TYPE Brief Research Report
PUBLISHED 15 July 2022
DOI 10.3389/frvir.2022.797993

OPEN ACCESS

Weight illusion by presenting
vibration to the ﬁngertip

EDITED BY

Jeremy Cooperstock,
McGill University, Canada
REVIEWED BY

Pascal E. Fortin,
École de Technologie Supérieure (ÉTS),
CanadaVincent Levesque,École de Technologie Supérieure (ÉTS),
Canada*CORRESPONDENCE

Giryeon Kim,
kim.giryeon.y2@s.mail.nagoya-u.ac.jp
SPECIALTY SECTION

This article was submitted to Haptics,
a section of the journal
Frontiers in Virtual Reality
RECEIVED 19 October 2021
ACCEPTED 27 June 2022
PUBLISHED 15 July 2022
CITATION

Kim G, Okamoto S, Akiyama Y and
Yamada Y (2022), Weight illusion bypresenting vibration to the ﬁngertip.
Front. Virtual Real. 3:797993.
doi: 10.3389/frvir.2022.797993
COPYRIGHT© 2022 Kim, Okamoto, Akiyama and
Yamada. This is an open-access article
distributed under the terms of theCreative Commons Attribution License(CC BY). The use, distribution or
reproduction in other forums ispermitted, provided the original
author(s) and the copyright owner(s) are
credited and that the original
publication in this journal is cited, in
accordance with accepted academic
practice. No use, distribution or
reproduction is permitted which does
not comply with these terms.

Giryeon Kim 1*, Shogo Okamoto 1,2, Yasuhiro Akiyama 1 andYouji Yamada 1
1
Department of Mechanical Systems Engineering, Nagoya University, Nagoya, Japan, 2Department ofComputer Science, Tokyo Metropolitan University, Hachioji, Japan

It is difﬁcult for humans to perceive weight accurately, because the perceptionof weight is produced by the process of multisensory integration. This implies
that, by manipulating certain factors, the weight of an object could beperceived differently from the actual weight. Here, the effects of vibration
on weight perception were investigated using behavioral tests andquestionnaires. As a behavioral test, from a number of identically appearing
non-vibrating boxes of different weights, participants had to select a box thatthey perceived to be of the same weight as a vibrating box. They were also
asked whether vibration affected the perceived weight of the box. Even
though they reported that vibration created an illusion of weight, theresults of the behavioral test did not show a statistically signiﬁcant effect ofvibration on perceived weight. Furthermore, we investigated how thefrequency of vibration affected the illusion and found that the weightillusion requires smaller acceleration of vibration at lower frequencies,
such as 30 Hz. The illusion was more intense at lower frequencies than at
higher frequencies, such as 200 and 300 Hz. Thus, this study demonstrated
that vibrotactile stimuli presented to the ﬁngertips produce a weight illusion:vibrating objects are perceived to feel heavier. Even though the principles ofthis illusion are still unknown, the effect is concrete, and our approach allows
easy implementation in virtual reality applications.
KEYWORDS

ﬁngertips, haptics, threshold, vibration, weight illusion

1 Introduction
Weight is expressed as mass, which is deﬁned as the amount of force acting on an
object, divided by gravitational acceleration. However, it is difﬁcult for humans toperceive weight accurately, because the perception of weight is produced by theprocess of multisensory integration. In other words, by manipulating certain factorsthat affect the perception of weight, weight could be perceived differently from theactual weight.
The size-weight illusion is a representative example of weight illusion, in which alarger object feels lighter than a smaller one, even though their actual weights are thesame (Charpentier, 1891). The process of correcting the discrepancy between thephysical weight and the weight predicted by the internal model in the human brain

Frontiers in Virtual Reality

01

frontiersin.org

Kim et al.

