2017 IEEE World Haptics Conference (WHC)
Fürstenfeldbruck (Munich), Germany
6–9 June 2017

Envelope Effect Study on Collision Vibration Perception throughInvestigating Just Noticeable Difference of Time Constant
Nan Cao1 , Hikaru Nagano1 , Masashi Konyo1 , Shogo Okamoto2 , and Satoshi Tadokoro1
Abstract— It is known that human can feel the vibratory envelope on periodic sinusoidal vibrations; however, the role of theenvelope on non-periodic transient vibrations is still not clear.
This study investigated Just Noticeable Difference (JND) of thetime constant in the decaying sinusoidal vibration model, which
is one reasonable factor relating to discrimination of tappedmaterials. The authors conducted psychophysical experiments
to evaluate JNDs for two referenced time constants (10.8 and50 ms) among five frequencies (150, 250, 500, 800 and 1000 Hz).
The analysis showed that significant frequency effect on JNDs
was only found for the lower JNDs of reference time constant
50 ms. JNDs of the time constant was lower around 250 Hz(150 to 500 Hz, average JND was 12.8%) and was higher athigh frequencies (800 to 1000 Hz, average JND was 27.9%). No
significant frequency effects were found in the upper JNDs ofreference 50 ms (average JND was 23%) and upper JNDs ofreference 10.8 ms (average JND was 65%).

I. I NTRODUCTION
Human can perceive the frequency of amplitude modulated
sinusoidal vibration even when carrier frequency is higher
than human perceivable frequency range [1], [2]. This finding
can be translated as that human can perceive the envelope of
periodic sinusoidal vibrations. In terms of periodic sinusoidal
vibrations, the perceptual characteristics on envelope andfrequency of vibrations have been investigated by several
researchers; however, those characteristics for non-periodictransient vibrations such as collision vibration have not yet
been investigated.
An example of non-periodic transient vibration is collisionvibration. It occurs when we tap a surface, which waveforms
differ based on tapped materials and help us to perceive thedifferent characteristics of the tapped materials. The perceptual characteristics for collision vibrations which contribute a
discrimination of tapped materials have been investigated byseveral researchers in order to virtually represent collision
feeling by simulating transient collision vibrations. Okamura et. al [3] parametrically modeled collision vibrations
in which the amplitude, the frequency and the time constant (envelope) of vibrations partially reflect materials. They
used the model to realize the representation of the differencesin collision frequencies by using the frequencies different
from measured natural frequencies. These frequencies theyused elicited people to distinguish materials [4]. This model
combined with kinesthetic force displays has been used torepresent hardness sensation greater than the hardness limitedin the force devices [5]. These studies are based on the
1 The authors are with Graduate School of Information Sciences, Tohoku
University, Sendai, Japan. cao.nan@rm.is.tohoku.ac.jp
2 The author is with Graduate School of Engineering, Nagoya University,
Nagoya, Japan.

528

978-1-5090-1424-8/17/$31.00 ©2017 IEEE

findings that higher frequencies in the model lead to the perception of greater hardness. In a transient collision vibration,
the role of frequency has been investigated. However, effectsof the envelope as the time constant in the model have notyet been thoroughly investigated.
This study investigated the role of the envelope as thetime constant on collision perception through measuring justnotification difference (JND) of the time constant. JND is
frequently used to evaluate perceptual resolutions for target
parameters as several studies found for amplitude (e.g. [6])and frequency (e.g. [7]) of periodic vibrations. The relationships between hardness perception and mechanical parameters including time constant have been investigated [8], [9];however, perceptual resolutions for the time constant remain
to be investigated.
In order to efficiently generate the collision vibrations
caused by tapping, we need to investigate the perceptual resolutions for parameters in rendering models. For example, if
we want to generate perceptual different collision vibrations,
we can generate the vibrations by using two perceptuallydifferent time constants of generated model based on its
perceptual resolutions.
We investigated JND of the time constant at several different frequencies. Generally, the most sensitive frequencies forhuman are in the range 200–300 Hz, so for the time constant,
the highest perceptual resolution (lowest JND) range may
be also in the range of 200-300 Hz. High frequencies like
1000 Hz are not sensitive for human and their JNDs of thetime constant are expected to be high. By investigating JND
of time constant, we can find how it will be changed byfrequency, for example in which frequency range JND oftime constant will be the lowest or highest, whether the JND
of time constant was linearly changed by frequency and if not
in which frequency range the JND of time constant change
most rapidly.
II. M ETHOD
In this section, we introduced the subjects, experimentparameters, apparatus, and procedures.
A. Subjects
7 subjects (age from 21 to 28, 6 males, 1 female, all righthanded) took part in the study. All subjects had no motor or
sensory limitations by self-report.
B. Experiment Parameters
1) Stimuli: The vibration feedback model developed fromthe tapping data is the decaying sinusoidal waveform [3]TABLE IS TABLE RANGE OF TIME CONSTANT

