LeviPrint: Contactless Fabrication using Full Acoustic Trapping of Elongated Parts

Abstract

LeviPrint is a system for assembling objects in a contactless manner using acoustic levitation. We explore a set of optimum acoustic fields that enables full trapping in position and orientation of elongated objects such as sticks. We then evaluate the capabilities of different ultrasonic levitators to dynamically manipulate these elongated objects. The combination of novel optimization algorithms and levitators enable the manipulation of sticks, beads and droplets to fabricate complex objects. A system prototype composed of a robot arm and a levitator is tested for different fabrication processes. We highlight the reduction of cross-contamination and the capability of building on top of objects from different angles as well as inside closed spaces. We hope that this technique inspires novel fabrication techniques and that reaches fields such as microfabrication of electromechanical components or even in-vivo additive manufacturing.

Full text

LeviPrint: Contactless Fabrication using Full Acoustic Trapping of
Elongated Parts.
IÑIGO EZCURDIA, UpnaLab, Public University of Navarre, Spain
RAFAEL MORALES, Ultraleap Ltd, UK
MARCO A.B. ANDRADE, Institute of Physics, University of São Paulo, Brazil
ASIER MARZO, ISC, Public University of Navarre, Spain
LeviPrint is a system for assembling objects in a contactless manner using
acoustic levitation. We explore a set of optimum acoustic elds that en-
ables full trapping in position and orientation of elongated objects such as
sticks. We then evaluate the capabilities of dierent ultrasonic levitators
to dynamically manipulate these elongated objects. The combination of
novel optimization algorithms and levitators enable the manipulation of
sticks, beads and droplets to fabricate complex objects. A system prototype
composed of a robot arm and a levitator is tested for dierent fabrication
processes. We highlight the reduction of cross-contamination and the ca-
pability of building on top of objects from dierent angles as well as inside
closed spaces. We hope that this technique inspires novel fabrication tech-
niques and that reaches elds such as microfabrication of electromechanical
components or even in-vivo additive manufacturing.
CCS Concepts: •Hardware
→
Emerging architectures;•Applied comput-
ing →Computer-aided design.
Additional Key Words and Phrases: acoustic levitation, additive manufactur-
ing, contactless manipulation, robot arm, end-eector
ACM Reference Format:
Iñigo Ezcurdia, Rafael Morales, Marco A.B. Andrade, and Asier Marzo. 2022.
LeviPrint: Contactless Fabrication using Full Acoustic Trapping of Elon-
gated Parts.. In Special Interest Group on Computer Graphics and Interactive
Techniques Conference Proceedings (SIGGRAPH ’22 Conference Proceedings),
August 7–11, 2022, Vancouver, BC, Canada. ACM, New York, NY, USA, 9 pages.
https://doi.org/10.1145/3528233.3530752
1 INTRODUCTION
Fabrication in the form of assembly or additive manufacturing has
evolved considerably due to its combination with computer systems,
novel actuators and end-eectors. Additive manufacturing has been
booming since the last decade, it will not only be used to fabri-
cate objects by the Maker community but also in the aeronautical,
automobile, and medical sector for prosthetic as well as tissue en-
gineering. Manufacturing is usually complemented with assembly,
which is the placement of the parts that compose the nal object, a
common example is the pick&place of electronic components on a
printed circuit board (PCB).
Across ordinary assembly and manufacturing techniques, a com-
mon characteristic is that the parts or materials that are manipulated
Permission to make digital or hard copies of all or part of this work for personal or
classroom use is granted without fee provided that copies are not made or distributed
for prot or commercial advantage and that copies bear this notice and the full citation
on the rst page. Copyrights for components of this work owned by others than ACM
must be honored. Abstracting with credit is permitted. To copy otherwise, or republish,
to post on servers or to redistribute to lists, requires prior specic permission and/or a
fee. Request permissions from permissions@acm.org.
SIGGRAPH ’22 Conference Proceedings, August 7–11, 2022, Vancouver, BC, Canada
©2022 Association for Computing Machinery.
ACM ISBN 978-1-4503-9337-9/22/08. . . $15.00
https://doi.org/10.1145/3528233.3530752
or dispensed are in direct contact with the machine. Consequently,
special equipment is required to manipulate small or fragile compo-
nents, and the handling of liquids, powders or hot materials is chal-
lenging. Furthermore, contact-based processes inherently lead to
cross-contamination, so when dangerous materials or bio-materials
are employed, it is necessary to have multiple manipulators or ster-
ilise them between the changes of materials.
We propose to use acoustic manipulation as a contactless way of
distributing materials in additive manufacturing as well as placing
and orientating parts in assembly processes. Thereby, it is possible
to manipulate small and fragile parts as well as liquids or pow-
ders, bringing more versatility to the processes. There is less cross-
contamination since the manipulator does not touch the parts or
material. Moreover, it enables manufacturing scenarios not achiev-
able with traditional 3D printing, such as threading through cavities
or adding to the manufactured item on any direction.
Levitation and manipulation of small particles and droplets have
been achieved before but never combined in a full prototype for
contactless fabrication. Furthermore, there is no existing work on
how to trap in position and orientation elongated objects, this would
open new possibilities in contactless manufacturing since beams,
sticks or girders are vital for the rapid fabrication of robust and
lightweight structures.
In this article, we introduce LeviPrint a method to generate acous-
tic elds that fully trap small particles, droplets and, more impor-
tantly, manipulate and reorient elongated bodies such as sticks. Also
we present a fully working system to fabricate 3D structures using
contactless manipulation. The novel contributions are:
•
A method to optimally trap a stick. We analyze dierent acous-
tic elds in terms of their capability to trap in position and
orientation an elongated object.
•
Levitators capabilities. A study of the capabilities for dynamic
orientation of elongated objects inside dierent acoustic levi-
tators.
•
A Contactless Fabrication System. An integration of an acoustic
levitator, mechanical translator and droplet injector to realize
a working prototype.
In section 2, we analyze the existing research regarding the ca-
pabilities and uses of acoustic levitation for fabrication. Section 3
summarizes the main models employed to simulate the acoustic eld
generated by phased arrays and the forces that they exert on objects.
In section 4, we evaluate dierent methods to generate acoustic
elds to fully trap a stick. Section 5 presents the dynamic manipu-
lation capabilities of various levitators using the selected method.
