the amplitude of the sinusoidal shape has to
be 13% lower than the triangular shape to have the maximum
conformity.
The fitting of the cumulated Gaussian distribution shows
interesting parameters: the sinusoidal-triangular shape has
nearly the same amplitude a as the other single-shape tests. This
is an important answer, changing angled shapes to more smooth
ones or backward. This may be useful for acoustical design and
other purposes.
Also the average value µ lies close to the other parameters,
but with 16% even smaller.
The standard deviation has only half value of the other
parameters. This means that the regression curve is falling stiffer
than the others. Thereby the differentiation between the same
and different switches changes more rapidly.
Generally we find that the haptical similarity of sinusoidal
and triangular shapes is fully supported.
Additionally the shifting of the maximum occurrence
supports it even if the theoretical and the measured values do not
correspond. To find the reasons is part of further work.
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CONCLUSION
The tests we made support the theory in each step without
contradiction: the energy characteristic describes haptical
feeling of rotary switches more intuitive than the common
torque characteristics. This helps to find parameters for
intended purposes in haptical design of rotary switches.
We find a value of around 20% of torque difference for
just noticeable difference of rotary switches, when most of the
subjects can differentiate and some not.
Further there is an uncertainity in the decision of the
subjects of around 15% finding haptical differences between
two rotary switches.
The just noticeable difference function for this purpose
can be described with a cumulated Gaussian function
independent from the basic shape.
Further work will look more detailled into the
characteristics and their parameters. Especially the difference
of the shifted occurrence maximum between measurement and
the theory of the sinusoidal and the triangular shapes is in
focus.
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research for automotive applications, Proceedings of REM2005,
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[2] Goldstein, E. B.: Sensation and Perception. Wadsworth Publishing
Company, 2002.
[3] Levitt, H.: Transformed Up-Down Methods in Psychoacoustics. The
journal of the acoustical Society of America, American Institute of
Physics (AIP), Volume49, Number 2 (Part 2), p.467-477, 1971.
[4] Liter, J. C., Bülthoff, H. H.: An introduction to object recognition.
Zeitschrift für Naturforschung, Section C. Biosciences, 53 (7-8), 610621, 1998.
[5] Thurstone, L.L.: A law of comparative judgement. Psychological
Review, 34, p.278-286, 1927.
[6] Fanger, P.O.: Thermal Comfort. Analysis and Applications in
Environmental Engineering. New-York: McGraw-Hill, 1973.
Jörg Reisinger1, Jörg Wild2
Gerhard Mauter
Heiner Bubb3
Heilbronn University
Automotive Competence Center
A u d i A G, I n g o l s t a d t
Te c h n i s c h e U n i v e r s i t ä t M ü n c h e n
Lehrstuhl für Ergonomie
ABSTRACT
It is a general standard in the description of the haptical characterization of rotary switches to plot the torque vs. angle. This
graphical description is originated in the available measurement
technology: the availability of torque and position sensors.
However, it does not consider the human perception as it cannot
describe the intuitively perceived characteristics. Therefore most
people, except those with a lot of experience, are not able to
create a realistic haptical interpretation of the torquecharacteristic. The question that should be answered by this
research project is: what feedback does the user of a rotary
switch feel intuitively?
Previously we used different ways in order to describe the
haptical characteristic. We found a main hypothesis that the
description of the used up energy plotted vs. angle shows a
much better intuitive representation than the description of plotted torque vs. angle. We stated four additional hypotheses to test
this main hypothesis. These are the rest position, the similarity
and the amplitude of sinusoidal and triangular shape and the
asymmetry of shapes.
In order to evaluate these hypotheses, tests with subjects are
made. We use a rotary haptical simulator, by which the requested parameters can be changed. The whole test runs automatically and the subject controls the duration of the single tests
by himself.