10.3389/frvir.2022.797993

2 Methods

before lifting is considered to be a reason for the weightillusion (Ross, 1969), although this is still debated(Flanagan and Beltzner, 2000). In addition to the size ofthe object, material (Ellis and Lederman, 1999), color(Warden and Flynn, 1926), and brightness (Walker et al.,2010) create similar illusory effects. Overall, objects that are
expected to be heavier are perceived as being lighter. For
example, before they are lifted up, darker objects are expected
to be heavier than brighter objects. However, once they arelifted up, darker objects feel lighter, contrary to expectations(Walker et al., 2010). A similar illusion has also been reported
for other modalities. For example, blue objects, which areperceived as looking colder, are perceived as being warmer
when they are actually touched (Ho et al., 2014).
Proprioception is generally considered to be the dominant
mediator in weight perception; however, cutaneous cuesalso signiﬁcantly contribute to weight perception(Johansson and Westling, 1984; Johansson and Birznieks,
2004; van Beek et al., 2020). When the skin is stretched,
the sense of force increases in the direction of thisstretch (Matsui et al., 2013). In particular, when an object
is lighter, the inﬂuence of cutaneous cues is more prominentcompared to proprioception (Minamizawa et al., 2010; van
Beek et al., 2020). Haptic interfaces that activate cutaneous
sensations to present a sense of weight for virtual reality
applications have been studied previously (Minamizawa
et al., 2008, 2010; Guinan et al., 2012, 2014; Choi et al.,2017; Park et al., 2018).
Vibrotactile or vibratory stimuli have been investigated topresent the sense of force and weight by adjusting wave
parameters and the presentation timing of stimuli.
Asymmetric vibrations create a sense of force in the directionof larger amplitude of the vibrations (Amemiya and Maeda, 2008;
Culbertson et al., 2016; Tanabe et al., 2016). The presentation ofvibrations in accordance with hand movements makes objects
perceived to be heavier (Okamoto et al., 2011; Nagano et al.,2015).
Meanwhile, we found that presentation of sinusoidal
vibrotactile stimuli, unrelated to the motion of the hands andobjects, makes objects feel heavier during lifting. Broadly, thisphenomenon may be called an illusion. There have been noreports about this phenomenon, and there is no obvious
knowledge concerning this illusion. This study aimed toinvestigate the occurrences and properties of thisphenomenon. The effect of vibration on weight perception
and the frequency-dependence of the weight illusion were
investigated. Once these properties are revealed, continuous
vibrotactile stimuli, which are possible to implement with
inexpensive motors, can be employed in handheld controllersof commercial virtual reality gadgets and smart phones to present
illusory weight. This study was approved by the institutional
review board of the Hino Campus of Tokyo Metropolitan
University (H21-008).

Frontiers in Virtual Reality

2.1 Experiment 1: Effect of vibrotactile
stimuli on behavioral responses andintrospective weight perception
2.1.1 Participants
Fifteen male, right-handed and healthy university students
over the age of 20 years participated in the experiment. All
participants provided written informed consent.

2.1.2 Stimuli and apparatus
A cubic box (104.3 g), made of acrylic, with a side length of
65 mm, as shown in Figure 1A, was used as a weight stimulus.
The outside of the box was enclosed evenly with black tape
(MT-08-BK-50MM, DIATEX Co. Ltd., Japan) to make its
inside invisible and to prevent the ﬁngers from slipping. An
eccentric rotating mass vibration motor (TP-2528C-24, Three
Peace Co., Ltd., Japan) was ﬁxed inside the box. The motor
rotated around an axis perpendicular to the bottom surface ofthe box, and generated vibrations of 63.7 Hz, with anacceleration amplitude of 9.2 m/s2 in the normal directionof the contact surface of the ﬁngers holding the box. The
acceleration amplitude and vibration frequency of the box
were determined by the authors based on an informal
experiment, and the vibration was sufﬁcient to give theauthors the weight illusion.
To investigate the subjectively equivalent weight of thevibrating box, we prepared a total of 17 non-vibrating boxes(Figure 1B) that were identical to the vibrating box in appearance(Figure 1A). However, the weight of the non-vibrating boxes
varied exponentially from 74.5 to 138.5 g. The increment ratio in
the weight of the non-vibrating boxes was 1.04. The weight of thebox was adjusted by ﬁxing several weights inside the box, to thecenter of the bottom of the box. One of the non-vibrating boxes
had a similar weight to the actual weight of the vibrating box,with a difference in weight of less than 1 g.

2.1.3 Task
First, to investigate the subjectively equivalent weight ofthe vibrating box, we conducted a matching task using thevibrating box as the standard stimulus and the non-vibratingboxes as the comparison stimuli. The participants alternately
lifted the vibrating box and the non-vibrating box andcompared their perceived weights. They were instructed tolift each box slowly to prevent them from judging the weight ofthe box based on the inertial forces. The participants used only
their dominant hands for lifting, to eliminate the potential
differences in muscle strength between dominant and nondominant hands. There was no limit to the number of times
the boxes could be lifted, considering the difﬁculty incomparing the weights. Then, participants selected one of
the non-vibrating boxes that they perceived as being closest in

02

frontiersin.org

Kim et al.

10.3389/frvir.2022.797993

FIGURE 1(A) Vibrating box and its schematic diagram. An eccentric mass vibration motor present inside the box makes the box vibrate. (B) Non-vibratingboxes that are identical to the vibrating box in appearance, but with different weights. (C) Lifting the box with ﬁve ﬁngers in Experiment 1. (D) Lifting
the voice coil oscillator in Experiments 2 and 3.

2.2 Experiment 2: Acceleration andfrequency dependency of weight illusionweight to the vibrating box. This task was considered as one
trial. Each participant completed nine trials, which differed interms of the number and placement of the non-vibratingboxes. More speciﬁcally, in order to prevent theparticipants from learning the weight of the non-vibratingboxes in the repeated trials, a different number of nonvibrating boxes (9–17), which included the same weight as
the vibrating box, were used for each trial, and they wereplaced randomly. To mitigate skin numbness owing tovibration, the participants were instructed to hold the box
for no more than 3 s. Participants could rest to avoid fatigue
after each trial.
Second, to investigate the perception of the weight of thebox, participants compared the same box between thevibrating and non-vibrating conditions. They were thenasked to report whether the box in the vibrating condition
felt 1) heavier, 2) the same, or 3) lighter than in the nonvibrating condition. The vibration did not last longer than 3 s,
as explained above.
In both experiments, participants were instructed to holdeach box with the pads of all ﬁve ﬁngers and to lift the box
without placing their elbows or wrists on the desk, as shown in
Figure 1C. Moreover, to cancel the sound generated by thevibration of the box, pink noise was played throughheadphones.

