Proceedings of the 2006 IEEE/RSJ
International Conference on Intelligent Robots and Systems
October 9 - 15, 2006, Beijing, China
Detection Threshold and Mechanical Impedance of the
Hand in a Pen-Hold Posture
Ali Israr1, Seungmoon Choi1,2 and Hong Z. Tan1
1
2
Haptic Interface Research Laboratory
Purdue University
West Lafayette, IN, USA
Currently at Virtual Reality and Perceptive Media Laboratory
POSTECH
Pohang, Kyungbuk, Republic of Korea
israr@purdue.edu, choism@postech.ac.kr, hongtan@purdue.edu
the stylus of a force-feedback device, it is necessary to
estimate detection thresholds using the same hand posture
under similar contact conditions.
A question relevant to this study was whether detection
thresholds should be specified in force and/or displacement
for force-feedback devices that are widely used in haptics
research. Whereas most sensory substitution devices such as
tactile aids for the hearing impaired are position displays [9,
10] (and therefore it makes sense to specify thresholds in
displacements), almost all haptic interfaces for teleoperation
and virtual environments are force displays [11, 12] (and we
are not aware of any data on force threshold except for a
previous study of our own [13]). In the present study, we
measured both acceleration and force data at human detection
threshold levels and studied their relationship.
The second objective of the present study was to estimate
the mechanical impedance of the human hand while holding
the stylus of a force-feedback device in a pen-hold posture.
Mechanical impedance is an important measure relating force
to position (and/or its derivatives). Numerous previous studies
have investigated the mechanical impedance properties of the
human skin for developing biomechanics models that can
guide the design of new haptic devices [14-18]. In the present
study, we first determined the mechanical impedance of our
apparatus in unloaded condition, and then in loaded condition
with the human hand as the load. The difference between the
mechanical impedance estimates from the loaded and
unloaded conditions provided an estimate of the impedance
due to skin contact alone (cf. [18]).
In the rest of this section, we review the literature on
detection threshold and mechanical impedance in Sec. 1.A and
1.B, respectively. We then present the methods used in the
psychophysical experiments in Sec. II. Experimental results
are shown in Sec. III. We discuss the results in Sec. IV,
followed by conclusions in Sec. V.
Abstract – We report position and force detection thresholds
for sinusoidal waveforms in the frequency range 10-500 Hz
delivered through a stylus. The participants were required to
hold the stylus in a way similar to that of holding the stylus of a
force-feedback device. A minishaker moved the stylus along its
length so that the majority of vibrations were presented
tangentially to the skin of the hand. The measured position
thresholds decreased initially with an increasing stimulus
frequency and formed a U-shaped curve in the high frequency
region. The thresholds of high frequency vibrations were lower
than those reported previously for vibrations that were
perpendicular to the skin, but were similar to the thresholds
reported earlier using vibrations that were tangential to the skin.
A similar force threshold curve was obtained using a force sensor
attached to one end of the stylus. Mechanical impedance of the
skin derived from velocity estimates and force measurements
indicated that the skin and tissues in the hand holding the stylus
can be modeled with mass-, damper- and spring-like elements. A
comparison of the mechanical impedance from the present study
with those reported previously showed similar results for
vibrations delivered in the tangential and normal directions to
the skin.
Index Terms - detection threshold, vibrotactile stimuli, position
threshold, force threshold, mechanical impedance.
I. INTRODUCTION
We investigated the detection thresholds for sinusoidal
motions of a stylus held by the hand. Several of our previous
studies had required the availability of detection thresholds for
the human hand while holding the stylus of a force-feedback
haptic device, so that the perceived intensity of proximal
stimuli could be estimated [1-5]. To the best of our
knowledge, such data are not yet available in the literature.