Two basic principles are used for the tests: In the first case
two haptical characteristics are compared. The applied method is
the interpretation of the yes-no answers to the question if the
characteristics are equal. In the second case the subjects have the
task to assign the haptical feeling to one of the graphic representations. The hypotheses are confirmed with 25 subjects on
80 single tests each. Clear tendencies can be found that confirm
the hypothesis in each test without any contradiction.
The test is also designed to give answers about the
just noticeable difference of haptical discrimination in connection with rotary switches. Furthermore it can be shown that the
just noticeable difference is independent of the shape of the
torque characteristics.
design of switches for an intended purpose.
Our research focuses on this question. The haptical
interpretation of the common torque vs. angle curve has hard
specific problems. These problems can only be solved with a
lot of experience and knowledge. In [1] we described these
problems in detail and showed an alternative way towards a
correct haptical interpretation. This paper describes shortly the
common problems of the torque characteristics, an alternative
description theory and their evaluation with tests in detail, as
well as we have a look at the identification of just noticeable
differences (JND) comparing rotary switches.
2
As mentioned before, the usual way to describe rotary-switch
characteristics is plotted torque vs. angle. This way to describe
switches has its roots in the availability of measurement
technologies. Torque or force sensors and also spatial sensors
for displacement are available. It requires additional
mathematical operations to get other units like speed, energy
or power. It suggests itself that the first step would be using
the given units for a characterization instead of any other. We
do the second step.
Our approach uses a plot of energy vs. angle. It can be
interpreted with a topological shape which is generating the
torque-profile idealized by differentiation. So this can be
mathematically described with an integration of the torque
against the angle as shown in (1). This energy E is necessary
to get from position ϕ1 to position ϕ2.
ϕ2
E = ∫ M dϕ
1
INTRODUCTION
For the haptical description of rotary switches the spatial plot of
torque vs. angle is the industrial standard. There is one big
question in the design of rotary switches:
How has this torque characteristic to look like to get a favored
haptical feeling? This knowledge is essential to get the haptical
1
2
3
e-mail: reisinger@hs-heilbronn.de
e-mail: wild@hs-heilbronn.de
e-mail: bubb@lfe.mw.tum.de
(1)
ϕ1
The following paragraphs describe the mentioned
problems with the torque-characteristics and their behavior
using the energy characteristics.
2.1
K e y w o r d s : Haptic, Rotary Switch, Rotary Encoder, Haptical
Description, Torque Perception, Torque Detection, Haptic Interface, Just Noticeable Difference, Psychophysics
GENERAL PROBLEMS WITH THE TORQUE
CHARACTERISTICS
Rest position
The first obvious problem is the rest position. It is usually
identified at the bottom of the characteristic curves (see
figure 1). Meanwhile the torque characteristic’s rest position is
usually in the middle of the characteristic curves when passing
the zero value as shown in figure 1.
Contrary to expectations no difference in shape is felt,
only the amplitude seems to be smaller on the triangular curve.
This could be seen as low pass behavior or a Fourier series
effect, but the rest position and the asymmetric shapes (see 2.3
below) would not fit into this theory.
The energy characteristic, as shown in figure 4, provides a
different view.
Torque characteristics
25
real
20
rest position
Torque in mNm
15
10
5
0
-5
-10
Energy characteristics
120
-15
expected
rest position
-25
0
9
18
Angle in degree
27
100
36
Figure 1: Rest position problem in the torque characteristics.
Energy in mNm
-20
80
60
40
20
This is a correct engineering description because the zero
torque is needed for a stable rest position, but it does not fit
human perception.
The energy characteristics have both expected and real rest
positions in the same position (see figure 2).
Energy in mNm
80
60
40
20
0
9
18
Angle in Degree
27
36
Figure 2: Rest position in the energy characteristics
Similarity of sinusoidal and triangular shapes
Torque in mNm
36
Energy of triangular shape
Asymmetrical shape
Torque Characteristics
25
The second problem is a strong haptical similarity of sinusoidal
and triangular torque-shapes as shown in figure 3. The haptical
perception is very similar while the graphics differ a lot.
