Perceived Hardness by Tapping: The Roleof a Secondary Mode of Vibration
Kosuke Higashi, Shogo Okamoto, Hikaru Nagano, Masashi Konyo
and Yoji Yamada

Abstract Humans can discriminate among the hardness of objects by tapping theirsurfaces. The damped natural vibration caused by tapping and its frequency are
known to be the cue for the perception of hardness. This study is an investigationof the characteristics of this perception of hardness, as induced by vibration stimuli
including multiple frequency components. We performed a comparative experimentusing several damped vibration stimuli, which included either one or two frequency
components, and investigated the signiﬁcance of the secondary vibration mode andthe change in its frequency. We found that the presence of the secondary mode signiﬁcantly enhanced the perceived hardness; however, its frequency had a lesser eﬀect
on hardness perception.
Keywords Hardness perception ⋅ Tapping ⋅ Vibration ⋅ Frequency

1 Introduction
Humans use the vibrotactile cue caused by tapping the surface of an object when
judging the object hardness [6]. This fact is well known; however, it is astonishingthat little is known about the perceptual mechanism responsible for this perception ofhardness by tapping. The common understanding among researchers is that vibratory
stimulation of higher frequency [3, 7] and larger attenuation [4] leads to greater perceived hardness. As a result, materials with greater rigidity [6] and viscosity loss [4]are felt to be harder.

K. Higashi (✉) ⋅ S. Okamoto ⋅ Y. Yamada
Graduate School of Engineering, Nagoya University, Nagoya, Japane-mail: higashi.kousuke@d.mbox.nagoya-u.ac.jp
H. Nagano ⋅ M. Konyo
Graduate School of Information Sciences, Tohoku University, Sendai, Japan© Springer Nature Singapore Pte Ltd. 2018
S. Hasegawa et al. (eds.), Haptic Interaction, Lecture Notes
in Electrical Engineering 432, DOI 10.1007/978-981-10-4157-0_5

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K. Higashi et al.

There have been some attempts to simulate the dynamic characteristics of animpulsive contact between a ﬁngertip and an object in terms of either a reaction
force and acceleration [1, 2, 5]. Such stimulus mimicking the transient reaction oftapped object enhances the contact realism of objects [5]. Because one of the mostsigniﬁcant features of such transient reaction is multiple frequency components of
the waveform, it can be assumed that the vibration including higher-frequency component aside from the main component is felt harder than when the vibration merelycomprises a single or primary component. However, the hardness perception when
the natural vibration caused by tapping the object includes multiple frequency components has not been well studied.
In the present study, we investigated the perceptual roles of individual frequencycomponents in the case of vibrations that include multiple components. Especially,
we were interested in the role of the higher frequency component when the vibration consisted of two components, i.e., lower (primary) and higher (secondary) frequency components. We used a customized haptic interface based on a direct-driven
DC motor and prepared several natural vibration stimuli. Invited participants compared these stimuli in terms of their perceived hardness, and we then investigated
the signiﬁcance of the frequency of the higher frequency component.

2 Experiment
2.1 Damped Vibration Stimuli
We used a damped vibration stimulus that includes either one or two frequency components. The displacement of the vibration stimulus was determined by{x1 (t)x1 (t) + x2 (t)−txi (t) = ai vt exp( ) sin(2𝜋fi t)
𝜏ix(t) =(1)(2)

where x(t), vt , a, 𝜏, and f are the vibration displacement, tapping speed, amplitude
per tapping speed, time constant, and frequency of the vibration, respectively. We
compared ﬁve pairs of stimuli, which are listed in Table 1, by using a paired comparison method. Pair I included a vibration stimulus of 100 Hz and that of 100 and200 Hz. By making this comparison, we aimed to demonstrate that the presence ofthe secondary vibration mode could result in the perception of greater hardness. Inpairs II and III, we compared vibration stimuli including a single frequency component. Pair II included vibration stimuli of 80 and 100 Hz and pair III included thatof 160 and 200 Hz. In each pair, the frequency change was set to 20% decrease from
100 and 200 Hz, respectively. These comparisons would enable us to verify that thehigher frequency component is responsible for inducing the perception of greaterPerceived Hardness by Tapping: The Role of a Secondary Mode of Vibration
Table 1 Frequencies of the vibration stimuli for each stimulus pair
Stimulus pair
Stimulus 1
Stimulus 2
f1 (Hz)f2 (Hz)f1 (Hz)IIIIII
IV
V

100
80
160
80
100

–––
200
160

100
100
200
100
100

29

f2 (Hz)
200––
200
200

hardness. We also compared the answer rates between pairs II and III and investigated the diﬀerence of the perceptual reaction against the frequency change in thevicinity of 100 and 200 Hz. In pairs IV and V, we compared vibration stimuli including two frequency components. Pairs IV and V included vibration stimulus madeup of 80 and 200 Hz components and 100 and 160 Hz components respectively, andanother made up of 100 and 200 Hz components. These comparisons would showwhether the 20% frequency change was also eﬀective for hardness perception in theﬁrst or secondary mode of multiple-frequency vibration. By comparing the answer
rates between pairs IV and V, we investigated the diﬀerence of the perceptual reaction against the frequency change between the ﬁrst and second vibration mode. The
time constant of each vibration component was set to 𝜏 = 0.02 s. The amplitude ofan acceleration per tapping speed of each frequency component was set to 300 s−1
so that their max acceleration became equal. When expressed in displacement, theamplitude per tapping speed of the 100 Hz component was a = 7.6 × 10−4 s and thatof the 200 Hz component was a = 1.9 × 10−4 s. The amplitude of the 160 Hz component was the same as that of the 200 Hz component to enable us to focus on theeﬀect of the change in frequency.

