Frictional Planes are Felt Harderthrough a Force Display Device
Hongbo Wang

Shogo Okamoto

Tokyo Metropolitan UniversityHino, JapanTokyo Metropolitan UniversityHino, Japan

Abstract—An earlier study demonstrated that when two surfaces of equal hardness were stroked, the surface with higher
friction felt harder. This tribological paradox was the focusof our experiment. We used a force display device to stroke
objects with varied stiffness (300–700 N/m) and kinetic friction
coefficient (0–0.6). The device primarily involved proprioceptive
cues, limiting tactile cues. Participants used the device’s stylus
to explore objects and reported perceived hardness using themagnitude estimation method. Their motion was restricted tostroking with comfortable force. Results indicated that surfaces
with lower friction were perceived as softer. These findings
enhance our understanding of hardness presentation using hapticinterfaces that is a popular communication tool between man andcomputers in consumer electronics.
Index Terms—hardness, haptic interface, friction

II. M ETHODS
A. Stimuli
We used a commercial force display, Phantom Touch X(SensAble, Inc., CA), to render virtual planes with different
degrees of hardness and friction. The virtual planes are locatedparallel to the table. The virtual surface hardness, that is, thespring constant k (N/m) and kinetic friction µ were adjustablevariables.
Stiffness is defined by a spring constant following Hooke’s
law. When the stylus is pressed to a depth of d, an upward
reaction force is generated by
fz = kd.

I. I NTRODUCTION
Humans can judge objects’ softness by sliding their fingers
on them which is a common behavior in our daily lives [1].
They do not necessarily press or tap objects to test theirsoftness whereas pressing and tapping are typical exploratory
motions for judging hardness [2]–[5]. Sliding motions give riseto friction between a fingertip and an object’s surface. Hardness and friction perception are both major haptic qualities andare considered perceptually independent [6], [7]. However,recently, these two types of qualities have been found to beperceptually dependent. In a study conducted by Arakawa etal. [8], urethane rubbers that had been lubricated to be lessfrictional felt softer than those with more frictional surfaces
when their surfaces were rubbed.
Earlier studies [8], [9] tested only one type of rubber object
with the same hardness, which raises the first question. That is,whether the effect of friction on softness perception holds for awide range of object hardness. The second question is whether
the effect of friction on softness holds true when using haptic
interfaces, through which objects are touched via a probe. It
is possible that hardness is perceived differently between thetwo types of contact modes, i.e., bare finger and prove. Thusfar, no earlier studies have investigated either of these researchquestions. The findings of this research will provide guidancefor presenting softness by using force display devices that are
popular man-machine interfaces in consumer electronics.
This study was in part supported by MEXT Kakenhi #23H04360 and#20H04263.

979-8-3503-4017-4/23/$31.00 ©2023 IEEE(1)

The simulated kinetic friction force is defined as follows:
F= µfz 2−vµ = µ0Tan−1π0.05

(2)
(3)

In this study, v (m/s) and fz (N) represent the sliding velocityof the stylus and the load normal to the planes, respectively.
The coefficient of friction was set by µ0 . We used thearctangent function to prevent any discontinuity in the friction
force at zero speed, ensuring a continuous kinetic friction
force.
As outlined in Section II-C, we used a psychophysicalmethod of magnitude estimation where perceived hardness of astimulus is reported by using a number referring to a reference
stimulus. For the reference stimulus, parameters were set tok = 500 N/m and µ0 = 0.3, with a hardness magnitude of
10. The nine test stimuli were derived from combinations of
three k values (300, 500, and 700 N/m) and three µ0 values(0, 0.3, and 0.6).
B. Participants
Seven participants (six men and one woman; average age:23.0 years) were recruited for this experiment. The objectivesof this study were not explained to the participants before
the experiments. All the participants provided signed informed
consent prior to the experiment.

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Fig. 1. Experimental setting. Participants judged the hardness of test virtual
planes in compared with that of reference.

