LeviFab: Stabilization and Manipulation of Digitally FabricatedObjects for Superconductive Levitation
Yoichi Ochiai

Tatsuya Minagawa

Daitetsu SatoSatoshi Hashizume

University of Tsukuba,
Pixie Dust Technologies, Inc.
University of Tsukuba

Amy Koike

University of Tsukuba

Takayuki Hoshi

University of Tsukuba

The University of Tokyo
Pixie Dust Technologies, Inc.

Kazuki Takazawa

University of Tsukuba

University of Tsukuba

Ippei Suzuki

Atsushi Shinoda

University of Tsukuba

University of Tsukuba

Kazuyoshi Kubokawa
University of Tsukuba(a)(b)(c)Figure 1: (a) Fabricated bunny model floating on a hand, (b) strobescopic of sliding bunny on a rail, and (c) fabricated UFOmodel.

CCS CONCEPTS•Applied computing →Physics;

KEYWORDS
Levitation, Superconductivity, Digital fabrication
ACM Reference format:
Yoichi Ochiai, Tatsuya Minagawa, Takayuki Hoshi, Daitetsu Sato, Satoshi
Hashizume, Kazuki Takazawa, Amy Koike, Ippei Suzuki, Atsushi Shinoda,and Kazuyoshi Kubokawa. 2017. LeviFab: Stabilization and Manipulation ofDigitally Fabricated Objects for Superconductive Levitation. In Proceedingsof SIGGRAPH ’17 Posters, Los Angeles, CA, USA, July 30 - August 03, 2017,
2 pages.
DOI: 10.1145/3102163.3102233

1INTRODUCTION

Aerial manipulation of material objects is fascinating and is used inmany performance situations. Many scientific demonstrations andmagic shows employ these levitations. Acoustic, magnetic, electric,
and superconductive levitation are used in many situations. Adding
controllability and increasing the design space of these levitation
SIGGRAPH ’17 Posters, Los Angeles, CA, USA© 2017 Copyright held by the owner/author(s). This is the author’s version of thework. It is posted here for your personal use. Not for redistribution. The definitive
Version of Record was published in Proceedings of SIGGRAPH ’17 Posters, July 30 August 03, 2017, http://dx.doi.org/10.1145/3102163.3102233.

methods are often studied for use in entertainment applications
in graphics and HCI communities. In this study, we focus on superconductive levitation (Figure 1) because it has not been well
explored for entertainment applications.
Superconductive levitation requires special elements. It requires
low temperature for superconductive materials and to satisfy thiscondition, liquid nitrogen is often used. These superconductivelevitation requirements impose various difficulties. Moreover, thedemonstration of superconductive levitation shows levitation itself as “contents”. Thus, its levitated structure, manipulate path,and interactions have not been well considered for entertainment
applications. We are strongly motivated to redesign the demonstration of superconductive levitation in a more fascinating way bycomputational fabrication and manipulation methods.
Computational design methods of superconductive levitation
have wide applications in not only entertainment but also otherHCI context. Now superconductive levitation is limited levitationtime because of the temperature limit of superconductive material
however, 10 min levitation is enough to use in many HCI usages
such as showing the demo of 3D manipulation, discussion withlevitated physical icons, and discuss with 3D actuated characters.
We need to solve several problems in both fabrication and manipulation to achieve the 3D printed object levitation and manipulation by ways of superconductive levitation. First, we have toconsider the structure the 3D printed object with low temperature
3D printed material. Second, we have to design and consider theSIGGRAPH ’17 Posters, July 30 - August 03, 2017, Los Angeles, CA, USA
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Y. Ochiai et al.
obtained in the previous chapter is applied to the superconductor,the force F for lifting S can be regarded as Cm2 . Here, if we solve theproblem so as to balance the moment of R with respect to buoyancywith respect to S and the xy moment with respect to the center ofgravity of S, it can be formulated as follows.
Cm1 Mд = Cm2 (F − Mcд )Figure 2: Procedure of inner structure calculation.
structure of a 3D printed object to balance its body in midair byincluding a low temperature unit in the fabricated object. Third,
we have to solve the manipulation path of the levitated material
to consider its weight and acceleration. Finally, we have to solve
the manipulation methods by applying active electromagnet arrays.
For these problems, we use computational simulation methods ofheat transmutation and magnetic field estimation that float thesuperconductive material.