The majority of previous studies on displacement detection
thresholds have applied well-controlled stimuli to the skin
surface of a passively-supported hand (e.g., index fingerpad or
thenar eminence) in a direction that is perpendicular to the
skin (see, for example, [6]; and a review [7]). A recent study
by Brisben et al. [8] found lower detection thresholds for
vibrations transmitted through a hand-held tool in a direction
tangential to the skin of the palm. It is well known that many
factors, such as contact area, contact force, the use of a rigid
surround, and skin temperature can affect the detection
threshold levels. It follows that in order to assess the
perceived intensity of signals experienced by a hand holding
1-4244-0259-X/06/$20.00 ©2006 IEEE
A. Detection Threshold
Detection threshold is defined as the minimum stimulus
intensity that is barely perceivable by a human observer. It is
one of the most basic measures of human perception. Previous
psychophysical studies have shown that the human detection
threshold curve for sinusoidal vibrotactile displacement
variations is composed of two main segments when plotted
against stimulation frequency [7]. The low-frequency
472
segment, associated with the non-Pacinian channels, is
essentially flat. The high frequency segment, associated with
the Pacinian channels, decreases rapidly and then increases
again at the most sensitive frequency, forming a U-shaped
curve. The shape of the low- and high-frequency curves and
the most sensitive frequency vary depending on experimental
conditions such as contact area, contact force, contact
location, temperature of the skin, use of a rigid surround,
stimulus duration, the participant’s age, etc. In general, the
most sensitive frequency is in the range 200-300 Hz.
Bolanowski et al. measured detection thresholds in terms
of displacement on the glabrous skin of thenar eminence with
vibrations generated by a minishaker that were normal to the
skin [6]. The vibrations were confined in the area of
stimulation by an annulus surround and the temperature of the
skin was kept at 30º C. The results of their study, representing
a typical threshold curve, are as follows. The threshold curve
was flat from 0.4 to 3 Hz. It then decreased with a slope of −5
dB per octave from 3 to 40 Hz, and subsequently with a slope
of −12 dB per octave from 40 to 300 Hz. The most sensitive
frequency was at around 300 Hz. The threshold then increased
with a slope of about 2.7 dB per octave from 300 to 500 Hz.
Using a three-finger kinesthetic-to-cutaneous tactual
stimulator, Israr et al. obtained similar threshold levels with
vibrations presented normal to the skin of a fingerpad and
without a surround around the contact [19]. Compared to
Bolanowski et al.’s results, the threshold levels obtained by
Israr et al. were about 9 dB higher for frequencies below
about 20 Hz but were similar above 30 Hz. The most sensitive
frequency was around 200 Hz. The increase in threshold level
in the low and mid frequency region was mainly due to the
lack of surround restricting vibrations on the skin [20]. For
vibrations presented tangentially to the skin of a palm (in a
power grip), Brisben et al. [8] showed that the detection
thresholds at high frequency were lower than those reported in
[6, 19]. The slope of the threshold curve in the mid
frequencies was steeper (−15.7 dB per octave) than those
reported in [6, 19], and the most sensitive frequency was
between 150 and 200 Hz. The lower threshold in [8] might
have been due to a relatively large contact area in the palm
and/or direction of the vibrations (tangential as supposed to
perpendicular to the skin). For detection threshold expressed
in terms of force or torque, a recent study of ours measured
torque detection threshold when the participants held a
mechanical rotary switch held between the thumb and the
index finger [13]. The torque threshold curve exhibited a
similar trend as the displacement threshold curves reported in
[6] and [19].
In the present study, we measured displacement and force
detection thresholds while the participants held a stylus
connected to a minishaker in a pen-hold posture. Our results
are compared to those reported in [6] and [8].
Mathematically, it is the ratio of the applied dynamic force
( F ) to the velocity (ν ) of structural vibration; i.e., Z = F / v .
If both the force and velocity are periodic waveforms, then the
value of the mechanical impedance depends on the ratio of the
amplitude of the force, F, and that of the velocity, v, of the
waveforms, as well as the phase difference, φ , between the
waveforms; i.e. Z = ( F / v) e jφ .
The mechanical impedance of a structure can be
decomposed into many mechanical elements including mass
(inertia), damper (viscosity) and spring (stiffness). The
frequency response of each element is distinct. The mass
element shows a 20 dB/decade (6 dB/octave) slope in a dBlog plot of impedance vs. frequency, the damper a constant
line, and the spring a −20 dB/decade (−6 dB/octave) slope.