C. Procedures
Participants underwent brief training to acclimate to theforce-feedback device by stroking a virtual plane with limited
force. As shown in Fig. 1, two virtual planes were allocated oneither side of a visualization window: a reference plane and atest plane. The planes did not exhibit visual deformation, preventing visual assessment of their hardness. Participants useda stylus to stroke the virtual surface and reported perceived
hardness using the magnitude estimation method.
Magnitude estimation is a method that measures the subjective strength of a perceived stimulus, requiring participants
to compare a standard stimulus with the test stimulus. They
reported the ratio of subjective intensity of each test stimulus
to the modulus using a numerical value.
Nine test stimuli were presented in a random order in asingle set. Three sets of measurements were performed foreach participant, resulting in 27 trials for each individual.

Fig. 2. Mean magnitudes of perceived hardness acquired from seven participants on three stiffness planes (300, 500 and 700 N/m) with three coefficientsof friction µ0 (0, 0.3 and 0.6). The red line is the hardness of the reference
stimulus with k = 500 N/m and µ0 = 0.3. Its magnitude of hardness was
defined as 10. Error bars indicate the standard errors.

involving different stiffness values, close to those of human tissues [10], [11]. The participants judged the perceived hardness
when rubbing stimuli generated by the force display device.
The results suggest that the smaller the friction coefficient, thesofter the perception.
The main effect of stiffness was significant; hence, the participants could distinguish between different stiffness values.
However, this trend was not clear for the stimuli with µ0 = 0.6
as shown in Fig. 2. In a post-hoc manner, we applied a oneway ANOVA for the µ0 = 0.6 condition. The effect of stiffness
was not significant (F (2, 18) = 0.69, p = 0.51, η 2 = 0.071),
indicating that the perceptual effect of friction masked thedifference in stiffness.

The geometric means of the subjective hardness for all
the nine stimuli are shown in Fig. 2. The results from theANOVA reveal significant effects of stiffness (F (2, 54) =5.59, p = 0.0062, η 2 = 0.062) and friction (F (2, 54) = 53.27,
p = 1.67 × 10−13 , η 2 = 0.61) on subjective hardness. There
was no significant interaction observed between stiffness andfriction (F (4, 54) = 0.76, p = 0.55, η 2 = 0.017). Therefore,
the virtual surface was perceived harder with a larger kinetic
friction coefficient µ0 , irrespective of the stiffness values ofthe plane.

V. C ONCLUSION
We explored the influence of friction on hardness perception
in a virtual environment, using a range of stiffness and friction
coefficients. Participants assessed surface stiffness using astylus and a force display device. They were not allowed
to press surfaces without sliding motion. Subjective hardness
values were collected using the magnitude estimation method.
Results showed that surface friction significantly impacts hardness perception. Lower surface friction led to softer surface
perception. This contributes to our understanding of perceived
softness through haptic interfaces with practical applications
in virtual reality and gaming. This study has limitations tobe solved in the future, including variations in stimuli and asmall number of participants. These may have resulted in theweak statistical significance in the analyses. Finally, this paper
pertains to our another study [12], where two virtual objects
with different stiffness values are less correctly discriminatedwith larger kinetic friction. Collectively considering this study
and [12], kinetic friction influences softness judgment whilesliding over virtual objects through a stylus.

IV. D ISCUSSIONR EFERENCES

Previous studies demonstrated that surfaces with greater
friction coefficients were perceived harder when rubbed byfingers [8]. We designed an experiment using a haptic interface[1] N. Arakawa, T. Watanabe, K. Fukushima, and M. Nakatani, “Sensory
words may facilitate certain haptic exploratory procedures in facial
cosmetics,” International Journal of Cosmetic Science, vol. 43, pp. 78–87, 2021.

D. Data Analysis
For each test stimulus, the three magnitude values ofperceived hardness acquired from each participant were geometrically averaged. Then, we used a two-way (stiffness k× coefficient of friction µ0 ) repeated measures analysis ofvariance (ANOVA) to evaluate the statistical effects of stiffness
and friction on the perceived hardness.
III. R ESULT

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