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

A 3D-printed Haptic Material Library
for Quantifying the Force-Displacement Relationship*
Masashi Nakatani1 , Masataka Imura2 , Yoichi Yamazaki2 ,Taisuke Okazaki1 , Yoshihiro Asano1 , Ryota Nakamura1 , Noriko Nagata2 and Hiroya Tanaka1
Abstract— 3D printing technology enables us to develop acomposite shape of complex structures. This study describes
the methodology of how haptic materials are developed using
3D printers. We present a material library to study haptic
softness and texture perception.

I. INTRODUCTION
Haptic material perception of an object determines itsvalue. One can estimate the freshness of an apple by grasping
it. Similarly, one can predict the quality and the function of
a commercial product by touching it, although the haptic
impression does not necessarily reflect its value. This is a
motivation for why the study of haptic material perception
is interesting, especially for luxury products in the fashion,
the commercial electronics, and the automotive industry.
A 3D printer is a haptic display. Since the first proposalof personal fabrication, the advancement of the 3D printing
technology allows us to develop a product with high spatialresolution. Recent 3D–printing technology advances for developing the composite structures of inner structure, which iscalled metamaterials. These 3D–printed materials are widelyused as tactile stimuli in experimental psychology.
The advantage of using 3D printers in experimental haptics
is that we can easily manipulate several parameters of tactile
stimulus, such as braille dot size, the spatial frequency ofgratings, and the density of a 3D–printed object. Researchers
can systematically control the causal relationship betweenmechanical parameters of a material and material perception
using 3D–printed specimens rather than using complex,
natural materials.
In computer graphics, the bidirectional reflectance distribution function (BRDF) is widely used to render photorealistic scenes. Similarly, we can define the force-induced
displacement distribution function (FDDF), as a function ofreal variables that defines how displacement is produced byapplied force to a tangible object [1][2]. The FDDF is an
input-output relationship analogous with the BRDF, and canbe measured from tangible objects using a calibrated force
sensor and linear actuator. Once the FDDF is measured fora real object, we can estimate the haptic material perception(e.g., softness) based on a previous study in haptics. Once

the FDDF is measured for a target object, in theory, we canreconstruct a shape with the target FDDF value using 3D
printing technology. The simplest case is to reconstitute theforce-displacement relationship of a tangible object.
This study aims at developing haptic materials using 3D
printers for elucidating the mechanisms behind softness andtexture material perception. For this purpose, we provide two
examples of haptic materials as follows.
II. 3D– PRINTED HAPTIC MATERIALS
We decided to use OpenSCAD [3] to develop soft andtextured materials. In the accompanying papers, we discuss
how to quantify the softness and texture material perceptionof 3D–printed objects using the FDDF [1][2].
A. Parametric design of soft materials
For developing materials of different softness magnitudes,
we adopted mechanical metamaterials to achieve different
mechanical properties. Mechanical metamaterials contain alattice structure (Fig. 1a). Lattice structure is repeated toconstruct the 3D models of mechanical metamaterial (Fig.
1b). We confirmed we could fabricate seventy-two materials
in total using three 3D printers (Fig. 1c).
B. Parametric design of textured materials
We adopted canvas fabrics for developing textured materials. Canvas fabric is made with string of a certain diameter(Fig. 1d). By weaving strings of the same diameter, theroughness of the canvas fabric is defined (Fig. 1e). Basedon this, we developed 3D–printed canvas textures (Fig 1f).
aebcfFig. 1. Parametric design of soft materials (a, b) and textured materials (d,e). 3D Printed structures of different softness (c) and textures (f) are shown.

*This work was supported by JST COI Grant Number JPMJCE1314.
1 Facultyof Environment and Information Studies, Keio
University,
5322
Endo
Kanagawa,Japan{mn2598,htanaka}@sfc.keio.ac.jp
2 School of Science and Technology, Kwansei Gakuin University, Sanda, Hyogo 669-1337, Japan {m.imura, y-yamazaki,nagata}@kwansei.ac.jp
978-0-7381-2491-9/21/$31.00 ©2021 IEEEd585

R EFERENCES[1] M. Imura et al., “Feature quantification of material softness perception using the force-displacement relationship,” IEEE World Haptic
Conference 2021, Work-in-Progress Papers (accepted).
[2] Y. Yamazaki et al., “Feature quantification of material texture perception using a force-displacement relationship,” IEEE World Haptic
Conference 2021, Work-in-Progress Papers (accepted).
[3] OpenSCAD. https://openscad.org/