2.2.1 Participants
Thirteen male, right-handed and healthy university students
over the age of 20 years participated in the experiment. Allprovided written informed consent.

2.2.2 Apparatus and stimuli
To control the frequency and acceleration independently, an
oscillator that was different from Experiment 1 was used. A voicecoil oscillator (Vp408, Acouve Laboratory, Inc., Japan, 85 g) wasused to present the vibrotactile stimuli. The sinusoidal vibratory
signals were generated by a function generator (SG-4105, Iwatsu
Electric Co., Ltd., Japan) and were ampliﬁed using an audio
ampliﬁer (FX-AUDIO-FX252A, North Flat Japan Co., Ltd.,
Japan). Five frequencies (30 Hz, 60 Hz, 100 Hz, 200 Hz, and300 Hz) were tested. Fourteen levels of acceleration wereprepared for each frequency. Only for the 200 Hz, 18 levels
were provided to present sufﬁciently large range such that all
the participants could feel the illusory weight. These were in ageometric series, with a ratio of 1.25. The highest level ofacceleration for each frequency was determined to be
sufﬁciently greater than the value obtained in an informal
experiment involving ﬁve participants. Similarly, the lowest
level of acceleration was sufﬁciently smaller than anacceleration which did not cause the weight illusions. The
amplitudes of the sinusoidal acceleration of the strongest
stimuli for the ﬁve frequencies (30 Hz, 60 Hz, 100 Hz, 200 Hz,
and 300 Hz) were 10.6 m/s2, 14.1 m/s2, 19.4 m/s2, 151.7 m/s2, and154.5 m/s2, respectively. The acceleration amplitude of theweakest stimuli for the ﬁve frequencies were 0.6 m/s2, 0.8 m/s2,
1.7 m/s2, 4.3 m/s2, and 8.5 m/s2, respectively. Acceleration of thevibratory stimuli was measured using an accelerometer (Model2320B, Showasokki Co., Ltd., Japan) attached to the side of theoscillator and ampliﬁer (Model-4035-50, Showasokki Co., Ltd.,
Japan).

2.1.4 Analysis
The geometric mean of the weights of the non-vibratingboxes that participants selected as having a weight equivalent tothat of the vibrating box was calculated for each participant. We
then compared the arithmetic mean of these boxes among all
participants with the weight of the standard stimulus, using a ttest.
The proportion of the different answers in the introspective
experiment was tested by Z-test. We investigated whether the
proportion of respondents who answered that vibration made thebox feel heavier was signiﬁcantly different from 1/3.

Frontiers in Virtual Reality

03

frontiersin.org

Kim et al.

10.3389/frvir.2022.797993

2.2.3 Task

2.3.2 Apparatus and stimuli

The minimum acceleration amplitudes, i.e., the thresholds thatcaused a weight illusion were investigated for each of the ﬁve
frequencies. The experiment was conducted following method oflimits which is a psychophysical test about sensory threshold.
Participants held the oscillator in their dominant hands as shownin Figure 1D. The oscillator was held in a way that the vibration waspresented to the ﬁnger in a direction horizontal to the ground. The
oscillator was repeatedly switched on and off to present andwithdraw the vibrotactile stimuli with 3-s intervals to mitigate
skin numbness. The repetition was continuously conducted
multiple times; hence order effects of vibrating and still
conditions could be eased or cancelled. Participants were asked
to judge whether the vibratory stimulus made the oscillator feelheavier, lighter, or not. In ascending trials, the initial amplitude of
the acceleration was that for which the weight illusion was notexpected. Then, the amplitude of the acceleration was increased
gradually, and the trial was completed once the participant
experienced the increase in the weight. Descending trials started
with an acceleration at which the weight illusion was expected tooccur. The amplitude of the acceleration was then decreased
gradually, and the trial was completed when the participant nolonger felt the increase in the weight. For each frequency, three
ascending and three descending trials were alternately conducted. A
total of 30 trials (three ascending and three descending trials for eachof the ﬁve frequencies) were conducted for each participant.
As in Experiment 1, the participants lifted the oscillator using
the ﬁve ﬁngers, while avoiding touching the desktop with theelbows, and the sound cues were masked.