In section 6, we combine the insights from the previous sections to
1

SIGGRAPH ’22 Conference Proceedings, August 7–11, 2022, Vancouver, BC, Canada Ezcurdia, et al.
build a prototype that enables contactless fabrication mixing liquids,
particles and sticks. In the next section (7), we showcase some of the
structures build with the system. Finally, in section 8, we discuss
limitations and future work.
2 RELATED WORK
In this section, we review the manipulation capabilities of ultra-
sound and its uses in fabrication. We note that acoustic levitation
still lacks the capability of moving and orienting thin elongated
objects larger than the wavelength of sound. Also, integrated proto-
types that combine the required processes for fabrication (injection,
manipulation and fusing mechanism) have not been developed.
2.1 Fabrication: Assembly and Additive Manufacturing
Assembly can be dened as the process of picking the parts that
compose an object and placing them with the correct orientation
and position. This process can be observed at multiple scales; a
crane will position the girders for a building [Shapiro and Shapiro
1988], robot arms will position components of a car [Marvel et al
.
2018] and pick&place machines will pick electronic components
and place them on a PCB [Baby et al. 2017].
Additive manufacturing is dened as adding material layer by
layer into a nal object. This is opposed to carving or milling, in
which parts from a block of material are removed to create the nal
object. Multiple innovations have been added to additive manufac-
turing to enable multiple colors, the use of less support structure,
better layer distribution or non-planar 3d-printing [Dai et al
.
2018;
Etienne et al
.
2019; Hornus et al
.
2020; Song et al
.
2019]. However,
these techniques rely on direct contact between the dispenser (e.g.,
nozzle) and the objects that are being built. We reckon that acoustic
manipulation could be employed to create a contactless system.
2.2 Acoustic Manipulation
Acoustic Manipulation has the potential to become a fundamental
tool in contactless processing [Foresti et al
.
2013], given: the wide
range of particles that can be manipulated for a given operating
frequency (from the micrometre to the centimeter scale), materials
(plastic, metal or liquids), relative-high strength (larger ratio of input
power to radiation force) when compared with optical trapping, and
non-damaging eects on the trapped samples [Marzo et al. 2017].
Particles inside an acoustic eld are subjected to radiation forces
[Bruus 2012; Gor’kov 1962; Karlsen and Bruus 2015], it is possible
to design the elds so that these forces converge from all directions
into a point in which the particles get trapped [Brandt 2001]. In the
most basic conguration, an emitter opposed to a reector creates
a standing wave and particles are trapped at its nodes [Whymark
1975]. More complex arrangements allow for dynamic control of
the trapped particles.
The acoustic eld can be dynamically modied by adjusting the
phase or amplitude of the emitters, this allows to move particles in
3D using 4 opposed arrays [Ochiai et al
.
2014], this was simplied to
two-opposed arrays [Omirou et al
.
2015] and later to a single array
by using acoustic tractor beams [Marzo et al
.
2015]. However, acous-
tic tractor beams have trapping forces which are 8 times weaker
than regular standing waves [Marzo 2020], limiting its applications.
With the introduction of holographic methods, it was possible to
acoustically levitate multiple particles independently [Marzo and
Drinkwater 2019; Plasencia et al. 2020].
In most levitation methods, the particles are smaller than half
of the wavelength of the employed sound frequency [Zang et al
.
2017]. Near-eld levitation allows to levitate larger particles very
close to the acoustic emitter [Andrade et al
.
2017]. Also, virtual
vortices [Marzo et al
.
2018a] and other exotic elds [Inoue et al
.
2019]
can levitate larger-than-wavelength objects, but with limited force
and no dynamic capabilities. We do not consider levitation of solid
large objects (larger than the wavelength) particularly useful for
fabrication since they are not stable, occlude too much the acoustic
eld, and do not allow for complex designs with ne pieces.
A more interesting manipulation capability for fabrication would
be the control of the orientation of elongated objects. We note that
many fabricated items use beams, sticks or girders as building prim-
itives for the fast creation of strong and light structures. Ultrasonic
arrays are capable of 2D translation and rotation along one axis of
toothpicks [Foresti et al
.
2013]. Sub-wavelength asymmetric parti-
cles can be fully locked [Cox et al
.
2018] and controllably rotated
when enclosed inside a sphere of emitters [Helander et al
.
2020] but
not translated. However, there is no existing technique to fully trap
an elongated object enabling its reorientation and its repositioning.
Consequently, we propose dierent novel methods (Section 4) to
fully trap a stick in 6DoF and we compare them with a traditional
tweezers method [Marzo and Drinkwater 2019]. This would allow a
contactless system to employ segments as a building primitive.
2.3 Acoustic Fabrication
Using levitated particles as graphic representations is an emerging
eld [Fushimi et al
.
2019; Marzo and Drinkwater 2019; Ochiai et al
.
2014; Suzuki et al
.
2021] but the use of acoustic levitation in fabrica-
tion has not been that thoroughly explored. Acoustic Manipulation
has been used to pattern cells [Collins et al
.
2015], aerosols and small
particles [Shapiro et al
.
2021] in simple 2D patterns. Melde et al.[K
et al
.
2016] used a static holographic plate to form more complex 2D
patterns of particles that were fused together [K et al
.
2018]. In these
methods, the fabrication result is a 2D pattern that gets formed as a
whole because small particles follow the distribution of the acoustic
eld. We classify this as 2D printing and not 3D fabrication.
Primitives such as beads, threads, and fabrics have been levitated
[Fender et al
.
2021; Morales et al
.
2019]. However, in all these cases,
spherical particles were used as levitated buoys in which acoustically
transparent fabric was attached. This limits the materials, shapes,
rigidity and in general the possibility of having an additive process.
Automatic injection of droplets inside a levitation system has been
shown [Andrade et al
.
2018], also a static levitator was attached to a
robot arm to translate sub-wavelength particles in a contactless way
[Röthlisberger et al
.
2021]. However, no system integrates insertion,
manipulation and fusing of droplets or sub-wavelength particles;
moreover, there is no possibility of working with elongated parts.
One patent from Boing (United States) [Harkness and Goldschmid
2018] and another from Neurotechnology Ultrasound (Lithuania)
[Putkis 2018] present the idea of a contactless manufacturing sys-
tems, yet no full realization is shown, they present the concept.
2

LeviPrint: Contactless Fabrication using Full Acoustic Trapping of Elongated Parts. SIGGRAPH ’22 Conference Proceedings, August 7–11, 2022, Vancouver, BC, Canada
Optical tweezers have been used to manipulate micrometric spheres
to create microstructures [Sinclair et al
.