Previous studies have shown that all three mechanical
elements contribute to the mechanical impedance of the
human finger and other glabrous skin surfaces [14, 16-18]. In
one study [17], mechanical impedance measured at several
glabrous hand locations with normal vibrations showed
prominent spring-like properties of the skin in response to
mid-frequency vibrations and mass-like characteristics in
response to high-frequency vibrations. The viscous or
absorption properties were prominent in the resonant
frequency region (about 80-200 Hz) and in the low-frequency
region. Other studies have shown that mechanical impedance
varied with the grasping posture of the hand as well as the
location and area of the skin contacting the stimulator (see, for
example, [16]).
In the present study, a pen-shaped stylus was held by
participants in a manner similar to that of holding a pen or the
stylus of a force-feedback device. The stylus was excited
along its length, resulting in mostly tangential vibrations on
the skin surfaces of the hand holding the stylus. This was very
different from most previous studies where vibrations were
presented normal to the skin (although see [8, 15]). Another
difference between the present and previous studies is that we
applied threshold-level stimulation whereas many previous
studies used suprathreshold vibrations for determination of the
impedance model of the skin [14, 17]. In the present study, the
amplitudes of vibrations were very small, resulting in minute
skin stretches with little energy stored and/or absorbed by the
skin. It was expected that the viscous element would
dominate the mechanical impedance model of the finger skin
in the low/mid frequencies.
II. METHODS
A. Apparatus
The main component of the apparatus used in the present
study was a commercially-available mini-shaker (Bruel &
Kjaer, type 4810). A spare stylus from the PHANToM 1.0A
device (SensAble Technologies, Woburn, MA) was attached
to the minishaker in order to simulate the use of a typical
force-feedback haptic interface. An accelerometer (model
8794A, Kistler Instrument Corp., Amherst, New York) and a
force sensor (model Nano 17, ATI Industrial Automation,
B. Mechanical Impedance
Mechanical impedance ( Z ) is a measure of the resistance
in a mechanical structure against applied vibrations [14, 17].
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Apex, North Carolina) were fastened between the minishaker
and the stylus (see Fig. 1) through adapter plates. The bottom
adapter below the force sensor was fastened to the threaded
hole connected to the shaker actuator. The top adapter holding
the accelerometer was connected to the stylus by means of a
set screw. The apparatus was placed on several rubber pads
inside a metal enclosure that sat above a table. The stylus
protruded through a hole on top of the enclosure so that it
could be grasped by a hand. An arm rest was built to support
the participant's elbow and upper arm (see Fig. 2).
transformed into the frequency domain by taking the Fast
Fourier Transform (FFT) of the measured data. Mechanical
impedance was estimated by the ratio of the force/velocity
amplitudes, F/v, and was plotted against frequency under
unloaded condition. The ratio was highly linear (r2>0.99) and
a slope of 20 dB/decade indicated that only the inertial
element was dominant between the measured force and
position data (i.e., F = mx ) under unloaded condition.
B. Participants
Five males and five females (age 22-40 years old, average
28 years old) participated in the study. Nine out of the ten
participants were right-handed by self-report. Five of the
participants had either participated in other haptic perception
experiments in our laboratory before and/or were involved in
developing the hardware/software system used in the present
study. They were regarded as “experienced” users of forcefeedback and vibrotactile haptic devices. The rest of the
participants were regarded as “inexperienced.”
C. Procedure
The participant sat comfortably in front of a computer
monitor with the dominant hand holding the stylus. The
participant’s elbow and forearm rested on the arm rest that
supported a neutral wrist position (see Fig. 2). The participant
was instructed to hold the stylus like holding a pen or the
stylus of a PHANToM force-feedback device. Some
participants practiced by using the PHANToM device (not
shown) for a few minutes prior to the experiment. When the
stylus was held as instructed, the vibrations transmitted
through the stylus were mostly tangential to the skin in
contact. The areas of the skin touching the stylus are
illustrated by shaded ovals in the inset of Fig. 2.
Figure 1. Shaker assembly with one of the side panels removed.
The apparatus was controlled by a data acquisition board
(Nation Instruments PCI-6229, Austin, Texas) with an openloop control scheme. Command signals were generated from
the board that first passed through a 16-bit Digital-to-Analog
converter and then through a high-bandwidth linear audio
power amplifier (model LVC 608, AE Techron Inc., Elkhart,
Indiana) whose output was used to excite the minishaker
vertically (along the length of the stylus). The acceleration and
force data were captured by two 16-bit Analog-to-Digital
converters at a sampling rate of 10 kHz. The acceleration data
were integrated once and twice to obtain velocity and position
estimates, respectively, for further analysis of detection
threshold and mechanical impedance.