where Q(t) is the vibration produced by the contact, A is anattack amplitude, τ is a time constant and f is a frequency.
tQ(t) = Ae− τ sin(2π f t)

(1)

Considering an observed amplitude will be changed withthe change of time constant, dynamic amplitude was used tokeep the maximum value of waveform identical. This process
was to remove the perception effects of amplitude.
When Q0 (t0 ) = 0 and t0 = tan−1 (2π f τ)/2π f , Q(t0 ) = Q0
is the maximum value of the waveform. Set the maximum
value Q0 to be a constant value. Finally, the amplitudeadapted function of vibration model isQ0t

e− τ sin(2π f t)

(2)
e sin(2π f t0 )In addition, the generated vibration cannot reflect the input
vibratory profiles of signals because of physical characteristics of apparatus such as the frequency characteristics
of voice coil actuator. Therefore, we preliminary analyzed
frequency characteristics of the actuator and then modified
input signals using the frequency characteristics to generate
desired output. The frequency characteristic of the actuator
was measured and its result was shown in the Fig. 1.
P(t) =t− τ0Frequency (Hz)Lower boundary (ms)

150
250
500
800
1000

10.8
5.6
5
2.4
8

In order to get the JNDs at all test frequencies, a relatively high time constant of 50 ms was used based on the
preliminary experiments. A lower reference of time constant
was not used in this experiment because some subjects were
not able to distinguish the time constant at some frequencies
in the test range shown in Table. I. One of the results wasshown in the Fig. 3 by using the experimental procedurein this research. While the reference time constant was 30
ms and frequency was 800 Hz, the possible distinguish time
constant was not able to get due to the limited low boundaryof the time constant 2.4 ms.

Measured vibration
Fitting function curve
Starting point for fitting

0.4

voltage (V)60
40Gain (dB)

20

0.2
0
-0.2

0
-0.4
-20
-0.6
0

-40

0.05

0.1

0.15

0.2

0.25

t (s)
-60
0

500

1000

1500

2000

Fig. 2.

Frequency (Hz)The frequency characteristic of the vibrator2) Time Constant: The time constant was measured by theoutput signal of the piezo sensor rather than the input signal.
t
As shown in the Fig. 2, function y = A ∗ e− τ was foundby a least square fit to the positive and negative peaks ofthe vibration waveform. The maximum absolute value of the
waveform was set to be the start point for fitting the function.
Fig. 2 shows that time constant τ reflected the envelope shapeof the stimuli (fitting the peak values). When τ is bigger, theenvelope shape of stimuli is smoother and when τ is smaller,
the envelope shape is steeper.
5 times of the input time constant τi and output time
constant τo were measured. The standard error of five times
τo was calculated. The test time constants were used only
when the standard error was less than 5% of the averagevalue. Several input values were tested. Other stimuli withthe different time constant were linearly interpolated by thesevalues. The lower boundaries of the time constant at different
frequencies were shown in the Table. I.

14
12Time constant (ms)Fig. 1.

Time constant measured by piezo signal

10
8
6
4
2
0

10

20

30

40

50

Trail number

Fig. 3.