The voice coil oscillator (Vp408, Acouve Laboratory, Inc.,85 g), that was used in Experiment 2, was used to present thevibrotactile stimuli. Five sinusoidal vibration stimuli withdifferent frequencies were presented, that is, 30 Hz, 60 Hz,
100 Hz, 200 Hz, and 300 Hz. The amplitudes of accelerations
for the vibration stimuli were 4.4 m/s2 at 30 Hz, 9.5 m/s2 at 60 Hz,
13.8 m/s2 at 100 Hz, 59.8 m/s2 at 200 Hz, and 109.7 m/s2 at
300 Hz. The accelerations were 2 dB higher than the average
acceleration thresholds calculated from ﬁve participants in theearly stage of Experiment 2. This referred values were slightly
different to the overall results of Experiment 2, which analyzed
with 13 participants, with an average difference of 3.5%.

2.2.4 Analysis

2.3.4 Analysis

In the ascending trials, we calculated the threshold as the averageof the acceleration amplitude of the ﬁrst stimulus that caused theweight illusion and that of the stimulus presented immediately prior.
In the descending trials, the threshold was determined as the averageof the acceleration amplitude of the ﬁrst stimulus that no longer
caused the weight illusion and that of the stimulus presented
immediately prior. The thresholds for six trials weregeometrically averaged for each frequency and each participant.
Additionally, the displacement thresholds for eachparticipant were calculated by using the results of accelerationthresholds and their frequencies.

We planned to screen out the participants from the analysis
whose results differed signiﬁcantly between the two trials in thisexperiment. However, there was no such participant. We used
the mean ranks between the two trials as each participant’s
results. The rank results of ﬁve different vibrotactile stimuli
were compared using the Wilcoxon signed-rank test, with the
Bonferroni correction of p-values.

2.3.3 Task
Five types of vibration stimuli were presented to theparticipants, who were blinded to the frequencies, and theparticipants were asked to rank them in terms of the intensityof the weight illusion (the perceived weight). Different stimuli
could not be assigned the same rank. Participants held theoscillator with their dominant hand, as in Experiment 2, andwere presented stimuli one by one. Participants could experience
the vibrotactile stimulus as many times as they required, until they
could conﬁdently compare the intensity of the illusion of thedifferent stimuli. Each participant repeated this ranking task twice,with a few minutes apart. As in the previous experiments, theparticipants held the device with their ﬁve ﬁngers, while refraining
from placing their elbows on the desktop. The vibration did notlast longer than 3 s, and the vibratory sounds were masked.

3 Results
3.1 Experiment 1: Subjectively equal
weights and introspective reports

2.3 Experiment 3: Comparison of thesubjective intensity of the weight illusion
among different frequencies

The results of the introspective reports and subjectively
equivalent weights are summarized in Figure 2. Thirteen of
15 participants answered that the vibration made the box
seem heavier (signiﬁcantly greater than the chance level;z(14) = 16.97, p = 1.36 × 10–64, Z-test). On the other hand,
many participants selected boxes that were lighter than thevibrating box as having subjectively equivalent weights. The

2.3.1 Participants
Fifteen healthy university students (14 males and one female)over the age of 20 years, participated in the experiment after
providing written consent. They were all right-handed.

Frontiers in Virtual Reality

04

frontiersin.org

Kim et al.

10.3389/frvir.2022.797993

FIGURE 2
Point of subjective equality of weight and introspective report of participants. Error bars indicate standard errors.

FIGURE 3
The threshold of acceleration (A) and displacement (B) to create a weight illusion for each frequency. The illusion occurred with vibratory
accelerations or displacements above the line, but not those below the line.

2015). Therefore, the difference in this experiment (3.8%) was
smaller than the Weber ratio and is not substantially meaningful.

mean and standard error of subjectively equivalent weights
among the participants were 100.1 ± 2.0 g. This was 4.2 g(3.8%) less than the actual weight of the vibrating box(104.3 g), but the difference was not statistically signiﬁcant (t(14) = − 2.08, p = 0.056, two-tailed t-test) and the difference wassmaller than the discrimination threshold of weight. The
discrimination threshold of weight perception depends on themethod of lifting and the weights of the objects (Raj et al., 1985).
According to studies in which the entire arm was used to lift
objects weighing 50–200 g, the Weber ratio is between 6 and 13%(Brodie and Ross, 1984; Ross and Brodie, 1987; Hiramatsu et al.,Frontiers in Virtual Reality

3.2 Experiment 2: Minimum vibratory
intensities to cause the illusion
Figure 3A shows the acceleration thresholds that cause theweight illusion at each frequency. The 30 Hz frequency, thelowest frequency in this experiment, required the lowest
acceleration to create the weight illusion. As frequencies

05

frontiersin.org

Kim et al.