2004]. A prototype was capa-
ble of moving spherical particles and stacking them together using
biotin [Kirkham et al
.
2015]. However, optical tweezers are limited
to micrometric sizes. We note that the methods from optics are
not trivially adapted to acoustic manipulation because in optics, a
focus on the particle is sucient for trapping whereas in acoustics
more complex structured elds are required [Marzo and Drinkwater
2019].
The working methods presented in Section 4 to fully trap and
rotate sticks are novel contributions, there is no previous work
describing and showing a method to fully trap an elongated object.
3 MODELS
In this section, we dene the models employed in this work and the
common physical denitions that will be used throughout it.
3.1 The Emied Complex Acoustic Field
The piston model is employed [O’Neil 1949] to calculate the com-
plex acoustic eld generated by a single emitter that has a radiating
part in the shape of a piston vibrating at a single frequency. In the
complex pressure, the magnitude represents the amplitude and the
angle, the phase. An ultrasonic phased array is formed by multiple
emitters operating at the same frequency and varying their ampli-
tude and phase in a controlled way. The total eld generated by an
array of 𝑛emitters is the addition of their emitted elds:
𝑃(𝒙)=
𝑛

𝑖=1
𝑃0𝐽0(𝑘𝑟 sin 𝜃𝑖)
𝑑𝑖
𝑒𝑖(𝜑𝑖+𝑘𝑑𝑖),(1)
where
𝑃0
is the amplitude power of the transducer, dened by its
eciency and driving voltage amplitude.
𝐽0
is the Bessel function
of order zero.
𝑘=
2
𝜋/𝜆
is the wavenumber and
𝜆
is the wavelength.
𝑟
is the radius of the piston,
𝑑𝑖
is the distance from the emitter
𝑖
to the point
𝒙
in space.
𝜃𝑖
is the angle between the normal of the
emitter and the transducer to point 𝒙vector.
This models is commonly used and implemented in various frame-
works [Marzo et al
.
2018b], it is designed to work in open space
where there are no large obstacles in the eld. In this paper, the
trapped particles and structures being built do not aect signi-
cantly the acoustic eld since they are not fully solid. An analysis
of the eect of occlusions on the trapping force can be nd in Sup-
plementary Information 1.
3.2 Potential, Radiation Forces and Stiness
The Gor’kov potential approximates the radiation forces exerted
on a small sphere that is inside an arbitrary acoustic eld. It can be
dened in terms of the complex acoustic pressure
𝑝
and its spatial
derivatives 𝑝𝑥,𝑝𝑦and 𝑝𝑧. The Gor’kov potential 𝑈is given by:
𝑈=𝐾1|𝑝|2−𝐾2|𝑝𝑥|2+𝑝𝑦
2+|𝑝𝑧|2
𝐾1=
1
4𝑉 1
𝑐2
0𝜌0
−1
𝑐2
p𝜌p!
𝐾2=
3
4𝑉 𝜌0−𝜌p
𝜔2𝜌0𝜌0+2𝜌p!.
(2)
The volume of the spherical particle is
𝑉
,
𝜔
is the angular fre-
quency of the emitted waves, and
𝑐
and
𝜌
are the speed of sound
and the density, respectively. Their subindex 0and
𝑝
refer to the
propagation medium and the particle material.
The lower the potential is at a position, the stronger the object
will be trapped there. In general, the potential can be visualized as
a heightmap and thus minima in the eld represent wells where the
particles will roll in and get trapped. The radiation force acting on
a particle can be obtained from the gradient of the potential:
F=−∇𝑈 . (3)
Another measure of strength of a trapping position is the posi-
tional stiness, which represents how converging the forces are at
that position. The Laplacian operator (convergence of the gradient)
can be applied to the potential to get a mathematical representation
of the stiness.
𝑠𝑡 𝑖 𝑓 𝑓 𝑛𝑒𝑠𝑠 =∇2𝑈=𝑈𝑥𝑥 +𝑈𝑦 𝑦 +𝑈𝑧𝑧,(4)
where
𝑈𝑎𝑎 =𝜕2𝑈
𝜕𝑎2
and
𝑎=𝑥, 𝑦, 𝑧
are the Cartesian axes. Large
positive values of stiness represent large converging forces.
3.3
Torques and Rotational Stiness on Elongated Objects
In Supplementary Information 2, we show that the torque and forces
acting on a stick can be approximated as the summation of the
forces or torques acting on constituent spheres. Potential, forces
and stiness are linear functions of each other, therefore our sphere
decomposition approximation can be applied to them. We performed
a converging analysis to determine that decomposing the stick into
small spheres separated by 𝜆/8is sucient.
When the acoustic eld acts on a stick, there is a torque that will
aect the orientation. We calculate the torque as the addition of
the torques exerted on each constituent sphere. The torque from a
sphere is the cross product between the force on that sphere and
the vector that joins the sphere to the center of mass of the object:
𝝉=r×F,(5)
where ris the positional vector from the location where the force
is applied and Fis the force acting on that part of the object. The
rotational stiness can be obtained by dierentiating the torque on
small rotations of the stick.
3.4 Summary
Potential, Force, Positional Stiness, Torque and Rotational Stiness
will be used throughout the paper to characterize the trapping on
an object. These properties were calculated on the simulations but
only the most informative ones will be reported. Potential provides
a basic measurement, the lower the better, it is not dimensional
3

SIGGRAPH ’22 Conference Proceedings, August 7–11, 2022, Vancouver, BC, Canada Ezcurdia, et al.
and gives information both for translation and orientation trapping.
Forces should be analyzed along dierent positions of the objects,
since the forces at the trap are 0 and push towards the trap, i.e., they
become positive when the objects shifts towards negative positions
and vice-versa. Positional stiness represents the trapping force
convergence with a single value, the higher the better, however
it does not provide topological information such as the reach of
the trap. Torque and rotational stiness have similar features to
force and positional stiness respectively but acting on orientation
instead of position.
4 FULLY TRAPPING A STICK
In this section, we derive and analyze algorithms that generate an
acoustic eld capable of fully trapping a stick inside an acoustic
eld. The stick has to be trapped in position (3 Dof) and orientation
(3 DoF). All methods were evaluated attending to their trapping
performance in position and orientation.
We analyzed levitators with dierent geometries (Fig. 1), they
were composed of ultrasonic emitters of 1 cm diameter with the
following parameters for Eq. 1:
𝑟
= 4.5 mm and
𝑃0
= 2.4, which
correspond to a real existing emitter (e.g., model MA40S4S - Murata).
