2021 IEEE World Haptics Conference (WHC)
July 6-9, 2021. Montreal, Canada

Feature Quantification of Material Softness Perception
Using the Force-Displacement Relationship*Masataka Imura1 , Yoichi Yamazaki1 , Masashi Nakatani2 , Taisuke Okazaki2 , Rino Uesaki2 ,Noriko Nagata1 and Hiroya Tanaka2
1.0

Normalized force

Abstract— To establish haptic interchangeability between ordinary materials and metamaterials, the FDDF (Force-inducedDisplacement Distribution Function) has been proposed forquantifying material properties. This paper describes how
material softness is quantified using the FDDF.

I. INTRODUCTION
The FDDF (Force-induced Displacement DistributionFunction) is an input-output relationship that can represent
the physical features associated with the haptic perceptionof a material [1]. Concrete expression of the FDDF depends
WHC
on the mode of interaction with the object [2]. This paper
describes the implementation of the FDDF for the case ofpressing a soft object to quantify the features pertaining tomaterial softness perception and reports on the substitutability of an ordinary object by a metamaterial.

Principal components
1st2nd3rd
4th0.50-0.5Raw data

-1.0
0.0

going
returning

0.2

0.4

0.6

0.8

1.0

Normalized displacement

Fig. 1.

Computed principal components with raw measurement data.
gelurethanerubberspongeswitch (A)switch (B)II. PROCEDURE FOR COMPUTING FDDF (PRESS)In the proposed method, a force-displacement relationshipis adopted to represent the FDDF when a soft object ispressed. To represent the force-displacement relationshipwith a small number of parameters, principal component
analysis (PCA) is used to construct an appropriate basis.
Force-displacement curves for various materials can beobtained using hardness testing machines or computer simulations. The round trip displacement is divided into a goingdisplacement and a returning displacement.
As a pre-processing step, the measured M Forcedisplacement curves are resampled with a fixed number ofsamples N to compensate for differences in the numberof samples due to different measurement conditions. Eachforce-displacement (F-D) curve is represented as a series ofnormal forces.
To focus on the profile of the F-D curves, the force andstroke of each curve are normalized by the maximum valueof the normal force and the maximum value of the pushin amount, respectively. Then, for each normalized push-inamount, the average value of all data is subtracted. The dataobtained in this way are subjected to PCA to obtain a basis
function suitable for representing the F-D curve.
*This work was partially supported by JST COI Grant Number JPMJCE1314.
1 School of Engineering / Kwansei Gakuin Institute of Kansei Value Creation, Kwansei Gakuin University, Sanda, Hyogo 669-1337, Japan. e-mail:{m.imura, y-yamazaki, nagata}@kwansei.ac.jp
2 Faculty of Environment and Information Studies, Keio University, Fujisawa, Kanagawa 252-0882, Japan. e-mail: {mn2598,htanaka}@sfc.keio.ac.jp
978-0-7381-2491-9/21/$31.00 ©2021 IEEEswitch (C)metamaterial (A)metamaterial (B)Fig. 2.

3D visualizations of the principal component scores.

III. MEASUREMENTS AND RESULTS
We measured the F-D relationship of the materials usinga three-axis force sensor (YAWASA MSES5012-1-SL, Tec
Gihan, Kyoto, Japan). The diameter of the spherical contactor
was 30 mm. A 115 F-D curves of ordinary materials,including gels, urethanes, rubbers, sponges, and several typesof push switches, and 103 curves of 3D-printed materials
with different structures were obtained.
Fig. 1 shows the computed principal components with raw
measurement data. The contribution ratios of the first four
principal components are 89.2%, 6.9%, 2.0%, and 0.63%, respectively. Fig. 2 is a scatter plot of the principal componentscores of the measured materials. From the overlapping areasof several types of materials (gels, sponges, and rubbers) andmetamaterials, we can see that the softness of some gels,sponges, and rubbers can be expressed by 3D printing bychanging the structure of the metamaterials.
R EFERENCES[1] M. Nakatani et al., “A 3D-printed haptic material library for quantifying
the force-displacement relationship,” IEEE World Haptics Conference
2021, Work-in-Progress Papers (accepted).
[2] Y. Yamazaki et al., “Feature quantification of material texture perception using the force-displacement relationship,” IEEE World Haptics
Conference 2021, Work-in-Progress Papers (accepted).

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