10.3389/frvir.2022.797993

FIGURE 4
Box plots of intensity ranks of illusion by frequencies. * and ** indicate signiﬁcant differences at 5 and 1% levels, respectively. Signiﬁcantdifferences were investigated using the Wilcoxon signed-rank test with Bonferroni correction.

behaviors of participants are adapted through repeated trials(Flanagan and Beltzner, 2000; Grandy and Westwood, 2006;
Shadmehr et al., 2010). In the size-weight illusion, after a few
trials, the effects of different volumes on the lifting motions
disappear; however, the illusion remains (Flanagan and Beltzner,
2000; Grandy and Westwood, 2006). We consider that a similar
phenomenon to the size-weight illusion occurred in Experiment
1. This is potentially because the illusion of weight is caused not
only by proprioception but also by perceptual mechanisms,
which include other factors (Flanagan and Beltzner, 2000).
In Experiment 1, two of ﬁfteen participants did notexperience weight illusion. This may be because the intensityof the vibration stimuli used in Experiment 1 was not sufﬁciently
large to create an illusion for them. The frequency andacceleration amplitude of the vibration stimuli used inExperiment 1 were 63.7 Hz and 9.2 m/s2. In Experiment 2, asshown in Figure 3A, some people did not experience illusions at
this frequency and acceleration amplitude; however, when theamplitude of the acceleration was increased in Experiment 2, they
did experience the weight illusion.
The weight illusion by symmetric vibrations in this study andthe method to generate the force illusion by asymmetricvibrations (Amemiya and Maeda, 2008; Culbertson et al.,2016; Tanabe et al., 2016) are similar since they both use
vibratory stimuli. However, we speculate that they are basedon different principles. In the asymmetric vibration
presentations, the illusion of force is generated in the
direction of the greater vibration acceleration (Amemiya and
Maeda, 2008). If this acceleration is in the direction of gravity, theobject feels heavier. The effect of illusion is strong when theasymmetry of the stimulus is salient (Amemiya and Maeda, 2008;
Tanabe et al., 2016). On the other hand, the vibration stimulus

increased, larger accelerations were needed to create the illusion.
The threshold did not mostly exceed 10 m/s2 below 100 Hz, but
increased to approximately 35 m/s2 above 200 Hz. Figure 3B
shows the amplitudes of the vibratory displacements computedfrom the acceleration values. Contrary to the accelerationthresholds, the displacement thresholds decreased as thefrequency increased. This displacement threshold was morethan 100 times larger than the threshold for perceiving
vibration (Bolanowski et al., 1988; Brisben et al., 1999).

3.3 Experiment 3: Intensities of illusions
caused by different frequencies
Figure 4 shows box plots of the ranks of the intensity of theweight illusion for the ﬁve vibration frequencies. The larger ranks
indicate greater perceived weight. Based on participants’ responses,
the 30 Hz stimulus was associated with the greatest perceived
weight, which was signiﬁcantly different from the other stimuli, ata signiﬁcance level of less than 1%. However, except for the 30-Hz
stimulus, only the ranks for 60 and 300 Hz were signiﬁcantly
different at the 1% signiﬁcance level (T = 184, p = 0.004).

4 Discussion
4.1 General discussion
In Experiment 1, 13 of 15 participants reported experiencing
weight illusions, even though the subjectively perceived equal
weight was not substantially different between the vibrating andnon-vibrating boxes. Earlier studies have reported that the

Frontiers in Virtual Reality

06

frontiersin.org

Kim et al.

10.3389/frvir.2022.797993

generated with the lowest power in Experiment 2 was 60 Hz.
Hence, a frequency close to 60 Hz should be used when the powersource of a voice coil oscillator is of concern. If the magnitude of
the weight illusion is prioritized, use of 30 Hz is recommended,because this frequency causes the most intense perception ofweight increase. It should be noted that small size vibrotactile
oscillators are typically designed to exhibit resonant frequencies
at approximately 100 Hz or higher (Jones and Singhal, 2018).
Therefore, effective illusions may not be achieved when using theresonances of small vibrotactile actuators.

presented in this study was vertical to gravity, and the vibration
was symmetrical. Hence, the principles underlying the illusory
weight can be different between the method using the symmetricvibration and that using the asymmetric vibration.
Based on the results of Experiment 3, the frequency thatgenerated the strongest weight illusion was 30 Hz. In thisfrequency range, fast-adapting type I (FAI) mechanoreceptor
units are readily activated (Bolanowski et al., 1988). Considering
the limitations of our apparatus, it was not possible to test
frequencies below 30 Hz. In addition, since the vibration
could stimulate other types of afferent units and could betransferred to the hand and arm, it is not possible to conclude
that the FAI units in the ﬁngertips mediated the weight illusion.
Hence, the present study does not exclusively support the role of
the FAI units for the weight illusion.
One of the possible causes of the weight illusion is the tonic
vibration reﬂex. When muscle spindles are activated by mechanicalstimuli applied from above the skin, unrelated to actual muscle
activity, proprioceptive sensations are induced (Goodwin et al.,
1972; Burke et al., 1976). This phenomenon is known as the tonic
vibration reﬂex. In the present study, the vibrotactile stimuli might
have activated the ﬂexor muscles of the ﬁngers and thereby createda weight illusion. The frequency range that is sensitive to the tonic
oscillatory reﬂex differs, depending on the muscle. The leg muscles
are most activated at 30–50 Hz (Cardinale and Lim, 2003; Zaidell
et al., 2013), which is consistent with the experimental results ofthis study. On the other hand, the forearm muscles are moststrongly activated at 100–150 Hz (Martin and Park, 1997). We
could not ﬁnd earlier studies that reported investigating suitablefrequencies for the tonic vibration reﬂexes of the ﬁngers.
Moreover, depending on the activated muscle, objects may not
only feel heavy, but may also feel light (Martin and Park, 1997).
Therefore, further experiments are needed to determine whether
the tonic vibration reﬂex was the cause of weight illusion in thepresent experiments.
In the present study, extra grip force (motor command)might have been generated to prevent the vibrating objects fromslipping, which might have inﬂuenced the perceived weight.
Some participants commented on the automatic or
involuntary increase in grip force because of the vibration. If
the grip force increases, both the afferent signals regarding
muscle activity and central motor commands to the related
muscles, that is, a sense of effort (McCloskey et al., 1974;
Gandevia et al., 1981; Ross and Bischof, 1981; Enoka andStuart, 1992) could make the vibrating objects feel heavier.
However, we did not measure grip force during theexperiments, and there is no evidence to support this possibility.
The weight illusion occurred over a wide range of frequencies(30–300 Hz) in Experiments 2 and 3. However, the accelerationthresholds and magnitude of the weight illusion depended on thevibratory frequency. Thus, it is necessary to select suitablefrequencies when implementing with commercial vibratory
actuators. The frequency at which the weight illusion was