The levitators were selected between the most common geometries
in the literature for airborne acoustic levitation. Fixed two-opposed
inspired by TinyLev [Marzo et al
.
2017], two-opposed arrays of
16x16 emitters separated by 23 cm as in [Marzo and Drinkwater
2019; Morales et al
.
2019; Suzuki et al
.
2021], four orthogonal arrays
in a cube formation as in [Ochiai et al
.
2014]. We also tried with
variations of the cube in the shape of a triangle, cylinder and sphere.
The trapping algorithms will determine the emission phases of
the levitators in order to generate a eld that traps the stick. The
generated elds for the two-opposed levitator can be seen in Fig.
2, similar results were obtained for the other levitators. Similarly,
others were designed and evaluated, we just selected the 4 most
representative and eective ones. The methods are:
•
Trap at Center: It is the trivial method of creating a standing
wave focused at the center of the stick. It is the default method
for trapping sub-wavelength particles. We do not expect it to
be eective on a stick but the resulting forces and torques can
be used as a baseline for comparison with the other methods.
•
Traps at Sides: Two trapping nodes are generated at both
sides of the stick. A modied Iterative Backpropagation (IBP)
[Marzo and Drinkwater 2019] algorithm is employed to max-
imize amplitude in 2 pairs of focal points above and below
the stick, with a phase dierence of
𝜋
is forced between the
rst points of each pair. Thereby, high-amplitude is gener-
ated above and below the stick with low-amplitude at the
stick. Whilst Marzo and Drinkwater [Marzo and Drinkwater
2019] optimized trapping strength on individual particles,
this method traps an elongated body by creating two traps
at its sides. The traps were oset 2.5mm towards the stick
center, this was the optimum oset in terms of stiness (see
Supplementary Information 3).
•
Minimum Potential: Employs an optimizer to nd the emis-
sion phases that minimize the Gork’ov potential along the
stick. If we simplify to 2D, this can be seen as digging a poten-
tial well with the shape of the object that should be trapped.
A quasi-newton optimizer is employed with gradients ap-
proximated using nite dierences. The parameters were the
default ones from Matlab R2019 fminunc function (except,
TolFun=0.0025, TolX=eps, MaxIters=30). The result can be
interpreted as a strong trap at the center of the stick and two
smaller ones at the sides. The target function can be expressed
as:
𝑆𝑢𝑚𝐺𝑜𝑟 𝑘𝑜 𝑣 (𝜑1, ..., 𝜑 𝑁)=
𝑃

𝑖=1
𝑔𝑜𝑟𝑘 𝑜𝑣𝐴𝑡 (𝒑 𝒐𝒔 (𝒊))
Where
𝜑𝑛
is the emission phase of the
𝑛
transducer,
𝑃
is the
number of points that form the stick,
𝑝𝑜𝑠
is their position,
and 𝑔𝑜𝑟𝑘𝑜𝑣𝐴𝑡 is the Gork’ov potential at that point (Eq. 2).
•
Minimum Weighted Potential: Similar to the previous
method (Minimum Potential) but the 4 terms appearing in
Gork’ov potential (Eq. 2) were weighted using the factors 0.09
for p, 15.01 for px, 8.34 for py and 7.66 for pz. These weights
were obtained from the Traps at Sides method. The results in
Figure 2.c shows that the method tries to t as many traps as
possible along the stick.
The forces and torques acting on a stick under the elds generated
by the dierent methods can be seen in Fig. 3. The stick was 30 mm
length, 2 mm width and 1 mm height and placed at the center of
the levitator. Similar results were obtained for sticks between 2
wavelengths (1.6 cm) and a a length of 8 cm.
All the forces and torques but the Trap a center are converging
since the force is 0 at the neutral position or angle, but become
positive if the position or angle gets negative, and vice-versa. The
steepness of the curves at the neutral position or angle, characterize
the strength of the trap.
The most promising methods are Traps at Sides (TrapsAtSides)
and Minimum Potential (MinPot), the rest of the methods were
weaker on all of the axes, both in position and rotation. The trap
at center (traditional standing wave) does not have the capability
to trap along the x-position and the x-torque was marginal. The
MinPot algorithm produces elds that are
∼
10% stronger in force-Y,
force-Z and torque-X, however TrapsAtSides is
∼
25% stronger on
force-X, torque-Y, and torque-Z.
TrapsAtSides provides the overall stronger trapping forces and
torques. We also note that the elds obtained in TrapsAtSides can be
generated by a xed-levitator without phase control (Fig. 4) and is
applicable to sticks of dierent lengths since the trapping positions
are relative to the ends of the stick. Furthermore, it is based on an
iterative method (IBP) and is computationally faster than the other
methods based on traditional optimization.
We note that the problem of fully trapping a stick is multi-variable
and required expert knowledge to analyze the results of the dierent
methods: e.g., the forces and torques in Figure 3, potentials in 5, and
stiness in Supplementary Information 4.
5 MANIPULATION CAPABILITIES OF THE LEVITATORS
In the previous section, we have selected the TrapsAtSides method
for generating elds that trap a stick in position and orientation.
4

LeviPrint: Contactless Fabrication using Full Acoustic Trapping of Elongated Parts. SIGGRAPH ’22 Conference Proceedings, August 7–11, 2022, Vancouver, BC, Canada
-0.06 -0.04 -0.02 0 0.02 0.04 0.06
X
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
Z
500
1000
1500
2000
2500
3000
-0.06 -0.04 -0.02 0 0.02 0.04 0.06
X
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
Z
500
1000
1500
2000
2500
3000
3500
-0.06 -0.04 -0.02 0 0.02 0.04 0.06
X
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
Z
500
1000
1500
2000
2500
3000
3500
4000
4500
-0.06 -0.04 -0.02 0 0.02 0.04 0.06
X
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
Z
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
-0.06 -0.04 -0.02 0 0.02 0.04 0.06
X
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
Z
1000
2000
3000
4000
5000
6000
7000
-0.06 -0.04 -0.02 0 0.02 0.04 0.06
X
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
Z
1000
2000
3000
4000
5000
6000
7000
AB C D E F
Fig. 1. Dierent simulated levitator geometries and a vertical slice of the pressure field that they generate when applying the TrapsAtSides method on a thin
stick of 30 mm. A) Two-opposed fixed levitator. B) Two-opposed Levitator. C) Triangle levitator. D) Cube. E) Cylinder. F) Sphere.