Torque characteristics
25
27
The third problem is the use of curves which are not
symmetrical to the rest position. Applying such shapes causes,
for example, that a right turn is moving more easily than a left
turn. Subjects expected a symmetric behavior in each
direction. Figure 5 shows such an asymmetric shape.
20
15
Torque in mNm
2.2
18
Angle in Degree
Energy of sinusoidal shape
2.3
0
9
The result of the integration of the triangular shape as
shown in figure 3(b) is a parabolic energy characteristic, with
a very high similarity to a sinusoidal shape. Furthermore it can
be seen that the maximum amplitude of the triangular energy
shape is about 21 % smaller than the sine. A reduction of the
sinusoidal shapes maximum torque of about 21% can
compensate for this effect.
real = expected
rest position
100
0
Figure 4: sine and triangular shape in the energy characteristics
Energy characteristics
120
0
5
0
-5
20
-10
15
-15
10
-20
5
-25
0
Rest position
10
0
-5
9
18
Angle in degree
27
36
-10
-15
Figure 5: Asymmetric shape of the torque characteristics
-20
-25
0
9
Sinusoidal shape
18
Angle in degree
27
Triangular shape
Figure 3: Sinusoidal (a) and triangular (b) torque shape.
36
The more useful diagram is once more the energy
characteristics as shown in figure 6. Here it can be easily
imagined that a right turn is more easily performed than a left
turn. It can be interpreted as a topology with a hill and a mass
that should be moved.
Energy characteristics
50
3.2
The main hypothesis means that the energy characteristic is
more intuitive than the torque characteristic if significantly
more subjects assign the haptical perception to the energy
shape than to the torque shape. For this main hypothesis the
method of assigning haptical perception to graphical
description is suitable.
Energy in mNm
0
-50
-100
Rest
position
-150
left turn
-200
right turn
3.3
Rest position
-250
0
Main hypothesis
9
18
Angle in degree
27
36
Sub hypotheses
The main hypothesis can be split up into four sub hypotheses
that support the main hypothesis if they are all valid or not
opposite. So the main hypothesis is supported if the following
cases are fulfilled:
Figure 6: Shape of the energy characteristics
3.3.1
3
TESTING HYPOTHESES
The previously described theory is tested with a set of
hypotheses basing on the described problems. The following
paragraphs describe these hypotheses and the used testing
methods.
3.1
Used test methods
For the recent tests we are using the method of paired
comparison with the interpretation of yes-no answers and a
method of assigning haptical perception to graphical description.
3.1.1
Method of paired comparison (I)
The first test uses the method of paired comparison. Two
characteristics are applied to the haptical simulator. The focus
lies on the haptical differences, i.e. the subjects have to decide if
two applied haptical characteristics are the same or not. Their
decisions in form of ‘yes’ and ‘no’ answers are documented. The
applied characteristics change in shape and maximum torque
level.
The occurrences of the yes-no answers plotted vs. relative
differences are the basic principle for the interpretation. The
functionality of these methods is previewed in [1].
3.1.2
Method of graphical assignment (II)
The second test uses the assignment between haptical perception
and graphical description.
A haptical shape is applied to the simulator. This applied
haptical shape then has to be assigned to one out of six graphical
shapes. The selection contains both torque and energy shape. To
prevent any influences, the axes in the graphics are not labeled.
The occurrences of each graphic selection are the values for
this principle of interpretation.
3.1.3
Rest position (compare 2.1)
– If significantly more subjects locate the rest position in the
bottom of the graphical description than in the middle of it.
Principle (III) is useful for this test.
3.3.2
Similarity of sinusoidal and triangular curves (2.2)
This similarity offers three sub hypotheses.
– If significantly more subjects assign a triangular haptical
characteristic to a sinusoidal rather than to a triangular
graphical shape.
– If significantly more subjects identify sinusoidal and
triangular haptical characteristics as equal.