Frontiers in Virtual Reality

4.2 Limitations
The present study investigated the conditions under which
the vibration weight-illusion occurred, and the causes of thisperceptual effect were discussed, but not concluded. In
Experiment 3, the acceleration amplitudes of stimuli were
2 dB greater than the thresholds. We speculate that the more
intense vibratory stimuli are, the clearer changes in the weightperception are evoked. Optimal acceleration values for theperceptual effect remain studied. Further, most of theparticipants were male, and this gender imbalance may limit
the generalizability of our results.

4.3 Summary
In this paper, three different experiments were conducted toinvestigate the illusory phenomenon that sinusoidal vibrations
make objects feel heavy. In Experiment 1, 13 of 15 participants
reported that sinusoidal vibrations made the box feel heavier,whereas their behaviors were rarely inﬂuenced by the vibration.
In Experiment 2, all participants felt the weight illusion caused byvibrations of 30–300 Hz. The vibratory amplitudes to evoke theweight illusion differed among the frequencies. In Experiment 3,
lower frequency vibrations led to more intense effects. The
stimulus with 30 Hz vibration felt heaviest among the ﬁve
different vibrations.
Previously introduced tactile interfaces for weight and force
presentation used skin stretching (Minamizawa et al., 2008, 2010;
Guinan et al., 2012, 2014; Choi et al., 2017; Kamikawa andOkamura, 2018), dynamically controlled vibrotactile stimuli(Okamoto et al., 2011; Nagano et al., 2015), and asymmetricvibration (Amemiya and Maeda, 2008; Tanabe et al., 2016). They
require a specialized hardware or an oscillator with highresponsiveness. On the other hand, for the method used in
the present study, continuous vibrotactile stimuli can be
implemented even with an eccentric motor oscillator, which
has relatively low responsiveness. Further, our approachrequires acceleration amplitude of 70 m/s2 at the most to
induce the illusion, whereas asymmetric vibration requires
peak accelerations of greater than 80 m/s2 (Amemiya and07

frontiersin.org

Kim et al.

10.3389/frvir.2022.797993

revision. YA and YY contributed to the revision. The ideas of thepaper were formulated through a series of meetings to which all
authors contributed.

Maeda, 2008; Tanabe et al., 2016). Thus, our approach of using
continuous vibrotactile stimuli have implementation advantages
when compared to the methods used in earlier studies. However,
the effect of this weight illusion differs by individuals, so it is notsuitable for quantitative weight expression.

Funding
Data availability statement

This study was in part supported by MEXT Kakenhi#21H05819.

The original contributions presented in the study areincluded in the article/supplementary material, further
inquiries can be directed to the corresponding author.

Conﬂict of interest
The authors declare that the research was conducted in theabsence of any commercial or ﬁnancial relationships that could
be construed as a potential conﬂict of interest.

Ethics statement
The studies involving human participants were reviewed andapproved by Hino Campus of Tokyo Metropolitan University.
The patients/participants provided their written informed
consent to participate in this study.

Publisher’s noteAll claims expressed in this article are solely those of theauthors and do not necessarily represent those of their afﬁliatedorganizations, or those of the publisher, the editors and thereviewers. Any product that may be evaluated in this article, or
claim that may be made by its manufacturer, is not guaranteed or
endorsed by the publisher.

