Expressive Fused Deposition Modeling by Controlling
Extruder Height and Extrusion Amount
Haruki Takahashi
Meiji University
Nakano, Tokyo, Japan
haruki@meiji.ac.jp

Homei Miyashita
Meiji University
Nakano, Tokyo, Japanhomei@homei.com

Figure 1. Extrusion state of our technique. We focus on (red) the height position of the extruder and (green arrow) the amount of
extruded materials and explore the relationship between the combination of parameters and the behavior of extruded materials toextend the expression of the FDM 3D printer.
ABSTRACTACM Classification Keywords

Fused deposition modeling (FDM) 3D printers form objects
by stacking layers having a linear structure. To print finestructures, an appropriate choice of parameters is necessary,or printing error occurs. On the other hand, the printing error
is exploited as an expression technique. However, therelation between the printed structure and the parameters
causing the printing error is unclear. In this paper, we focus
on the height position of the extruder and the amount of
extruded material, and explore the combination of theseparameters to enhance the capability of FDM. By extending
an equation that calculates the amount of material from thelayer height, we investigate the behavior and structure ofmaterial extruded from various height positions. On the basisof experimental results, the printed structure is classified into
six categories according to the structural feature. We
describe these structural features and demonstrate examples
with new inherent expressions for FDM.

H.5.m. Information interfaces and presentation (e.g., HCI):
Miscellaneous;

Author Keywords

3D printing; fabrication; fused deposition modeling;
expression; printing error.

INTRODUCTION

Advances in digital fabrication techniques such as threedimensional (3D) printers have enabled people to accurately
and cheaply create 3D objects. In particular, fused deposition
modeling (FDM) printers have become famous and are
currently available in the market owing to their several
advantages: ease of use, choice of materials, and low runningcost [30]. Open-source 3D printers, especially those based on
RepRap project [13], are specialized as highly customizable
and are used by many manufacturers and researchers as thebasis for commercial 3D printers or for experimental
purposes.
FDM printers form an object by stacking thin layers, andeach layer consists of a fine linear structure called “road” [5].
To print a high-quality object, we need to control and pay
attention to each road by setting appropriate parameters or
the 3D printers will fail to print stable objects and cause aprinting error. On the other hand, this feature can be regarded
as a freedom that allows users to access a layer in detail. On
the basis of this feature and the printing error, a printing
technique has been proposed (e.g., hair-like structure [16]and a scrubber [4]). The printing technique that exploits
printing error requires parameters or ingenuity that is notcommonly used in ordinary printing. These parameters are
determined depending on each technique, and therelationship of the printed objects and an optimum value areunclear. Because many parameters are present to control a
3D printer and many of them causes printing error,investigating and discussing all combinations of parameters
are impossible. However, 3D printers and its software aredeveloped to prevent printing error. We have to understandthis relationship or the usage of parameters or the techniquethat exploits printing error will be lost, and the capability andexpression of FDM printers will become limited.
In this paper, we focus on the height position of the extruder
and the amount of materials (Figure 1). We investigate thestructure of a printed road and the behavior of extruded
material by extending the range of parameters in thisequation over the printing error, and we explore many
combinations while changing their values during printing.
Printed roads are classified into six categories according totheir structural feature, which is denoted as distribution.
Using our results, we implement design systems that enable
users to design an object with a new expression. We print
example objects to demonstrate new expressions for FDM.
We extend the capability of FDM without using any new
hardware and across various printing techniques.
RELATED WORK
3D printing error

Printing error, where users cannot obtain the desired results,
often occurs in FDM printers. To prevent a printing error, atroubleshooting guide for stable printing is provided (e.g.,
Simplify3D provides a troubleshooting guide [24]). Printing
errors can be classified into two steps according to its types:
printing process or printing quality.
First, a printer completely fails to print objects in the firstplace and cannot deposit roads on the platform or on
previously printed roads. This error is caused by several
problems such as lack of materials or setting error in theheight position of the extruder, and users must prevent thiserror by referring to the guide. On the other hand, objects
printed with error have quite stimulated and excited users ina different manner from the original objective. A few
enthusiasts form a community to share pictures of the error
and investigate the causes of trouble in 3D printing [8].
In addition, a technique that exploits the error as a novel
printing technique has been proposed. Laput et al. presented
a printing technique that can fabricate hair-like structures by
exploiting the stringing (oozing) phenomena [16]. Kanada
presented a method of 3D printing generative arts [14]. This
technique consists of reflecting light control using thedensity of the filament. To change the density, the amount ofmaterials is controlled, and such uneven extrusion is called
over/under extrusion. Reiner et al. presented a method thatcan produce continuous tone imagery using an FDM 3Dprinter with two nozzles [21]. The contour of each layer isdefined using sine pattern modulation and is overlaid over
one another while shifting the modulation phase. This idea isconsidered as layer shifting. Blit It Inc. [4] provided a 3D
printed scrubber called the O'Rourke Scrubber in its system.
This scrubber is printed by extruding materials from a highposition while randomly moving the extruder. Solid