– If there is the significant maximum occurrences of the
relative difference of the maximum torque between sinusoidal
and triangular shapes lays shifted to the right around 21%.
For the test of these principles both the method of paired
comparison (I) and the method of graphical assignment (II) are
suitable.
3.3.3
Asymmetric curve (2.3)
– If significantly more subjects assign a falling shape
(compare the energy characteristic, similar to the main
hypothesis), the method of graphical assignment (II) is
suitable.
4
EQUIPMENT
Figure 7 shows the haptical display we used for these tests.
Drawing the stopping point in an existing graphical
description (III)
In this test the subject has to locate the rest position in a
prepared graphical shape. The occurrences of located rest
positions are the basis of this interpretation.
Figure 7: Simulator for rotary switches.
It is a single degree of freedom device, designed for haptical
research on rotary switches in our laboratory (see [1]). We use
an aluminum knob with a diameter of 35.5 mm. For this test two
characteristics can be changed via a toggle switch by the subject
himself. Actually a set of 16 different haptical characteristics can
be stored to the simulator. During the whole test different sets
are load to the simulator.
As a base for the tests we use a seat box where the simulator
is built-in and also the keypad for the recording of the answers is
mounted. The design of the seat box is oriented at the working
place of a car-driver as shown in figure 8a.
The simulator is mounted in the centre console of the seat
box obviating special haptical expectations caused by its size.
Thus only the knob is visible for the subjects. Moreover the
console is covering the simulator avoiding acoustical influence
to the subject as shown in figure 8b.
Keypad for the
subject’s answers
(a)
supervisor
Seat box with
integrated rotary simulator
(b)
Toggle switch
and LED display
Knob of the rotary
haptical simulator
Figure 8: Test setup with the seat box (a) and the integrated rotary
haptical simulator with toggle switch for changing the haptical
characteristics by the subject (b).
As shown in figure 8b the toggle switch is located next to
the simulator knob. The LED’s next to it indicate the subject if
the test can be continued.
graphics in the second test. A program based on the National
Instruments’ Labview controls the whole setup (simulator and
documentation). The tests are designed in an Excel-sheet and
the answers of each subject are documented in a separate copy
of this sheet. The summarization of all single tests is made by
a second software tool.
5
PARTICIPANTS
25 participants take part in the experiment. The group consists
of subjects with professions like economic and technical
students, employees, housewives and workers and is not
especially selected.
The subjects have to fill in a questionnaire with personal
questions about sex, handedness, age, profession, hobbies,
sports, music instruments, driven car and earlier contact with
haptical design. A presentation leads the participant to the
topic and furthermore shows him step by step the tasks he has
to fulfill. This has to be done very carefully to prevent
influence on the results. The subjects are requested to play
with the knob intensively: to turn left and right, slow and fast.
They can control the duration of the test themselves and can
switch between the two applied characteristics as often as they
like.
5.1
Order of the tests
One question that should be answered of this research project
was: what feedback does the user of a rotary switch feel
intuitively? Therefore it is important to know about previous
haptical knowledge of the subjects and rather obviate
influencing information.
Thus the order of the tests plays an important role: The
subjects are confronted with the graphical description as late
as possible.
The test starts up with the paired comparison of haptical
characteristics.
After this the participants are led to the comparison of
haptical perception with graphical description. Therefore they
are called upon drawing their haptical percept. Previous tests
have shown that this kind of test will not lead to a result, but it
is useful for getting familiar with the following tasks (see [1]).
In the following task the subjects have to do the haptical
assignment to one out of six graphs. Here the first usual
characteristics appear, but without clear definition.
In the final task the subjects see the same characteristics as
haptically applied to the simulator. Now they have to locate
the rest position in the graph.
6
EXPERIMENT 1: HAPTICAL ASSIGNMENT TO A
GRAPHICAL DESCRIPTION (3.1.2)
In this experiment the subjects have to assign the haptical
impression to one out of six graphical shapes as seen in Figure
9. The shapes have just a qualitative not a quantitative
character. In previous tests the ability of subjects was tested to
see if they were able to fulfill this task ([1]).