Distinguished time constant out of test range

3) JND: This psychophysical parameter is defined byWeber’s Law as the detectable difference between a reference
stimuli and test stimuli. JND of the time constant in this529

research was calculated as following,
JND =|tct − tc0 |
× 100
tc0

(3)

Where the tct is the time constant of test stimuli andthe tc0 is the time constant of reference stimuli. Both sides
of JNDs were investigated in this research. When the test
time constant was lower than the reference time constant,the calculated JND was called lower JND. When the test
time constant was higher than the reference time constant,the calculated JND was called upper JND.
C. Apparatus
As shown in Fig. 4, a subject gripped the actuator toperceive collision vibrations to measure gripped normal
force.
Collision vibration was apparatus consisted of an actuator(Vp210, ACOUVE LABORATORY, INC., JAPAN), amplifier and the PC. The vibrator was hanging in the air bysewing thread. A force sensing resistor was attached on thecenter of the actuator to measure the subjects’ force grippingon the actuator.
Grip on the actuator

Force sensing
resistor

Actuator

Foam for resting arm

Fig. 4. Experimental apparatus. Actuator was hanging in the air and subject
gripped the actuator by thumb and index finger.

Piezoelectric vibration sensor (VS-BV02, NEC TOKIN,
JAPAN) was used to measure the vibration of the actuator.
D. Design and Procedure
The subject sat comfortably in front of a PC and gripped
the actuator with his or her thumb and index finger. The
subject’s forearm rested on a big foam. According to thevalue of force sensing resistor, the subject was instructed
to grip the actuator with a constant force (around 0.25 N)
by the thumb and index finger of right hand. After subject
reached the required force, one short test run was completed
by each subject to get familiar with the procedure. The orderof the measurement runs was randomized distributed for eachsubject.

530

5 test frequencies (150, 250, 500, 800 and 1000 Hz) wereused. 250 Hz and 1000 Hz were chosen because in general,the most sensitive frequency is in the range 200 - 300 and the1000 Hz is the highest frequency in human haptic perceptual
range. 500 Hz was also an important frequency and many
haptic devices generate the frequency up to 500. 150 (lower
than human most sensitive range) and 800 Hz (higher than
500 Hz but may occur in collision vibration by tapping hardmaterials) were selected to better analyze the frequency effectin the human perceptual frequency range.
JNDs were obtained by an adaptive staircase method witha 1down-1up progression rule combined with a 3 interval
forced choice answer paradigm (3IFC) [10]. In this method,
JNDs obtained were corresponding to 50 percent point on
the psychometric function [10].
On each trial, the subject was presented with 3 stimuli.
There was 1.5-sec long interval between each stimulus. Oneof the stimuli was the test stimuli while the other two were
the same reference stimulus. The subject’s task was to findout the different one (test stimulus) out of the 3 stimuli
by pressing a corresponding key (”1”, ”2”, ”3”) on the
keyboard. Subjects were not instructed about what kind ofdifferences were between the test and reference stimulus.
Instead, at the beginning, the initial test stimuli was set
easily to be distinguished and subjects were able to find out
the differences between the reference and test stimulus bythemselves in the first several trails.
Due to the long time experiment (around 2 hours), subjects
might lose their concentration some time so they could repeat
the same 3 stimulus by pressing the key (”space”) but theorder of stimulus would be changed by every repeat. The
subject was suggested to choose their answer for the firsttime feeling.
Both sides of JNDs (upper and lower JNDs ) were tested
for the reference time constant 50 ms. In addition, upper
JNDs were tested at the time constant 10.8 ms. For all the
tests, the former 6 step sizes were set to be 5 ms (for fast
converge) and the following last 12 step sizes were set to be
1 ms (for finer resolution). A test series was terminated after
18 reversals.
Each measurement run lasted about 6 to 10 minutes andsubjects had 3 minutes break between 2 runs. The entire
experiment took about 2 hours.
III. R ESULTS
5 subjects took part in the tests of reference 50 ms and 5
subjects (3 subjects also did tests in reference 50 ms) took
part in the tests of reference 10.8 ms. For each subject witheach frequency, JND was calculated by the mean of the last
12 reversals of the staircase.
For reference 50 ms of the time constant, the average upper
JNDs of all subjects and standard errors were shown in theFig. 5, while the average of lower JNDs and standard errors
were shown in the Fig. 6. For reference 10.8 ms of the time
constant, the average of upper JNDs and standard errors wereshown in the Fig. 7.