A B
CD
Fig. 2. Amplitude fields around a 30 mm stick for dierent trapping methods
on the Two-opposed levitator. A) Trap at center, B) Traps at sides (2.5mm
inward oset) C) Minimum Potential, D) Minimum Weighted Potential.
In this section we will analyze the capabilities of the levitators
presented in Fig. 6 to orientate the sticks by changing their emission
phases. For each levitator, a stick of 30 mm length, 2 mm width and
1 mm height was placed at the center. Then, it was rotated along
each axis applying the trapping method at each step and calculating
the potential on the stick.
The potentials while rotating (Fig. 5) indicate that all arrange-
ments can rotate the stick around the Z-axis. The two-opposed
levitator provides a good balance between manipulation capabilities
and being open at the sides, it can rotate a stick around the Z-axis
and in Y-axis with a limited angle
∼
30 degrees. The cube arrange-
ment provides full rotations around the Z- and Y-axis, being able to
orient the sticks as needed in the piece, this is crucial to fabricate
vertical structures and shorings, it just lacks the capability to fully
rotate the stick around itself. The cylinder was not superior than
the cube, it is more complex to fabricate and less uniform on the
potentials along the rotations. The triangle arrangement is not a
good alternative since it has less working volume than the cube and
less manipulation capabilities. The sphere can orientate the stick
around any axis with uniform potential but it is cumbersome to
use in a fabrication system. Similar conclusions were derived from
analyzing the positional and rotational stines (See Supplementary
Information 4).
6 SYSTEM PROTOTYPES
In this section, we combine the trapping and manipulation capa-
bilities of an acoustic levitator with a mechanical manipulator that
complements the levitator. Thereby, the manipulation of the stick is
performed by the dynamic levitator in some DoFs whereas other
DoFs are covered by the mechanical manipulator. We note that this
control strategy can be easily integrated into the kinematic chains
of most control software.
In section 5, we obtained the manipulation capabilities of dierent
levitators, we have constructed the 3 most promising levitators 6 to
experimentally realize the manipulations. The levitators were built
using MA40S4S (Murata) emitters which are 1 cm in diameter and
made of plastic, its parameters for Eq. 1 are
𝑟
= 4.5 mm and
𝑃0
= 2.4
for a 15 Voltage peak-to-peak (Vpp) square excitation signal. For
larger operating voltages,
𝑃0
scales linearly with the Vpp. The bowl
design is based on TinyLev [Marzo et al
.
2017]. The at arrays are
based on SonicSurface [Morales et al. 2021].
The basic operation of the fabrication prototypes is as follows.
An acoustically transparent foundation is placed at the center of
the working volume before starting the fabrication process, the
foundation is the initial part where other parts or matter will be
added. The system starts by trapping with the levitator a droplet
of glue dispensed by a syringe pump. Then, the droplet is levitated
into the position where the next piece is going to be added. The
system picks sticks or particles from an acoustically-transparent
repository and positions them in contact with the previously placed
glue, UV light is applied to cure the glue. This process is repeated
for all the parts.
The main prototype is a xed two-opposed levitator attached to a
7-DoF robot arm, a secondary prototype made of a a cube levitator
5

SIGGRAPH ’22 Conference Proceedings, August 7–11, 2022, Vancouver, BC, Canada Ezcurdia, et al.
A B C D E F
Fig. 3. Forces and torques exerted on a stick by the field generated by dierent methods: Minimum weighted potential, minimum Potential, Trap at side and
Trap at center. A) Forces exerted in the X-Axis. B) Forces exerted in the Y-Axis. C) Forces exerted in the Z-Axis. D) Torque exerted in the X-Axis. E). Torque
exerted in the Y-Axis. F) Torque exerted in the Z-Axis.
Fig. 4. Pressure fields generated by a fixed-levitator. A) a standing wave
creates a trap for holding a single sub-wavelength particle when the emiers
are driven with the same signal. B) TrapsAtSides are generated when a halve
of the emiers is driven with an inverse polarity signal (
𝜋
phase), this field
can fully trap a stick.
0 10 20 30 40 50 60 70 80 90
Rotation around X (º)
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
GorKovPotential(J)
10-6 GorkovPotential evolution rotating around X
Sphere
Cylinder
Cube
Triangle
Two Opposed
0 10 20 30 40 50 60 70 80 90
Rotation around Y (º)
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
10-6 GorkovPotential rotating around Y
0 10 20 30 40 50 60 70 80 90
Rotation around Z (º)
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
10-6 GorkovPotential evolution rotating around Z
A B C
Fig. 5. Gor’kov potential on a stick inside dierent levitators applying the
TrapsAtSides method as it rotates around a A) x-axis, B) y-axis, and C) z-axis.
The stick is 30 mm long, 2 mm wide and 1 mm height.
mounted on a translation stage was tested, but the rst prototype
was easier to operate.
6.1 Two-opposed Fixed Levitator + Robot Arm
A 7-DoF robotic arm (UR-3) is attached to a xed two-opposed levi-
tator (see Fig. 7.C). The xed levitator is composed of two spherical
arrays of 60 emitters each, with 4 concentric rings. It generates a
eld that traps the stick, using the Traps At Sides method from
Section 4, see Fig. 4. A dynamic two-opposed levitator could also
be used to add more DoFs to the levitator but for this system it was
decided that the levitator would only be in charge of trapping and
the robot arm would provide the manipulation DoFs. Alternatively,
Fig. 6. Constructed levitators. A) a fixed single-axis levitator with bowl
geometry. B) two-opposed flat phased-arrays. C) four orthogonal flat arrays
in a cube structure.
Fig. 7. Examples of levitators aached to a robotic arm to complement or
boost their missing manipulation DoFs. A) Fixed single-axis levitator with
bowl geometry. B) Four orthogonal flat arrays in a cube structure.
the xed single-axis levitator can be held by a human to manu-
ally perform the steps involved in LeviPrint: trapping, releasing,
translating, orientating and rotation.
6.2 Cube Levitator + Mechanical Stage
A cube levitator was attached to a translation stage. The levitator
can orientate the stick to have the desired alignment as well as
providing limited translation capabilities. The cube was attached to
a mechanical translation stage that could provide larger ranges in
the translation DoFs.
7 FABRICATION RESULTS
We illustrate the capabilities of LeviPrint by combining various
building primitives such as sticks, beads and droplets to fabricate
robust, lightweight and complex structures.