Author contributions
GK contributed to the design and implementation of thestudy and writing. SO contributed to the design of the study andReferences
Amemiya, T., and Maeda, T. (2008). Asymmetric oscillation distorts theperceived heaviness of handheld objects. IEEE Trans. Haptics 1, 9–18. doi:10.
1109/toh.2008.5

Flanagan, J. R., and Beltzner, M. A. (2000). Independence of perceptual andsensorimotor predictions in the size–weight illusion. Nat. Neurosci. 3, 737–741.
doi:10.1038/76701

Bolanowski, S. J., Jr, Gescheider, G. A., Verrillo, R. T., and Checkosky, C. M.
(1988). Four channels mediate the mechanical aspects of touch. J. Acoust. Soc. Am.
84, 1680–1694. doi:10.1121/1.397184

Gandevia, S., Killian, K., and Campbell, E. (1981). The effect of respiratory muscle
fatigue on respiratory sensations. Clin. Sci. 60, 463–466. doi:10.1042/cs0600463
Goodwin, G. M., McCloskey, D. I., and Matthews, P. B. (1972). Proprioceptive
illusions induced by muscle vibration: Contribution by muscle spindles toperception? Science 175, 1382–1384. doi:10.1126/science.175.4028.1382

Brisben, A., Hsiao, S., and Johnson, K. (1999). Detection of vibration transmitted
through an object grasped in the hand. J. Neurophysiol. 81, 1548–1558. doi:10.1152/
jn.1999.81.4.1548

Grandy, M. S., and Westwood, D. A. (2006). Opposite perceptual and sensorimotor
responses to a size-weight illusion. J. Neurophysiol. 95, 3887–3892. doi:10.1152/jn.00851.2005

Brodie, E. E., and Ross, H. E. (1984). Sensorimotor mechanisms in weight
discrimination. Percept. Psychophys. 36, 477–481. doi:10.3758/bf03207502

Guinan, A. L., Montandon, M. N., Caswell, N. A., and Provancher, W. R. (2012). “Skinstretch feedback for gaming environments,” in Proceedings of IEEE International
Workshop on Haptic Audio Visual Environments and Games, Munich, Germany,
October 8–9, 2012, 101–106.

Burke, D., Hagbarth, K.-E., Löfstedt, L., and Wallin, B. G. (1976). The responses ofhuman muscle spindle endings to vibration of non-contracting muscles. J. Physiol.
261, 673–693. doi:10.1113/jphysiol.1976.sp011580
Cardinale, M., and Lim, J. (2003). Electromyography activity of vastus lateralis
muscle during whole-body vibrations of different frequencies. J. Strength Cond. Res.
17, 621–624. doi:10.1519/00124278-200308000-00032

Guinan, A. L., Montandon, M. N., Doxon, A. J., and Provancher, W. R. (2014).
“Discrimination thresholds for communicating rotational inertia and torque using
differential skin stretch feedback in virtual environments,” in Proceedings of IEEE
Haptics Symposium, Houston, TX, Feburary 23–26, 2014, 277–282.

Charpentier, A. (1891). Analyse experimentale de quelques elements de lasensation de poids. Arch. de Physiol. Norm. Pathol. 3, 122–135.

Hiramatsu, Y., Kimura, D., Kadota, K., Ito, T., and Kinoshita, H. (2015). Control
of precision grip force in lifting and holding of low-mass objects. Plos One 10,
e0138506. doi:10.1371/journal.pone.0138506

Choi, I., Culbertson, H., Miller, M. R., Olwal, A., and Follmer, S. (2017). “Grabity:
A wearable haptic interface for simulating weight and grasping in virtual reality,” inProceedings of Annual ACM Symposium on User Interface Software andTechnology, Quebec City, Canada, October 22–25, 2017, 119–130.

Ho, H.-N., Iwai, D., Yoshikawa, Y., Watanabe, J., and Nishida, S. (2014).
Combining colour and temperature: A blue object is more likely to be judged aswarm than a red object. Sci. Rep. 4, 5527. doi:10.1038/srep05527

Culbertson, H., Walker, J. M., and Okamura, A. M. (2016). “Modeling and design ofasymmetric vibrations to induce ungrounded pulling sensation through asymmetric skindisplacement,” in Proceedings of IEEE Haptics Symposium,Philadelphia, Pennsylvania,
April 8–11, 2016, 27–33.

Johansson, R. S., and Birznieks, I. (2004). First spikes in ensembles of humantactile afferents code complex spatial ﬁngertip events. Nat. Neurosci. 7, 170–177.
doi:10.1038/nn1177

Ellis, R. R., and Lederman, S. J. (1999). The material-weight illusion revisited.
Percept. Psychophys. 61, 1564–1576. doi:10.3758/bf03213118

Johansson, R. S., and Westling, G. (1984). Roles of glabrous skin receptors andsensorimotor memory in automatic control of precision grip when lifting rougher
or more slippery objects. Exp. Brain Res. 56, 550–564. doi:10.1007/bf00237997

Enoka, R. M., and Stuart, D. G. (1992). Neurobiology of muscle fatigue. J. Appl.
Physiol. 72, 1631–1648. doi:10.1152/jappl.1992.72.5.1631

Frontiers in Virtual Reality

08

frontiersin.org

Kim et al.