A calibration routine was performed to develop an inputoutput relationship for the apparatus at test frequencies by
fitting a least-square straight-line through the controlled
vibration input (in volts) and measured position data (in mm)
at several amplitude levels. The routine was performed
without loading the apparatus and with the human hand load.
The input-output relation was well represented by a straightline (r2>0.99) in the operating range with a significant
(p<0.0001) slope at each test frequency. The estimated slope
and intercept of the straight-line fit were used to compensate
the command signal in order to reach the desired output
vibration levels. Force and position measurements were
Figure 2. Experimental setup.
Seven test frequencies (10, 20, 40, 80, 160, 320, and 500
Hz) were used. They were chosen to be equally spaced on a
logarithmic scale except for the highest frequency. The order
of the test frequencies was randomized for each participant.
The duration of the stimulus was fixed at 1 sec with Hanning
windowing (100-msec rise and fall) to reduce transient effects.
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Thresholds were obtained by a three-interval, forced-choice,
one-up three-down adaptive method (See [21][22] for reviews
on adaptive methods). In this method, three consecutive
correct responses led to a reduction in the stimulus intensity
and one incorrect response an increase, both by a predefined
step size. Thresholds obtained this way correspond to the
79.4 percentile point on the psychometric function. On each
trial, the participant was presented with three 1-sec long
stimulus intervals with a 250-msec inter-stimulus interval.
One randomly-selected interval contained the test stimulus
and the other two contained no signal. The participant's task
was to indicate which one of the three intervals contained the
stimulus by pressing a corresponding key ("1", "2" or "3") on
the keyboard. The initial stimulus amplitude was chosen to be
well above the expected detection threshold level. The step
size was initially set to 4-dB (for faster convergence) and then
reduced to 1-dB (for finer resolution) after the first three
reversals (a reversal occurred if the stimulus amplitude
changed from increasing to decreasing, or vice versa). A test
series was terminated after 12 reversals at the 1-dB step size.
Visual and audio cues marked the start and end of each
interval. The participant was required to enter a response after
the end of the third interval. A new trial started right after the
participant’s response. Participants wore earplugs and
headphones that played pink noise to block auditory cues from
the apparatus.
The participants were allowed to feel the vibrations before
each test condition. At the end of the experiment session, the
stimulus intensity as a function of trial number was plotted.
The participant was asked to repeat the series if the data failed
to converge to a threshold level upon visual inspection by the
experimenter.
Each series took about 4-6 minutes.
Participants were asked to take a 5-minute break between test
conditions. The entire experiment took about 50 minutes. No
correct-answer feedback was provided during the experiment.
Before the experiment, the total contact area between the
participant’s hand and the stylus was estimated. The
participant’s hand was painted with washable paint. A sheet
of paper was wrapped around the stylus. The participant was
then asked to hold the stylus as instructed for a few seconds,
so that a good impression of the contact area was made. The
contact area was estimated by scanning the sheet of paper into
an AUTOCAD® program. The measured total contact area
ranged from 400 to 711 mm2 (average 550 mm2) for all
participants.
D. Analysis of position threshold
For each series, the last 12 reversals (six peaks and
valleys) at the 1-dB step size were used to calculate
position detection threshold (mean of the averages of the
peak-valley pairs) and its standard deviation (from the
averages) for each participant at each test frequency.
position peaks and valleys were taken as force peaks and
valleys. Recall that the force measurements were captured by
the force sensor that was fastened between the accelerometer
and the minishaker (see Fig. 1). In order to get accurate force
measurements applied on the hand holding the stylus, the
sensor should have been clamped or grounded, so that the
forces due to the inertia of the supporting structures could be
eliminated. In most previous studies, the force sensor was
placed directly in contact with the skin to measure forces due
to skin contact [14, 17]. This was not possible in the present
study due to multiple contact locations between the stylus and
the skin of the hand holding the stylus. Therefore, we took the
approach of subtracting forces measured in unloaded
condition from those in loaded condition, in order to isolate
the net forces applied to the hand holding the stylus.