6

LeviPrint: Contactless Fabrication using Full Acoustic Trapping of Elongated Parts. SIGGRAPH ’22 Conference Proceedings, August 7–11, 2022, Vancouver, BC, Canada
7.1 Basic Joints
Fig. 8. Types of joints between sticks. A) Bu joint: Two sticks are connected
end to end forming a longer segment. B) L-joint: Two sticks are connected
end to end at 90 degrees, the angle can be adjusted, more glue should be
used since the contact surface is small. C) T-joint. D) Mitered joint: An
L-joint reinforced with a third stick connecting the L at 45 degrees.
Joining sticks together is the main novel capability of LeviPrint.
For doing so, a droplet of glue is levitated into the main object at the
place where the next stick will be placed. The stick is then levitate
to come in contact with the glue. UV light is applied to cure the glue.
The types of joints can be seen in Fig. 8. We note that also beads
can be used to connect sticks.
7.2 Fabricating with Particles
Instead of using sticks, only particles (a.k.a beads) are joined together
using glue between them. The use of sub-wavelength spherical
particles as the building parts enables more exible designs in terms
of shapes since they can be connected from anywhere. However, the
process is longer since more parts are needed for the same length
when compared to sticks, also the nal result is denser and not
necessarily stronger (Fig. 9.A).
7.3 Fabricating with UV Resin
UV-resin droplets can be used for manufacturing objects with free-
form shapes. Droplets are repeatedly moved into its target position
and cured until the nal objects is formed. The droplets have a dish
shape because of the pressure of the standing wave, the droplet can
be oriented so that it is aligned with the building direction. We have
manufactured a loop of 1cm diameter (see Fig. 9.B).
7.4 Complex Objects
The methods presented in the previous subsections can be combined
to build more complex objects. We built a cube using orthogonally
placed sticks via L joints, we also built a bridge connecting two sep-
arated metallic meshes, using dierent joints to provide a stronger
structure (see Figs. 9.C and 9.E).
7.5 Adding on Top of Other Objects
Sticks, particles and droplets can be levitated on top of existing solid
objects if they are approach from certain angles. The solid object
cannot be directly located between the levitated part and the arrays
since it would block a signicant amount of the eld. However, the
solid object can be located in front of the levitated part without
signicantly disrupting the eld. We showcase the addition of parts
into a spherical object in Fig. 9.F.
7.6 Building Inside a Container
Fabric, meshes and sponges are acoustically translucent to the ul-
trasound eld. Therefore, LeviPrint can fabricate inside containers
made of these material, from the outside. In Fig. 9.D, we fabricate a
boat inside a metallic mesh bottle. The sticks and glue are introduced
inside the bottle through a small aperture at the side. In airborne
Leviprint, the materials of the container are limited but if LeviPrint
would be adapted to operate in aqueous media, it could assemble
microscopic objects in cell-culture media and perhaps even inside
living beings (See 9.D).
Fig. 9. Fabricated items. A) Particles joined together to build a loop. B) Glue
droplets being levitated to its final position to be cured for building a loop.
C) Twelve orthogonally placed sticks via L-joints to build a cube. D) A stick
being levitated inside a container towards its final position. E) Fieen sticks
joined via bu joints, L joints and miter bu joints to form a bridge. F)
Adding multiple primitives at dierent angles into a solid spherical object.
8 DISCUSSION
Fig. 10. Another primitives that have been successfully levitated using
stick. A) A circle was hold in mid-air using the two-opposed levitator. B)
An airplane created by three sticks, using an array on top of a reflective
surface. C) a levitated square. D) droplet of milk on a hydrophobic surface.
E) electronic components Soic8 levitating over a table.
The individual steps involved in the results were conducted by
a robot arm and an automatized software. The robot arm is pro-
grammed to perform the required movements to grab and place
7

SIGGRAPH ’22 Conference Proceedings, August 7–11, 2022, Vancouver, BC, Canada Ezcurdia, et al.
each primitive. However, for practicality reasons, on some occasions
there was human intervention. We highlight that all the actions that
were carried out manually could also have been performed by the
programmed robotic arm, droplet dispenser and UV lamp.
Apart from sticks, we tested other primitives such as circles,
squares, triangles and crosses. For these primitives, TrapsAtSides
was not directly applicable and we employed the MinPot method.
These primitives were levitated but we did not explore them since
they can be composed with the basic primitives (see Fig.10. A-C).
The levitators presented here were based on various arrays facing
each other. However, the developed methods are also applicable
when a single array is placed on top of an acoustically reective
surface. The DoFs are limited to 1 DoF rotation and 2D translations
at a plane located a a quarter wavelength above the surface. Printed
circuit boards or functionalized substrates can be used as surfaces
(see Fig.10.D and E).
Given that the fabricated structures are made of thin segments
such as sticks, beads or cured glue, the fabricated object does not
cause a signicant disruption on the acoustic eld since its "ll rate"
is quite low (i.e., it is like a wireframe object). However, if complete
solid objects were manufactured, we foresee two strategies that
should be followed. First, the order in which the parts are added
should be planned so that they approach the object from an operative
angle that does not block signicantly the ultrasound emitted from
the arrays. As future work, it would also be possible to consider
reections caused by the object.
The emitters were driven at 70%of their maximum power so
denser materials could be employed if a non-prototype system with
extra cooling and electronics to handle more voltage was designed.
The prototypes operated in air at 40 kHz, thus the wavelength
𝜆
=8.6mm determines the scale of the objects that can be manipulated,
long sticks give exibility in this regard. We reckon that decreasing
the frequency to work with larger objects is not a feasible research
direction; however, operating in water-based media at Mhz range
would enable to control micrometric bio-structures on cell-friendly
cultures and even in-vivo.
The maximum weight for sticks is that of 8 cm length of balsa
wood (16 mg). The system can recover from external perturbations
like shaking of the robot arm or weak wind since Acoustic levitation
has converging forces and torques [Marzo et al
.
2015]. The typical
positioning accuracy is around 0.2 mm for levitating system oper-
ating at 40 kHz in air [Marzo et al
.
2015], but moving into smaller
wavelengths would increase this accuracy to the micrometres range
[K et al
.
2018]. Translation speeds vary from 1 cm/s [Marzo et al
.
2015] to 8 m/s [Hirayama et al
.