10.3389/frvir.2022.797993

Jones, L. A., and Singhal, A. (2018). “Perceptual dimensions of vibrotactile
actuators,” in Proceedings of IEEE Haptics Symposium, Francisco, CA, March
25–28, 2018, 307–312.

Raj, D. V., Ingty, K., and Devanandan, M. (1985). Weight appreciation in thehand in normal subjects and in patients with leprous neuropathy. Brain 108,
95–102. doi:10.1093/brain/108.1.95

Kamikawa, Y., and Okamura, A. M. (2018). Comparison between forcecontrolled skin deformation feedback and hand-grounded kinesthetic force
feedback for sensory substitution. IEEE Robot. Autom. Lett. 3, 2174–2181.
doi:10.1109/lra.2018.2810940

Ross, H. E., and Bischof, K. (1981). Wundt’s views on sensations of innervation: areevaluation. Perception 10, 319–329. doi:10.1068/p100319
Ross, H. E., and Brodie, E. E. (1987). Weber fractions for weight and mass as afunction of stimulus intensity. Q. J. Exp. Psychol. Sect. A 39, 77–88. doi:10.1080/
02724988743000042

Martin, B. J., and Park, H.-S. (1997). Analysis of the tonic vibration reﬂex:
Inﬂuence of vibration variables on motor unit synchronization and fatigue. Eur.
J. Appl. Physiol. 75, 504–511. doi:10.1007/s004210050196

Ross, H. E. (1969). When is a weight not illusory? Q. J. Exp. Psychol. 21, 346–355.
doi:10.1080/14640746908400230

Matsui, K., Okamoto, S., and Yamada, Y. (2013). Relative contribution ratios ofskin and proprioceptive sensations in perception of force applied to ﬁngertip. IEEE
Trans. Haptics 7, 78–85. doi:10.1109/toh.2013.71

Shadmehr, R., Smith, M. A., and Krakauer, J. W. (2010). Error correction, sensory
prediction, and adaptation in motor control. Annu. Rev. Neurosci. 33, 89–108.
doi:10.1146/annurev-neuro-060909-153135

McCloskey, D., Ebeling, P., and Goodwin, G. (1974). Estimation of weights andtensions and apparent involvement of a “sense of effort”. Exp. Neurol. 42, 220–232.
doi:10.1016/0014-4886(74)90019-3

Tanabe, T., Yano, H., and Iwata, H. (2016). “Properties of proprioceptive
sensation with a vibration speaker-type non-grounded haptic interface,” inProceedings of IEEE Haptics Symposium, Philadelphia, Pennsylvania, April
8–11, 2016, 21–26.

Minamizawa, K., Fukamachi, S., Kawakami, N., and Tachi, S. (2008). “Interactive
representation of virtual object in hand-held box by ﬁnger-worn haptic display,” inProceedings of IEEE Symposium on Haptic Interfaces for Virtual Environment andTeleoperator Systems, Reno, Nevada, March 13-14, 2008, 367–368.

van Beek, F. E., King, R. J., Brown, C., Luca, M. D., and Keller, S. (2020). Static
weight perception through skin stretch and kinesthetic information: Detection
thresholds, jnds, and pses. IEEE Trans. Haptics 14, 20–31. doi:10.1109/toh.2020.
3009599

Minamizawa, K., Prattichizzo, D., and Tachi, S. (2010). “Simpliﬁed design of
haptic display by extending one-point kinesthetic feedback to multipoint tactile
feedback,” in Proceedings of IEEE Haptics Symposium, Waltham, Massachusetts,
March 25–26, 2010, 257–260.

Walker, P., Francis, B. J., and Walker, L. (2010). The brightness-weight illusion.
Exp. Psychol. 57, 462–469. doi:10.1027/1618-3169/a000057
Warden, C. J., and Flynn, E. L. (1926). The effect of color on apparent size andweight. Am. J. Psychol. 37, 398. doi:10.2307/1413626

Nagano, H., Okamoto, S., and Yamada, Y. (2015). Vibrotactile cueing for biasing
perceived inertia of gripped object. Haptic Interact. 277, 17–20. doi:10.1007/978-4431-55690-9_4

Zaidell, L. N., Mileva, K. N., Sumners, D. P., and Bowtell, J. L. (2013).
Experimental evidence of the tonic vibration reﬂex during whole-body vibrationof the loaded and unloaded leg. Plos One 8, e85247. doi:10.1371/journal.pone.
0085247

Okamoto, S., Konyo, M., and Tadokoro, S. (2011). Vibrotactile stimuli applied toﬁnger pads as biases for perceived inertial and viscous loads. IEEE Trans. Haptics 4,
307–315. doi:10.1109/TOH.2011.16
Park, J., Oh, Y., and Tan, H. Z. (2018). Effect of cutaneous feedback on theperceived hardness of a virtual object. IEEE Trans. Haptics 11, 518–530. doi:10.
1109/toh.2018.2854721

Frontiers in Virtual Reality

09

frontiersin.org