III. RESULTS
Figure 3 shows the position detection threshold curve at
test frequencies used in the experiment. Each point represents
the average over the ten participants and the corresponding
standard error. For comparison, the figure also shows a dashed
line representing the detection thresholds reproduced from
Bolanowski et al. [6], and a solid line representing those from
Brisben et al. [8]. The shape of the threshold curve found in
the present study was very similar to those reported earlier:
the threshold level decreased as frequency increased, reached
a minimum at around 160-320 Hz, and increased again at
higher frequencies. The slope of the threshold curve in the
frequency range 10-160 Hz varied from −10 dB per octave
(10-20 Hz) to −18 dB per octave (40-80 Hz) with an average
slope of −13 dB per octave. The slope was 6 dB per octave
between 320 and 500 Hz.
six
the
six
six
Figure 3. Measured position detection thresholds and
comparison to the published detection thresholds.
A two-way ANOVA with frequency and participant as
independent variables showed that both the frequency and
participant factors as well as their interaction term were
significant (for frequency F(6,350)=17087, for participants
F(9,350)=287, interaction term F(54,350)=57, all p<0.0001).
In order to examine the possible effect of participants’ prior
E. Analysis of force data
Force data were processed in a manner similar to the
position threshold data. The force values corresponding to the
475
experience with using haptic devices, a two factor ANOVA
(frequency and experience) was conducted. The results
showed no significant difference in threshold between the
experienced and inexperienced participants (F(1,406)=0.49,
p=0.48).
The force detection thresholds are shown in Fig. 4 for all
participants. The error bars present the standard errors of the
means. The shape of the force threshold curve was similar to
that of the position threshold curve. The force threshold
decreased with the increase of test frequency and exhibited a
U-shaped curve at high frequencies after achieving a
minimum at around 160 Hz. The slope in the frequency range
10-160 Hz varied from −1.6 dB per octave (between 10 and
20 Hz) to −19.5 dB per octave (between 40 and 80 Hz and
between 80 and 160 Hz) with an average slope of −12 dB per
octave. The rising slope was 21 dB between 320 and 500 Hz.
Similar to the position threshold data, a two-way ANOVA
showed that both the frequency and participant factors as well
as the interaction term were significant (for frequency
F(6,350)=3087, for participants F(9,350)=251, interaction
term F(54,350)=57, all p<0.0001). The effect of experience
was also similar to that exhibited by the position threshold
data: not significant (F(1,406)=0.09, p=0.76).
The average mechanical impedance of the skin was
calculated by the ratio of the average force data (Fig. 4) to the
average velocity data at the threshold levels. The impedance
of the skin as a function of frequency is presented in Fig. 5.
For frequencies below 40 Hz, the mechanical impedance of
the skin was roughly constant (−36 to −38 dB re 1 N-sec/mm
peak). It then decreased initially with a slope of −7 dB per
octave between 40 and 80 Hz and subsequently with a slope
of −16 dB per octave between 80-160 Hz. The impedance
was almost constant between 160-320 Hz and then rose with a
slope of 16 dB per octave between 320-500 Hz.
IV. SUMMARY AND DISCUSSION
The position threshold curve obtained in the present study
was similar to those obtained in [6] and [8] (compare curves
in Fig. 3). The average slope of the threshold curve in the
present study and those of the previous studies are very
similar at high frequencies. The lower slope in the midfrequency portion found in Bolanowski et al. [6] was mainly
due to the use of a surround around the contact area that
restricted the spread of mechanical vibrations across the skin
surface [7, 19, 20]. Our threshold data at 10 Hz (26 µm) and
20 Hz (8.5 µm) were above those reported in [6, 8]. Our
lowest threshold level was obtained at 320 Hz (0.06 µm),
which was at a higher frequency compared to 150 Hz (0.03
µm) obtained in [8] but similar to 300 Hz (0.13 µm) obtained
in [6]. The discrepancies in the threshold level are mainly due
to the differences in experimental conditions including contact
site (multiple sites at the fingerpads and along the sides of
digits in the present study, thenar eminence in [6], palm in
[8]), contact area (single or multiple contacts), direction of
vibration (normal or tangential) and the use of a surround (in
[6] but not in [8] or the present study). It has been shown in
both [8] and [15] that the fingerpad is more sensitive to
tangential vibrations than normal vibrations. In general, the
overall shapes of the curves are similar, including a steep
slope at around mid/high frequency region and then a Ushaped curve at high frequency region. The most sensitive
frequency lies around 200-300 Hz.