2 PRINCIPLES
2.1 Superconductive levitation(2)

At that time, when M becomes equal to or less than F , the model
levitates in the air while still at the specified position. The position
is a spatial position having a magnetic force intensity satisfying
F = Mд + Mcд . The shell thickness of R is R and li is the thicknessof the heat insulating material in R. To adjust M so as to satisfy
the above formula, space is created inside by adjusting R. Further,
it is decided by temperature transfer simulation to be describedlater, and its weight is fed back to again determine the position
and internal structure of the superconductor. To stabilize R, it
is necessary to minimize the distance v between Cm1 and Cm2 .
However, when Cm2 is moved away from the outer wall of themodel, the levitation distance decreases by the same amount. Thereis a trade-off of this problem.

where M(H ) is the magnetization curve which has a hysteretic
property [Brandt 1989].
Although we intended to consider the Meissner effect and the flux
pinning effect separately, we could not find an explicit expressions
as far as we surveyed. It seemed that the micro characteristicsof flux pinning had been well theoretically explored rather thanthe macro characteristics. Therefore, we measure the vertical andhorizontal forces and use the measured values in designing.
We make rails by arranging a lot of small neodymium magnets
or electromagnets. We form an S-N-S formation in the transverse
direction of the rail, and a uniform formation in the longitudinal direction. These kinds of rails are usually used in the demonstrationsof superconductive levitation [Miryala and Koblischka 2014].

2.2.2 Calculating Inner Structures. Figure 2 outlines the method.
First, as step 1, determine the thickness R of the exterior of themodel. Find the volume V and the center of gravity Cm1 from thegiven model and the density of filaments used in the 3D printer.
The levitation weight per superconductor is 750 g, and the required
number of superconductors is decided.
Then, in Step 2, the insulator enclosing the predetermined number of superconductors (H : 11 mm × R: 25 mm) is obtained and thethickness li of the insulator is determined. The thickness of thisinsulator is a parameter for determining the surface temperaturelater. Where to place the insulator including the superconductor isdetermined by the position of the center of gravity and the shapeof the model underneath. If there is only a structure whose crosssectional area S is less than the size of the superconductor × thearea (the cross-sectional area including the insulator) at a placeclose to the bottom of the model, it is searched as it is. In the casewhere there is no structure that fills the cross sectional area only
in a place larger than the levitation distance of the superconductor,
the model cannot be levitated unless it is expanded.
As Step 3, place this insulator in the model. Find the part thatis close to the center of gravity of the model and has a cross sectional area S or more and insert it. Stretch the top of the insulator
to penetrate the exterior of the model. After that, find Mall andcenter of gravity Call from the weight of the insulator including
the superconductor and the weight of the model.fifiNext, a vector
V from Call to Cm2 is obtained, and voxel carving is performed
such that x = y = 0 among the v(x, y, z). If there is no need toperform voxel carving, it ends there. Then, the interior is filled withvoxels from the bottom of the model so that z of vector V from
Call to Cm2 becomes small. The smaller z, the more stabilized thestabilization.

2.2

REFERENCES

We use YBa2 Cu3 O7 as superconductive material in this study. It isclassified into type II superconductors [Brandt 1989]. The materials
in this class exhibit more stable levitation than those in type I superconductors. While the materials of type I superconductors arelevitated solely based on the Meissner effect (perfect diamagnetism),
those of type II superconductors are levitated based on the combination of the Meissner effect and flux-line pinning effect. Magnetic
flux lines penetrate the materials of type II superconductors at theinhomogeneities, and resist the force that makes the penetration
position (pinning). Due to the hysteretic property of the pinningeffect, the materials can be not only levitated over magnets, butalso suspended under them.
The force F on a small superconductor volume V magnetizedparallel to a magnetic field H is written as
F = µ 0 M (H ) ∇H(1)Stabilization

2.2.1 Theory. The schematic diagram of a model floating in
air is shown in Figure 2. Cm1 is the center of gravity of a given
model R, M is the mass of R, Cm2 is the center of gravity of thesuperconductor S, Mc is the mass of S. When the magnetic flux H

EH Brandt. 1989. Levitation in physics. Science 243, 4889 (1989), 349–355.
Santosh Miryala and Michael Rudolf Koblischka. 2014. Experimenting with a superconducting levitation train. European Journal of Physics Education 5, 4 (2014).