The test is designed to give answers about the in 3.2 and
3.3 described hypotheses: the main hypothesis, the similarity
of sinusoidal and triangular curves and the asymmetric shapes.
Figure 9: Input field for the recording of the answers.
The keypad consists of eight push buttons (see figure 9).
There are two buttons in green (yes) and red (no) color for
answering the first test. Six additional blue buttons are also
mounted on the keypad. They are used for the assignment to
6.1
Main hypothesis
Figure 10 and Table 1 show the results of testing the main
hypothesis. This summary shows the relative occurrence of
selected torque and energy shape. The remaining selections
are put together in one single group.
results of the test main hypothesis
Table 2: Results of experiment 1c:
Percentage of selections of the asymmetric shape.
13%
Torque
Shape
43%
Energy
Torque shape (asymmetric sine)
Energy shape (falling sine)
Falling saw tooth shape
Sine shape
Integrated falling saw tooth shape
44%
different
others
Figure 10: Results of experiment 1a:
Percentage of selections and ranges in the single tests.
We receive a sum of 56% for the “extended” energy and
36% for the “extended” torque characteristics. This supports
the basic trend.
6.4
Table 1: Results of experiment 1:
Percentage of selections and ranges in the single tests.
Shape
Torque shape
Energy shape
Different remaining
Percentage
of selections
13%
43%
44%
Range of
selections
(0% to 28%)
(32% to 62%)
(0% to 28%)
It can be seen clearly that the energy shape is the most
commonly selected group. The consistency of the remaining
group can be seen clearly in the range of the selections. There is
only a maximum selection of 28% while the energy shape is
selected in each single test from 32% up to 62%. Comparing the
range of the torque shape with the range of the remaining
selections shows nearly no difference: this means that other
shapes are selected as often as the torque shapes. It shows
clearly that the torque shape is selected randomly like the other
shapes.
This distribution shows a test of χ2 = 20,167 which results in
a very high statistical significance value (SPSS: 0,000%).
6.2
Similarity of sinusoidal and triangular curves
(2.2 and 3.3.2)
This test is a subset of the main hypothesis; anyway we have a
closer look at it. When a triangular torque-characteristic is
applied to the subject, most of them identify a sinusoidal or very
similar parabolic shape (56%). Only 8% of the subjects identify
the torque shape. Thereby other shapes are identified in the same
range (0% to 16%).
6.3
Asymmetric shape (2.3. and 3.3.3)
This subset needs some more interpretation because the
selections are not made so clearly.
Table 2 shows: the energy shape is once again identified in
32%. The shape of the “falling ramp” is selected in 24% and
also 28% select the “integrated falling saw tooth” shape. This
shows that it is very difficult for the subjects to fulfill this task in
this special case. The torque shape is only selected by 8% clearly the least selected.
For a more clear interpretation we determine the general
trend of the shapes: The “falling saw tooth” shape is also falling
off, similar to the energy shape. The wide bottom of the
“integrated falling saw tooth” shape has more similarity to the
torque shape for we decide to put these in another group. Even if
these values are not the real shapes they can partly explain their
huge rate in the table.
Percentage
of selections
8%
32%
24%
8%
28%
Location of the rest position (2.1 and 3.3.1)
The location of the rest position is an additional test with the
goal to find the preferred location of the rest position: at the
bottom of the shape for the energy characteristic and in the
middle of the curve for the torque characteristic (compare
figure 1). The subjects can feel a sinusoidal characteristic
(sine, because energy and torque shape are nearly the same)
and have to draw the rest position into the graph.
The result of the test shows, at 49% for the energy
characteristic, also a clear tendency supporting the main
hypothesis.
7
EXPERIMENT 2: METHOD OF PAIRED HAPTICAL
COMPARISON (3.1.1)
This test uses the method of paired haptical comparison in a
special way: The haptical perception of a rotary switch is a
multidimensional problem, i.e. changes in, for example,
‘shape’ cannot be described with one single adjective.