2019] for lighter particles, in our
system the sticks were translated at up to 4 cm/s. We note that these
limits are system-specic, systems operating at higher voltage, with
less separation or working in water-based solutions instead of air
would trap more weight, move faster or provide more accuracy.
9 CONCLUSION
LeviPrint is a technique for fabricating objects in a contactless way
using acoustic levitation on primitives such as beads, sticks and
droplets. We have presented an optimum acoustic eld to trap elon-
gated parts. Afterwards, we analyzed the capabilities of dierent
levitators to allow dynamic manipulation of the stick by chang-
ing the emission phases. We designed a levitator integrated with a
robotic arm to enable contactless fabrication of complex objects. We
hope that the presented methods help other researchers to use acous-
tic contactless fabrication in other elds such as bio-engineering
or micro-fabricated machines, and in general that it broadens our
concept of additive manufacturing.
ACKNOWLEDGMENTS
This research was funded by the EU Horizon 2020 research and inno-
vation programme under grant agreement No 101017746 TOUCH-
LESS. We thank Iruña Tecnologías de Automatización for allowing
us to use the robotic arm.
REFERENCES
Marco AB Andrade, Thales SA Camargo, and Asier Marzo. 2018. Automatic contactless
injection, transportation, merging, and ejection of droplets with a multifocal point
acoustic levitator. Review of Scientic Instruments 89, 12 (2018), 125105.
Marco AB Andrade, Fábio TA Okina, Anne L Bernassau, and Julio C Adamowski. 2017.
Acoustic levitation of an object larger than the acoustic wavelength. The Journal of
the Acoustical Society of America 141, 6 (2017), 4148–4154.
Ashly Baby, Chinnu Augustine, Chinnu Thampi, Maria George, Abhilash AP, and
Philip C Jose. 2017. Pick and place robotic arm implementation using Arduino. IOSR
Journal of Electrical and Electronics Engineering 12, 2 (2017).
E H Brandt. 2001. Suspended by sound. Nature 413, 6855 (2001), 474–475. https:
//doi.org/10.1038/35097192
Henrik Bruus. 2012. Acoustouidics 7: The acoustic radiation force on small particles.
Lab Chip 12 (2012), 1014–1021. Issue 6. https://doi.org/10.1039/C2LC21068A
David J Collins, Belinda Morahan, Jose Garcia-Bustos, Christian Doerig, Magdalena
Plebanski, and Adrian Neild. 2015. Two-dimensional single-cell patterning with one
cell per well driven by surface acoustic waves. Nature communications 6, 1 (2015),
1–11.
L. Cox, A. Croxford, B. W. Drinkwater, and A. Marzo. 2018. Acoustic Lock: Position
and orientation trapping of non-spherical sub-wavelength particles in mid-air using
a single-axis acoustic levitator. Applied Physics Letters 113, 5 (2018), 054101. https:
//doi.org/10.1063/1.5042518 arXiv:https://doi.org/10.1063/1.5042518
Chengkai Dai, Charlie CL Wang, Chenming Wu, Sylvain Lefebvre, Guoxin Fang, and
Yong-Jin Liu. 2018. Support-free volume printing by multi-axis motion. ACM
Transactions on Graphics (TOG) 37, 4 (2018), 1–14.
Jimmy Etienne, Nicolas Ray, Daniele Panozzo, Samuel Hornus, Charlie CL Wang,
Jonàs Martínez, Sara McMains, Marc Alexa, Brian Wyvill, and Sylvain Lefebvre.
2019. CurviSlicer: Slightly curved slicing for 3-axis printers. ACM Transactions on
Graphics (TOG) 38, 4 (2019), 1–11.
Andreas Rene Fender, Diego Martinez Plasencia, and Sriram Subramanian. 2021. Artic-
uLev: An Integrated Self-Assembly Pipeline for Articulated Multi-Bead Levitation
Primitives. In Proceedings of the 2021 CHI Conference on Human Factors in Computing
Systems. 1–12.
Daniele Foresti, Majid Nabavi, Aldo Klingauf, and Dimos Poulikakos. 2013.
Acoustophoretic contactless transport and handling of matter in air. Proceedings of
the National Academy of Sciences 110, 31 (2013), 12549–12554.
Tatsuki Fushimi, Asier Marzo, Bruce W Drinkwater, and Thomas L Hill. 2019.
Acoustophoretic volumetric displays using a fast-moving levitated particle. Applied
Physics Letters 115, 6 (2019), 064101.
Lev P. Gor’kov. 1962. On the forces acting on a small particle in an acoustical eld in
an ideal uid.
William A Harkness and Josh H Goldschmid. 2018. Free-form spatial 3-D printing
using part levitation. US Patent 9,908,288.
Petteri Helander, Tuomas Puranen, Antti Meriläinen, Göran Maconi, Antti Penttilä, M
Gritsevich, Ivan Kassamakov, Ari Salmi, Karri Muinonen, and Edward Haeggström.
2020. Omnidirectional microscopy by ultrasonic sample control. Applied Physics
Letters 116, 19 (2020), 194101.
Ryuji Hirayama, Diego Martinez Plasencia, Nobuyuki Masuda, and Sriram Subramanian.
2019. A volumetric display for visual, tactile and audio presentation using acoustic
trapping. Nature 575, 7782 (2019), 320–323. https://doi.org/10.1038/s41586-019-
1739-5
Samuel Hornus, Tim Kuipers, Olivier Devillers, Monique Teillaud, Jonàs Martínez, Marc
Glisse, Sylvain Lazard, and Sylvain Lefebvre. 2020. Variable-width contouring for
Additive Manufacturing. ACM Transactions on Graphics (TOG) 39, 4 (2020), 131–1.
Seki Inoue, Shinichi Mogami, Tomohiro Ichiyama, Akihito Noda, Yasutoshi Makino, and
Hiroyuki Shinoda. 2019. Acoustical boundary hologram for macroscopic rigid-body
levitation. The Journal of the Acoustical Society of America 145, 1 (2019), 328–337.
8

LeviPrint: Contactless Fabrication using Full Acoustic Trapping of Elongated Parts. SIGGRAPH ’22 Conference Proceedings, August 7–11, 2022, Vancouver, BC, Canada
Melde K, Mark AG, Qiu T,and Fischer P. 2016. Holograms for acoustics. Nature, 518–22.
Melde K, Choi E, Wu Z, Palagi S, and Fischer P Qiu T. 2018. Acoustic Fabrication via
the Assembly and Fusion of Particles. Adv Mater.