250Time constant JND (%)

Time constant JND (%)

100

80

60

40

20

0

200

150

100

50

0
150 250

500

800

1000

150 250

500

800

1000

Frequency (Hz)Frequency (Hz)Fig. 5. Reference 50 ms: the average upper JND and standard error oftime constantFig. 7. Reference 10.8 ms: the average upper JND and standard error oftime constant
TABLE IIL OWER JND OF REFERENCE 50 MS : T HE RESULT OF A MULTIPLE
COMPARISON TEST PERFORMED BY USING THE B ONFERRONI METHODTime constant JND (%)

100

80

60

40

20

0
150 250

500

800

1000

Frequency (Hz)Frequency 1

Frequency 2

Mean difference

P-value

150
150
150
150
250
250
250
500
500
800

250
500
800
1000
500
800
1000
800
1000
1000

5.55
0.22
-9.60
-16.77-5.33-15.15-22.32-9.82-16.98
-7.17

1.00
1.00
0.49
0.02
1.00
0.04
0.00
0.45
0.02
1.00

Fig. 6. Reference 50 ms: the average lower JND and standard error oftime constant

7.1, p = 0.0017).
Two-way ANOVA with frequency and subject as independent variables were calculated separately for upper JNDs ofreference 50 ms, lower JNDs of reference 50 ms and upper
JNDs of reference 10.8 ms.
For upper JNDs of reference 50 ms, it showed no significant influence of the frequency (F(4, 24) = 1.88, p = 0.1625)
and the subjects (F(4, 24) = 2.59, p = 0.0762). It meant that
the JNDs of time constant were similar among frequencies.
For lower JNDs of reference 50 ms, it showed significant influences of both the frequency (F(4, 24) = 7.85, p =0.0011) and the subject (F(4, 24) = 5.85, p = 0.0043). A
multiple comparison test was performed by using the Bonferroni method to investigate which compared frequencies had asignificant difference on the JNDs of the time constant. The
results were shown in the Table. II. The first two columnsof Table. II showed the frequencies that were compared. The
third column showed the mean differences between the JNDs
of compared frequencies. The fourth columns show the pvalues for the compared frequencies. It showed that small pvalues occurred in the compared frequencies between 1000
and 150, 1000 and 250, 1000 and 500, 800 and 250 Hz(significantly different).
For upper JNDs of reference 10.8 ms, it showed nosignificant influences of the frequency (F(4, 24) = 2.26, p =0.1076) and significant influence of the subjects (F(4, 24) =IV. D ISCUSSION
Our experiment investigated the JNDs of time constantbased on the collision vibration model. To the best of ourknowledge, the perceptual resolution of collision vibration
parameters has not been investigated. Our research attributes
to understand the perceptual resolution of time constantwhich is a parameter in collision vibration model.
A. Sensitive frequency of time constant
3 kinds JNDs of the time constant (upper JND of reference
50 ms, lower JND of reference 50 ms and upper JND ofreference 10.8 ms) were tested in our experiment. The resultsof two-way ANOVA showed significant differences amongfrequencies only occurred for lower JND of reference 50 ms.
For lower JNDs of reference 50 ms, Fig. 6 showed thatthe shape of average JNDs had two parts, 2 slopes occurredat the frequency range ( -0.138 %/Hz lower than 250 Hz and0.085 %/Hz higher than 250 Hz) and lowest JND occurred at
250 Hz. The results of two multiple comparison tests showedthat 1000 Hz was significantly different from 150, 250, 500
Hz while 250 Hz was significant from 800. Average JNDs
of 800 and 1000 Hz were higher than JNDs of 150, 250,
500Hz. So it may mean the JNDs of the time constant werelower when the frequency was lower than 500 Hz (sensitive,
average JND was 12.8%) and the JNDs were higher when531