Therefore we limit these variations on the basic shape and in
the amplitude. In this case a comparison method (equal or
different) as described in [2], [3] or [4] is used.
The high number of possible variations requires further
restrictions: We use different basic shapes like sine, triangle,
rising and falling saw tooth and asymmetric sine. These
shapes are applied haptically to the subjects. We use two
torque amplitudes as basic values for the tests. Based on these,
percentage variations of the torque amplitude are applied.
The subjects’ task is to differentiate if the two applied
haptical characteristics are the same or not (yes-no answer).
7.1
Basic description and just noticeable difference
The following hypotheses can be evaluated with this test: (I)
sine-triangle similarity and (II) sine-triangle amplitudedifference. Additionally the just noticeable differences of
rotary switches are in focus.
For this test the relative difference of the maximum torque
of the curves is chosen for the abscissa. The maximum torque
of each pairing is the reference magnitude. The mathematical
definition to calculate the abscissa values xi is shown in (2).
The index of a single test is i.
xi =
M i ,1 − M i , 2
; M i ,1 > M i , 2
M i ,1
(2)
The relative occurrences of the ‘yes’ answers are assigned
to the ordinate. Each measuring point contains the answers of
25 subjects.
This setup generates a plot of relative occurrences vs.
relative torque difference.
To get more continuity in the graph, additional tests
focusing on the existing gaps in the abscissa are made. These
additional tests show reproducible results which are added to the
existing ones.
Finally we fit a function of a cumulated Gaussian
distribution into the measured values. The least square fit
method is used for this. The error is normalized by dividing by
the number of tests. The used equation for the cumulated
Gaussian distribution F(x) is shown in (3). The parameters we
use are the amplitude a, the average µ and the standard
deviation σ.
2
x − 1 ⎛ t −µ ⎞
⎛
⎞
⎜
⎟
1
2
⎜
⎝ σ ⎠
⋅ ∫e
F ( x ) = a ⋅ ⎜1 −
dt ⎟⎟
(3)
⎜ σ ⋅ 2π −∞
⎟
⎝
⎠
We test three different shapes: (a) a rising saw tooth shape,
(b) a sinusoidal shape and (c) a falling saw tooth shape. These
shapes show extreme differences in the haptical feeling getting a
better haptical quality from (a) to (c). Additionally we compare
the sinusoidal and the triangular shape (d). Figure 11 shows the
applied haptical shapes.
Applied haptical shapes
30
Torque in mNm
20
Rest
position
10
0
-10
-20
-30
0
9
18
Angle in degree
27
36
Rising saw tooth shape (a)
Sinusoidal shape (b)
Falling saw tooth shape (c)
Triangular shape (d)
Figure 11: Applied haptical shapes.
Figure 12 shows, as an example, the results of experiment 2
realized with the falling saw tooth shape.
Table 3 shows that the parameters of the Gaussian
distribution (amplitude a, average µ, standard deviation σ). They
are very similar for each tested shape. The changes in the
Table 3: Parameters of the
Gaussian distribution, for each tested pairing.
Generally all the basic JND functions can be described
Results of the sinusoidal shape experiment
relative ocurrency of
the 'yes'-answers
100%
a
0,86
0,85
0,83
0,83
µ
0,25
0,21
0,19
0,16
σ
0,12
0,12
0,10
0,06
Amplitude a, average µ, standard deviation σ.
parameters of (a)-(c) are negligibly small and are in the range of
measuring errors in this experiment.
60%
40%
20%
0%
0%
10%
20%
30%
40%
50%
relative difference of the maximum torques
measured values
regression function
Figure 12: Results of the test with a falling saw tooth.
with nearly the same parameters. This leads to the conclusion
that the basic shape of a haptical characteristic does not
influence the just noticeable difference.
