Kinetic Friction Deters Softness Judgment during
Sliding Motion
Hongbo Wang

Shogo Okamoto

Tokyo Metropolitan UniversityHino, JapanTokyo Metropolitan UniversityHino, JapanAbstract—We explored the impact of friction on hardness
perception during sliding interactions, an aspect not commonly
examined in earlier studies that primarily focused on hardness
perception during compression. Using a commercial force display,
we simulated virtual surfaces with two levels of stiffness, 400 and
500N/m, and coefficients of kinetic friction of 0 and 0.5. Eightparticipants engaged in a user study and selected the harderone among two virtual surfaces with different hardness whilesliding their surfaces. The correct answer proportion was 0.77 on
average under the frictionless condition; however, it significantly
decreased to 0.66 under the frictional condition. These findings
indicate the importance of friction in conveying haptic softness
in consumer electronics, where haptic interfaces are popular
communication interfaces between humans and computers.
Index Terms—hardness, haptic interface, friction

Fig. 1. Experiment to investigate the effect of friction on softness judgment
during sliding motions using a commercial haptic interface. Assessors stroked
the surfaces of virtual objects using a stylus to judge the harder one among
the two objects with different degrees of stiffness. The tests were conductedunder two friction conditions, i.e., minimum and moderate kinetic friction.

I. I NTRODUCTION
II. M ETHODS
Haptic interfaces are valuable communication channels between humans and computers in consumer electronics. Among
haptic information delivered by such interfaces, the hardness
or softness of the virtual objects is a fundamental cue. Earlierstudies have discussed how well such information can bepresented when virtual objects are pressed or tapped without asliding motion (e.g., [1]–[4]). However, humans employ bothpressing and sliding motions equally frequently in investigating softness quality in their daily lives [5], [6]. Recently,
Arakawa et al. have found that human criteria for softness
judgment differ between pressing and sliding motions, and thatfriction influences softness perception in the latter case [7].
Nonetheless, in an earlier study that investigated the effect of friction on softness perception during stroking exploration [7], only rubber and human skin with the same hardness
were explored using bare fingers. The effects of friction on
softness perception should also be examined using specimens
with different hardness values and via exploratory methods
that are different from direct touch by bare fingers so as togeneralize the influence of friction on softness perception.
Hence, in this study, we employed a haptic interface in which
virtual objects are touched via a stylus, and through which thehardness and friction of the objects can easily be controlled.
This study contributes a new aspect to the literature on haptic
communication between humans and computers.

979-8-3503-4017-4/23/$31.00 ©2023 IEEEA. Stimuli
We employed a Phantom Touch X force display (SensAble
Technologies Inc., MA, USA) to depict virtual planes withvarying levels of hardness and friction. The virtual planes werepositioned parallel to the desktop.
The hardness was instrumented using Hooke’s law, that is,a linear spring with stiffness coefficient k. When the pressing
depth of the stylus into the plane is d, the reaction force normal
to the plane is determined as follows:
fz = kd.

(1)

The stiffness values used in this experiment were k = 400 N/m
and 500 N/m. These values were selected for two main
reasons. First, these values are challenging to be discriminatedsuch that the mean success proportion would be approximately
0.75. Second, these specific values are within the device’s
maximum output capability of 7.9 N, ensuring regular operation without exceeding force limits.
The virtual objects were not visually deformed while interacting with the stylus of the haptic interface such that thehardness difference could not be judged from visual cues.
This study was in part supported by MEXT Kakenhi #23H04360 and#20H04263.

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The kinetic frictional force was defined as follows:f=µ =−sgn(v)µfz
 
 v 
2µ0
Tan−1
π0.05(2)(3)where sgn(v) indicates the sign of v, and v (m/s) is thesliding velocity of the stylus on the plane, and fz (N) is
the load normal to the plane. The nominal value of thefriction coefficient is µ0 . An arctangent function was used
to eliminate any discontinuities in the frictional force at zerovelocity. This ensures a seamless transition of the kinetic
friction force near zero speed. The denominator of the arctangent function provides the range over which the kinetic
force undergoes a gradual change. The denominator of thevelocity was determined through preliminary tests to maintainthe stability of the frictional force without evident sensiblevibrations. Because static friction leads to frictional vibrations
that disrupt the smooth stroking motion, it was not rendered.
Therefore, the focus of this study was to investigate the effects
of kinetic friction. Two nominal coefficients of friction wereused: µ0 = 0 and 0.5.
B. Participants
The experiment involved a group of nine individuals (eightmales and one female; mean age, 23.0 years). The aims of
the study were not disclosed to the participants before theexperiment. Written informed consent was obtained from all
the participants before the experiment commenced.
C. Procedures
Before the main experiment, the participants underwent
a training session divided into two stages. The first stage
involved familiarizing themselves with the manipulation of
the force feedback device. Participants stroked the surfaces of
two planes with friction coefficients of 0.25 and hardness of
350 N/m and 500 N/m. Note that their difference was 150 N/m,which was greater than that of the main experiment. They
could continue their exploration for as long as they wanted.
Two planes were randomly assigned to each side of the screen.
The participants then selected the harder one. The accuracyof each selection was returned to the participants. Once theparticipants made correct judgments five times in a row, they
progressed to the second stage.
In the second stage, the participants stroked each plane
twice and selected the harder plane. Once they made fivecorrect judgments consecutively, they proceeded to the main
experiment. This stage ensured that the participants could
understand the difference in hardness using only the two
sliding motions. One male participant did not pass the second
stage; therefore, eight participants participated in the main
experiment.
In the main experiment to compare the two hardness values,i.e., k = 400 N/m and k = 500 N/m, the participants
conducted 20 trials under each of the frictionless (µ0 = 0)
and frictional (µ0 = 0.5) conditions. Two frictional conditions
were presented in randomized order.

Fig. 2. Accuracy of the eight participants in judging the two planes withdifferent stiffness (400 and 500 N/m) under two different friction conditionsµ0 (0 and 0.5). Error bars indicate the standard errors. ** indicates asignificant difference at p < 0.01.

D. Data analysis
The difference in accuracy proportions between the twofriction conditions was calculated for each participant. Subsequently, a one-sample t-test was employed to test the meandifference among all the participants so as to investigate theeffect of friction on the ability to judge hardness.
III. R ESULT
Under the frictionless condition, that is, µ = 0, the hardnessof the two virtual planes was correctly determined as 0.77 ±0.026 (mean ± standard error). However, when µ0 = 0.5,
the proportion decreased to 0.66±0.028. Friction significantly
lowers the proportion of correct judgements (t(7) = 5.15, p =0.0013). The kinetic friction affected the participants’ ability
to judge the stiffness of the planes while sliding their surfaces.
IV. C ONCLUSION
Earlier studies have primarily investigated humans’ ability
to judge hardness when objects are being pressed. Hence, they
did not undergo any evident sliding motion. This study investigated the effects of sliding friction on hardness judgment
while sliding objects’ surfaces. A user study revealed thatparticipants’ judgment was less accurate with greater kineticfriction. This suggests that frictional conditions should be considered when humans interact with soft objects. In the future,
tests should be conducted to determine whether similar effects
can be observed using actual compliant materials. Finally, thispaper pertains to our another study [8] demonstrating that thevirtual objects with kinetic friction are perceived harder thanthose with little friction.
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