2.2 Apparatus
We developed the haptic display shown in Fig. 1. The main components of this apparatus are a dial, DC motor (RE40, Maxon motor), current controller (ADS50/10,Maxon motor), and microcomputer (mbedLPC1768, ARM). The participant wasable to experience a vibration stimulus by using their ﬁngertip to rotate the dial to acertain angle, which was measured by a rotary encoder installed on the DC motor.
The vibration of (1) was presented in the tangential direction of the dial. The tangential displacement of the dial can be described as x(t) = r𝜃(t) where r and 𝜃 are theradius of the dial and its rotational angle, respectively. The control system employeda feedforward control method operated at 5 kHz.

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K. Higashi et al.

Fig. 1 One degree-of-freedom force display with direct DC motor drive

2.3 Tasks
The participants were ﬁve right-handed males in their twenties and thirties. They
operated the haptic display and compared the two vibration stimuli presented in pairs.
They were able to switch the presented stimulus by using a keyboard and judged
which stimulus was felt harder. Each of the ﬁve stimulus pairs listed in Table 1 wastested 20 times. In total, 100 comparisons (5 pairs × 20 repetitions) were performed
for each participant, and these 100 pairs were presented in randomized order.

2.4 Results
Table 2 and Fig. 2 show the answer rates at which the stimulus including a higher
frequency component was judged to be harder.

Table 2 Probability at which higher frequency components induced greater hardness perception
Stimulus
Participants
pairABCDEAverage
IIIIIIIVV

0.9
0.9
1.0
0.8
0.7

1.0
0.9
1.0
0.9
0.85

0.75
0.95
0.7
0.85
0.65

1.0
0.95
0.95
0.95
0.8

0.9
0.95
0.9
0.85
0.3

0.91
0.93
0.91
0.87
0.66

Perceived Hardness by Tapping: The Role of a Secondary Mode of Vibration

31Fig. 2 Answer ratio at
which vibration with greater
frequency is felt harder. n.s.:
not signiﬁcant, +: p < 0.1,**: p < 0.01

The t-test between the average answer rate of each stimulus pair and a chancelevel of 0.5 showed that pairs I–IV indicated signiﬁcant diﬀerence (p < 0.01) andpair V indicated signiﬁcant tendency (p < 0.1). For pair I, all participants agreed
that the stimulus including the secondary mode felt harder than that with only aprimary mode. They answered that the stimulus with the higher frequency seemed
to be harder for the single-frequency vibration of pairs II and III. By comparing theanswer rates of pairs II and III, we could not conﬁrm the signiﬁcant diﬀerence of theperceptual reaction against the frequency change between the vicinity of 100 and
200 Hz. For the vibration including multiple frequency components of pairs IV andV, almost of all participants answered that the stimulus with the higher frequency
component was felt harder just like pairs II and III. However, the comparison forpairs IV and V showed that the answer rate of pair V tended to be less than that ofpair IV (p < 0.1).

3 Discussions
The results for pairs II and III indicate that the 20% frequency changes in the vicinity of 100 and 200 Hz clearly aﬀected the hardness perception. However, comparing
the results of pairs IV and V, the frequency change of the secondary mode was less
eﬀective than that of the primary mode for all of the participants, even though the frequency of each component was changed just like in pairs II and III. Nonetheless, thepresence of the secondary mode is apparently eﬀective as indicated by the answers
for pair I. Our experiment indicated that the presence of the secondary mode significantly enhanced our perception of hardness; however, changing its frequency had alesser eﬀect on the hardness perception than for the vibration with a single-frequencycomponent. This aspect of human hardness perception may lead to a reasonable rendering of object hardness, even if it is diﬃcult to present high-frequency vibrations
because of limitations in the hardware or software of haptic interfaces.

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K. Higashi et al.

4 Conclusions
This study addressed the characteristics of hardness perception by vibration stimuli including multiple frequency components. By comparing ﬁve types of stimulus
pairs, we investigated the eﬀects of a secondary vibration mode as well as the eﬀectof changing its frequency. The experimental results suggested that the presence ofthe secondary mode signiﬁcantly enhanced perceived hardness; however, changing
the frequency of this mode was less eﬀective in terms of hardness perception unlike
the single-component vibration stimuli.
Acknowledgements This study was partly supported by JSPS Kakenhi (15H05923), and ImPACT(Tough Robotics Challenge).

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