Jonas T. Karlsen and Henrik Bruus. 2015. Forces acting on a small particle in an
acoustical eld in a thermoviscous uid. Phys. Rev. E 92 (Oct 2015), 043010. Issue 4.
https://doi.org/10.1103/PhysRevE.92.043010
Glen R Kirkham, Emily Britchford, Thomas Upton, James Ware, Graham M Gibson,
Yannick Devaud, Martin Ehrbar, Miles Padgett, Stephanie Allen, Lee D Buttery, et al
.
2015. Precision assembly of complex cellular microenvironments using holographic
optical tweezers. Scientic reports 5, 1 (2015), 1–7.
Jeremy A Marvel, Roger Bostelman, and Joe Falco. 2018. Multi-robot assembly strategies
and metrics. ACM Computing Surveys (CSUR) 51, 1 (2018), 1–32.
Asier Marzo. 2020. Standing Waves for Acoustic Levitation. In Acoustic Levitation.
Springer, 11–26.
Asier Marzo, Adrian Barnes, and Bruce W. Drinkwater. 2017. TinyLev: A multi-emitter
single-axis acoustic levitator. Review of Scientic Instruments 88, 8 (2017), 085105.
https://doi.org/10.1063/1.4989995 arXiv:https://doi.org/10.1063/1.4989995
Asier Marzo, Mihai Caleap, and Bruce W Drinkwater. 2018a. Acoustic virtual vortices
with tunable orbital angular momentum for trapping of mie particles. Physical
review letters 120, 4 (2018), 044301.
Asier Marzo, Tom Corkett, and Bruce W. Drinkwater. 2018b. Ultraino: An Open
Phased-Array System for Narrowband Airborne Ultrasound Transmission. IEEE
Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 65, 1 (2018), 102–111.
https://doi.org/10.1109/TUFFC.2017.2769399
Asier Marzo and Bruce W.Drinkwater. 2019. Holographic acoustic tweezers. Proceedings
of the National Academy of Sciences 116, 1 (2019), 84–89. https://doi.org/10.1073/
pnas.1813047115 arXiv:https://www.pnas.org/content/116/1/84.full.pdf
Asier Marzo, Sue Ann Seah, Bruce W Drinkwater, Benjamin Sahoo, and Sriram Subra-
manian. 2015. Holographic acoustic elements for manipulation of levitated objects.
Nature communications 6, 1 (2015), 1–7.
Rafael Morales, Iñigo Ezcurdia, Josu Irisarri, Marco A. B. Andrade, and Asier Marzo.
2021. Generating Airborne Ultrasonic Amplitude Patterns Using an Open Hardware
Phased Array. Applied Sciences 11, 7 (2021). https://doi.org/10.3390/app11072981
Rafael Morales, Asier Marzo, Sriram Subramanian, and Diego Martínez. 2019. LeviProps:
Animating levitated optimized fabric structures using holographic acoustic tweezers.
In Proceedings of the 32nd Annual ACM Symposium on User Interface Software and
Technology. 651–661.
Yoichi Ochiai, Takayuki Hoshi, and Jun Rekimoto. 2014. Pixie Dust: Graphics Generated
by Levitated and Animated Objects in Computational Acoustic-Potential Field. ACM
Trans. Graph. 33, 4, Article 85 (jul 2014), 13 pages. https://doi.org/10.1145/2601097.
2601118
Themis Omirou, Asier Marzo, Sue Ann Seah, and Sriram Subramanian. 2015. LeviPath:
Modular Acoustic Levitation for 3D Path Visualisations. In Proceedings of the 33rd
Annual ACM Conference on Human Factors in Computing Systems (Seoul, Republic
of Korea) (CHI ’15). Association for Computing Machinery, New York, NY, USA,
309–312. https://doi.org/10.1145/2702123.2702333
HoT O’Neil. 1949. Theory of focusing radiators. The Journal of the Acoustical Society of
America 21, 5 (1949), 516–526.
Diego Martinez Plasencia, Ryuji Hirayama, Roberto Montano-Murillo, and Sriram
Subramanian. 2020. GS-PAT: High-Speed Multi-Point Sound-Fields for Phased
Arrays of Transducers. ACM Trans. Graph. 39, 4, Article 138 (jul 2020), 12 pages.
https://doi.org/10.1145/3386569.3392492
Osvaldas Putkis. 2018. Contactless manipulation apparatus, assembly method and 3d
printing. US Patent App. 15/765,126.
Marc Röthlisberger, Marcel Schuck, Laurenz Kulmer, and Johann W Kolar. 2021. Con-
tactless Picking of Objects Using an Acoustic Gripper. In Actuators, Vol. 10. Multi-
disciplinary Digital Publishing Institute, 70.
Jenna M. Shapiro, Bruce W. Drinkwater, Adam W. Perriman, and Mike Fraser.
2021. Sonolithography: In-Air Ultrasonic Particulate and Droplet Ma-
nipulation for Multiscale Surface Patterning. Advanced Materials Tech-
nologies 6, 3 (2021), 2000689. https://doi.org/10.1002/admt.202000689
arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/admt.202000689
Lawrence K Shapiro and Howard I Shapiro. 1988. Construction cranes. Scientic
American 258, 3 (1988), 72–79.
Gavin Sinclair, Pamela Jordan, Johannes Courtial, Miles Padgett, Jon Cooper, and
Zsolt John Laczik. 2004. Assembly of 3-dimensional structures using programmable
holographic optical tweezers. Optics Express 12, 22 (2004), 5475–5480.
Haichuan Song, Jonàs Martínez, Pierre Bedell, Noemie Vennin, and Sylvain Lefebvre.
2019. Colored fused lament fabrication. ACM Transactions on Graphics (TOG) 38, 5
(2019), 1–11.
Shun Suzuki, Seki Inoue, Masahiro Fujiwara, Yasutoshi Makino, and Hiroyuki Shinoda.
2021. AUTD3: Scalable Airborne Ultrasound Tactile Display. IEEE Transactions on
Haptics 14, 4 (2021), 740–749. https://doi.org/10.1109/TOH.2021.3069976
RR Whymark. 1975. Acoustic eld positioning for containerless processing. Ultrasonics
13, 6 (1975), 251–261.
Duyang Zang, Kejun Lin, Lin Li, Zhen Chen, Xiaoguang Li, and Xingguo Geng. 2017.
Acoustic levitation of soap bubbles in air: Beyond the half-wavelength limit of sound.
Applied Physics Letters 110, 12 (2017), 121602.
9