The force threshold curve obtained in the present study is
perhaps the first of its kind (Fig. 4). The general shape of the
force curve was similar to that of the position threshold curve
(Fig. 3). The main difference between the force and position
threshold curves was that the force curve exhibited a lower
slope at low frequencies and a steeper slope at high
frequencies. The relationship between the position and force
thresholds can be better explained by considering the
mechanical impedance derived from them (Fig. 5).
The mechanical impedance of the skin obtained in the
present study exhibited all three components of mass, damper
and spring as reported in previous studies. The low slope at
low frequencies (< 40 Hz) indicated a prominent viscous
element. A stiffness component was observed in the midfrequency region (40 to 80 Hz) by the −7 dB per octave slope,
and an inertial component was dominant at high frequencies
(> 320 Hz) as shown by the rising slope of the curve in Fig. 5.
Figure 4. Measured force detection thresholds. Shown are group
averages and standard errors.
Figure 5. Mechanical impedance of the skin.
476
The shape of the mechanical impedance curve (Fig. 5) was
very similar to the one reported for the glabrous skin of the
hand in [17]. In [17], the low frequency skin impedance
ranged from 20-35 dB re 1 N-sec/m peak and had a resonance
frequency (i.e., frequency at the lowest impedance level)
between 100-200 Hz at the glabrous skin of the finger
(including distal, middle and proximal phalanges). The
amplitude of the impedance at the resonance frequency was
about −10 to +15 dB re 1 N-sec/m peak. The impedance then
increased as the frequency increased. The similarities between
the results from the present study and those reported by
Lundstrom [17] indicate that the mechanical impedance of the
skin is the same for sinusoidal vibrations presented either
normal or tangential to the skin.
was a post-doctoral research associate in the Haptic Interface
Research Laboratory at Purdue University when this work was
initiated. This work was supported in part by research grant
No. R01-DC00126 from the National Institute on Deafness
and Other Communication Disorders, National Institutes of
Health, and in part by a National Science Foundation award
under Grant 0098443-IIS.
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Psychophysics, vol. 63, pp. 1279-1292, 2001.
V. CONCLUDING REMARKS
In the present study, haptic force and position detection
thresholds for sinusoidal waveforms as well as the impedance
of the human hand were evaluated while the participants held
a stylus with a pen-hold posture. The low- and high-frequency
thresholds differed from previous studies in which vibrations
were presented normal to the skin and with an annulus
surround around the contact. However, the thresholds were
similar to those studies in which vibrations were presented
parallel to the skin and in the absence of the surround. The
overall shape of the force threshold curve was similar to that
of the position threshold curve. The estimated mechanical
impedance was dominated by damping effects in the low
frequency region and inertial effects in the high frequency
region. Overall, the mechanical impedance of the skin
associated with tangential vibrations found in the present
study was similar to those reported in previous studies using
normal vibrations.
The results of the present study have provided muchneeded empirical data on position and force thresholds that
have been specifically measured for the use of a stylus
attached to the end point of a force-feedback haptic device.
They can be used to assess the perceived intensities of
proximal stimuli while interacting with a virtual haptic
environment through a force-feedback device. We will be
using these data in the future for detailed analyses of haptic
perception of real and virtual objects. We will also investigate
if the mechanical impedance of the skin remains the same with
suprathreshold-level vibrations presented in a pen-hold
posture. To the extent that the mechanical impedance of the
skin depends on stimulation level, we will then investigate
trends in variations of the mechanical impedance as a function
of stimulus amplitude, in an effort to better understand the
interaction between the skin and proximal stimulus. Such
modeling efforts will be useful for the design of new haptic
interfaces in the future.
ACKNOWLEDGMENT
The authors wish to thank Roy B. Chung, Chanon M.
Jones and Monica Siepmann for their assistance with
debugging and data collection and analysis. The second author
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