the frequency was higher than 800 Hz (not sensitive, average
JND was 27.9%).
For upper JNDs of reference 50 ms, Fig. 5 showed thatthe curve of average upper JNDs had a stage shape andat frequencies 150, 250 and 500 Hz, JNDs were similar(average 17.9%) while at frequencies 800 and 1000 HZ,
JNDs were similar (average 30.8%). Average JNDs of 800
and 1000 Hz were also higher than average JNDs of 150,
250, 500Hz. However, the result of two-way ANOVA showedthat there was no significant effect of frequency. It may
mean that the JNDs of time constant did not have obvious
differences in the frequency range. The average JND of all
frequencies was 23%.
For upper JNDs of reference 10.8 ms, Fig. 7 showed thatthe curve of average upper JND also had a stage shape andat frequencies 150, 250 and 500 Hz, JNDs were similar(average 52.8%) while at frequencies 800 and 1000 HZ,
JNDS were similar (average 66%). Average JND of 800 and1000 Hz were also higher than JND of 150, 250, 500Hz.
However, the result of two-way ANOVA shows that there
was no significant effect of frequency. It may mean that the
JNDs of the time constant do not have obvious differencesin the frequency range. The average JND of all frequencies
was 65%.
In conclusion, the sensitive frequency of time constant
was around 250 Hz (150 to 500 Hz, average JND was
12.8%) and it was not sensitive at high frequencies (800
to 1000 Hz, average JND was 27.9%) for the lower JNDs
of reference 50 ms. JNDs of the time constant did not haveobvious differences in the upper JNDs of reference 50 ms(average JND was 23%) and upper JNDs of reference 10.8
ms (average JND was 65%).
B. Time constant range effects on JNDs
The average upper JNDs of lower reference 10.8 ms were
bigger than the JNDs of reference 50 ms and relative higher
standard errors occurred. In the research [11], Hatzfled et al.
investigated the JND of force near the absolute threshold andevery subject was tested by using the individual thresholdat frequencies tested in [12]. They found JNDs are muchlarger than using the reference well above threshold. In our
research, we investigated JNDs of the time constant not theforce, however, the reference value may also affect the JNDs.
At lower reference 10.8 ms, subjects had significant effects
on JNDs of the time constant. The reason of subjects effects
on JNDs may be caused by their individual threshold on time
constant. In some frequencies, the reference time constant
10.8 ms may be near their threshold, so higher JNDs and big
differences between subjects occurred. In this research, we
did not investigate the threshold of the time constant because
the threshold of the time constant may be quite small. In our
tests, the smallest time constant were shown in the Table. I
could be easily perceived by subjects. However, the JNDs
(perception resolution) of the time constant may be largely
affected near the individual threshold.
Before we conducted these experiments, we assumed
that frequency would affect the JND of the time constant.

532

Considering the test range of time constant based on JNDs,
the time constant range (considering the differences among
subjects) was around 50 ms to 80 ms for the upper JNDs
of reference 50 ms, 30 ms to 50 ms for the lower JNDs ofreference 50 ms, 10.8 ms to 30 ms for the upper JNDs ofreference 10.8 ms. With the view of time constant range, theresults showed that there were no significant effects (subject
and frequency) at test range 50 ms to 80 ms, significant effect(frequency and subject) at the test range 30 ms to 50 ms andsignificant effects (subject) at the test range 10.8 ms to 30
ms. Therefore, for the high time constant range (e.g. 50 ms
to 80 ms), JNDs may be similar in the frequency range. For
the low time constant range (e.g. 10 ms to 30 ms), JNDs
may be largely affected by the individual threshold. Whilein the middle range of the time constant (e.g. 30 ms to 50ms), JNDs of the time constant may be significantly affectedby frequency. The perceptual threshold of the time constantand the effect of time constant range on perception resolution
need to be investigated in the future.
However, results of the experiment like the different
tendency between upper and lower JNDs may be due to thelimited subjects’ number. Further investigation is needed in
the future.
V. C ONCLUSION AND FURTHER WORKIn a transient collision vibration, the role of frequency has
been investigated. However, effects of the envelope as thetime constant in the model have not yet been thoroughly
investigated. This study investigated the role of the time
constant on collision perception through investigating justnotification difference (JND) of the time constant. The upperand lower JNDs of reference time constant 50 ms and upper
JNDs of reference time constant 10.8 ms have been tested in
the frequencies (150, 250, 500, 800, 1000 Hz). Significant
frequency effect on JNDs was found only for the lower JNDs
of reference time constant 50 ms. The sensitive frequency oftime constant was around 250 Hz (150 to 500 Hz, average
JND was 12.8%) and not sensitive at high frequencies (800
to 1000 Hz, average JND was 27.9%) for the lower JNDs
of reference 50 ms. JNDs of the time constant did not havesignificant differences in the upper JNDs of reference 50
ms (average JND was 23%) and upper JNDs of reference
10.8 ms (average JND was 65%). It suggests that perceptual
resolution of the time constant may be affected by frequency
in some range and relatively stable in some other range. The
effect of time constant range on perception resolution need
to be investigated in the future.
ACKNOWLEDGMENT
This work was partially supported by ImPACT Program
Tough Robotics Challenge.
R EFERENCES[1] P. Lamore, H. Muijser, and C. Keemink, “Envelope detectionof amplitude-modulated high-frequency sinusoidal signals by skinmechanoreceptors,” The Journal of the Acoustical Society of America,
vol. 79, no. 4, pp. 1082–1085, 1986.