The average value can be seen in the way that more than
half of the subjects identify differences bigger than 20% of the
maximum torque. In other words: if haptical differences have
to be felt, the amplitude of the switches will have to differ by
more than 20% to be significant for most of the subjects.
Another look at the amplitude parameter a shows that
there is an error of around 15% in the decision of the subjects.
This is of interest because only one shape is applied as a
pairing and it is not switched on the simulator during these
tests of 0% difference. This effect can be explained with the
situation the subjects are in: they concentrate on differences.
Thereby big differences will be identified clearly, while no or
even small differences cause uncertainty and thus to the
appearance of non-existing differences. This is a systematic
error. The main question is: how does this error influence the
parameters of the results. The answer could be given with the
method described in [5] and [6] where the decision has to be
made if a property of the first object is bigger or smaller than
the same property of the second one. This requires a
multidimensional analysis of the haptical differences basing
on the estimation with adjectives like ‘more’ or ‘less heavy’
for example.
7.2
Pairing
‘Rising saw tooth’ (a)
Sine (b)
‘Falling saw tooth’ (c)
sine – triangle (d)
80%
Sinusoidal compared with the triangular shape
To evaluate the sine-triangle similarity and the sinetriangle amplitude-difference the sinusoidal and the triangular
shapes are compared. Any other used combinations of
different shapes have no significant correlation.
Theoretically the results should show a high conformity to
support similarity, but with a maximum occurrence at around
21% to support the amplitude difference. It can be seen clearly
in figure 13 that there is the maximum occurrence not in the
origin of the graph, but shifted to the right.
The Gaussian distribution is used as a symmetric
regression function and identifies the maximum at around
13%. The maximum lies at around 13% and not at the
theoretically expected 21%. This difference can be influenced
by friction and other mechanical parameters and we plan to
investigate this more detailed. Regarding to this we see the
theory as supported.
8
Results of the sinusoidal-triangular shape exp.
relative ocurrency of
the 'yes'-answ ers
100%
80%
60%
Maximum
occurrence
40%
20%
Right shift
offset
0%
0,0%
10,0%
20,0%
30,0%
40,0%
50,0%
relative difference of the maximum torques
measured values
regression function
Figure 13: Results of the comparison of sinusoidal and triangular shape
with a Gaussian distribution as regression function.
For further analysis we transform the abscissa to get the
maximum to the origin of the graph. The 13% average value of
the Gaussian distribution is used for the transformation.
Background is that the amplitude of the sinusoidal shape has to
be 13% lower than the triangular shape to have the maximum
conformity.
The fitting of the cumulated Gaussian distribution shows
interesting parameters: the sinusoidal-triangular shape has
nearly the same amplitude a as the other single-shape tests. This
is an important answer, changing angled shapes to more smooth
ones or backward. This may be useful for acoustical design and
other purposes.
Also the average value µ lies close to the other parameters,
but with 16% even smaller.
The standard deviation has only half value of the other
parameters. This means that the regression curve is falling stiffer
than the others. Thereby the differentiation between the same
and different switches changes more rapidly.
Generally we find that the haptical similarity of sinusoidal
and triangular shapes is fully supported.
Additionally the shifting of the maximum occurrence
supports it even if the theoretical and the measured values do not
correspond. To find the reasons is part of further work.
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CONCLUSION
The tests we made support the theory in each step without
contradiction: the energy characteristic describes haptical
feeling of rotary switches more intuitive than the common
torque characteristics. This helps to find parameters for
intended purposes in haptical design of rotary switches.
We find a value of around 20% of torque difference for
just noticeable difference of rotary switches, when most of the
subjects can differentiate and some not.
Further there is an uncertainity in the decision of the
subjects of around 15% finding haptical differences between
two rotary switches.
The just noticeable difference function for this purpose
can be described with a cumulated Gaussian function
independent from the basic shape.
Further work will look more detailled into the
characteristics and their parameters. Especially the difference
of the shifted occurrence maximum between measurement and
the theory of the sinusoidal and the triangular shapes is in
focus.
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