[2] Y. Makino, T. Maeno, and H. Shinoda, “Perceptual characteristicof multi-spectral vibrations beyond the human perceivable frequency
range,” in World Haptics Conference (WHC), 2011 IEEE. IEEE,
2011, pp. 439–443.
[3] A. M. Okamura, J. T. Dennerlein, and R. D. Howe, “Vibration feedback models for virtual environments,” in Robotics and Automation,
1998. Proceedings. 1998 IEEE International Conference on, vol. 1.
IEEE, 1998, pp. 674–679.
[4] A. M. Okamura, M. R. Cutkosky, and J. T. Dennerlein, “Reality-basedmodels for vibration feedback in virtual environments,” IEEE/ASME
Transactions on Mechatronics, vol. 6, no. 3, pp. 245–252, 2001.
[5] K. J. Kuchenbecker, J. Fiene, and G. Niemeyer, “Improving contact
realism through event-based haptic feedback,” IEEE transactions on
visualization and computer graphics, vol. 12, no. 2, pp. 219–230,
2006.
[6] A. Israr, S. Choi, and H. Z. Tan, “Mechanical impedance of the handholding a spherical tool at threshold and suprathreshold stimulationlevels,” in Second Joint EuroHaptics Conference and Symposium on
Haptic Interfaces for Virtual Environment and Teleoperator Systems(WHC’07). IEEE, 2007, pp. 56–60.
[7] H. Pongrac, “Vibrotactile perception: Differential effects of frequency,
amplitude, and acceleration,” in 2006 IEEE International Workshop
on Haptic Audio Visual Environments and their Applications (HAVE
2006). IEEE, 2006, pp. 54–59.
[8] K. Higashi, S. Okamoto, H. Nagano, and Y. Yamada, “Effects ofmechanical parameters on hardness experienced by damped natural
vibration stimulation,” in Systems, Man, and Cybernetics (SMC), 2015
IEEE International Conference on. IEEE, 2015, pp. 1539–1544.
[9] K. Higashi, S. Okamoto, and Y. Yamada, “What is the hardness
perceived by tapping?” in International Conference on Human Haptic
Sensing and Touch Enabled Computer Applications. Springer, 2016,
pp. 3–12.
[10] H. Levitt, “Transformed up-down methods in psychoacoustics,” The
Journal of the Acoustical society of America, vol. 49, no. 2B, pp.
467–477, 1971.
[11] C. Hatzfeld and R. Werthschützky, “Just noticeable differences of
low-intensity vibrotactile forces at the fingertip,” in International

Conference on Human Haptic Sensing and Touch Enabled Computer
Applications. Springer, 2012, pp. 43–48.
[12] ——, “Mechanical impedance as coupling parameter of force anddeflection perception: experimental evaluation,” in International Conference on Human Haptic Sensing and Touch Enabled Computer
Applications. Springer, 2012, pp. 193–204.

533