Vibration [12] is a printing technique that can generate a
Moiré pattern on the surface of objects. A platform isintensively and vertically vibrated, and the amount ofmaterials being extruded is controlled by the change in the
distance between the nozzle and the platform. Artist Lia
developed software to produce custom Gcode to explore 3D
printing as a sculpture technique [17]. By exploring the
behavior of a 3D printer and its filament, the artist presented
a new type of sculpture and methodologies.
The other error is related to printing quality such as surface
roughness, dimensional accuracy, and strength. Functionalparts require stricter requirements than the prototypes. For
example, each part must be accurately and easily assembled
after printing, and the final product must work as designed.
Because many works related to 3D printers aim to address
such printing quality problems, investigations of therelationship between the parameters and printed objects havebeen conducted, and optimization methods have beenpresented [28]. However, these works are performed on theassumption that printing error should be avoided. Thus, therange of parameters investigated in each study is restrictive.
Objects printed with a printing error often have a more
complex and high-quality structure than the ordinary layerby-layer process. For example, thinner objects, which are
impossible to print using the traditional method, are printed
in 3D printed hair [16], and the surface roughness generated
by the layered process (e.g., staircase effects [7]) is notnoticeable. However, no investigation was conducted thatconsiders a printing error as a new expression.
Parameters for 3D printing

The 3D printing process involves many variables, and 3D
printers are controlled by setting several parameters todetermine these variables. Agarwala et al. divided thesevariables into four categories (operation-, machine-,material-, and geometry-specific parameters) and reported
that these parameters are interdependent [1]. When
researchers investigate parameters, several parameters areused as variables to achieve a particular goal, and the otherparameters are used as constant. For example, layer thickness
significantly affects surface roughness [2, 3], and printing
speed and paths affect the quality of layers and bonding ofadjacent roads [11, 25]. These parameter investigations areimportant not only for commercial 3D printers but also for
open-source 3D printers [9, 15].
A part of the process is modeled as a numerical expression[27]. This approach is called process modeling andconsidered as the most significant research to understand thebasic science behind the 3D printing process. Bellini
conducted a comprehensive experiment on the FDM process
and presented several models [5]. In addition, the spreadingof extruded materials [6], deformation of objects printed
using acrylonitrile butadiene styrene (ABS) materials [31],and pressure on the extruder (buckling phenomenon) [29]were investigated. Because these models are constructed inconstrained environment, some problems are encountered inapplying them to actual environment.
3D printing technique in HCIMany human–computer interaction (HCI) researchers havepresented a printing technique that can print objects using aunique structure or texture to achieve a new workflow andinteraction.
Mueller et al. presented WirePrint [18] that prints objects
using a wireframe mesh and allows users to quickly verify
their design. Gannon et al. presented Tactum [10] that
captures user skin-centric gestures for 3D modeling directlyon the body. Torres et al. focused on the feel aesthetics ofprinted objects and proposed HapticPrint [26] that allows
users to create a haptic design in passive 3D printed objects.
To control the touch feeling, various textures are attached tothe surface of objects. Schüller et al. focused on the surfaceof objects and proposed a framework to design an
appearance that mimics surfaces (also known as bas relief)[22]. Cilllia [19] is a bottom-up printing pipeline to fully
utilize the capability of high-resolution 3D printers, and asophisticated hair-like structure is printed. This structure not
only expands the expression of 3D printer but also enables
users to design a passive actuator and a sensor. Highresolution 3D printers and a microstructure enable users todesign deformable objects [23]. This structure is also called
metamaterial and has attracted attention. These works
provide an interaction technique through 3D printers andprinted objects. To improve and understand the performanceof 3D printers, a comprehensive study is needed.
EXPRESSIVE FUSED DEPOSITION MODELING

Figure 2. Schematic of the extrusion state.

approach differs from the mainstream, it is variable andbelongs to the HCI field. We first describe the process of
traditional FDM printers and how we extend the parameters.
PROCESS OVERVIEWParameters in Gcode

We use FDM 3D printers based on RepRap projects (opensource printer) whose printers can accept any Gcode. Gcode
is a series of commands to control a 3D printer and isgenerated by converting a 3D model using slicer software.
The following are sample codes:
12
3

G1 Z0.2
G1 X0 Y0 F3600
G1 X10 Y10 E4 F1800
︙

We extend the capability of the FDM printer to enable users
to print new and expressive objects. Such printing techniques,
which include the works we mentioned as related works,
allow FDM printers to output complex objects that are
difficult to print even by high-resolution 3D printers (e.g.
stereolithography, selective laser sintering, and PolyJet).
Moreover, these high-resolution 3D printers require a highresolution 3D model. Ease of use is not only a popular topic
in the HCI field but also a strong point of an FDM printer.
We allow users to easily express textures because ourexperiment is based on traditional parameter relationships.
Because texture is generated during printing by the behaviorof the materials, our technique does not require extra 3Dmodeling to design textures. Our technique only requires
new parameters without any new hardware or 3D modelingskills, and it differentiates an FDM printer from other typesof printers. We can provide a reason for choosing an FDM
printer as a rapid prototyping tool.

G1 is a command that controls the extruder and can accept
several parameters. The first line means that the extruder
vertically moves in the Z-axis direction (such movement isinserted at the start of each layer). The second and third lines
mean that the extruder horizontally moves on the XY-planeat a specific speed, and in the third line, the printer extrudes
4 mm of materials while moving to the end point (10 mm, 10mm). We focus on the parameter related to the height
position of the extruder and the amount of materials, which
are represented as parameters Z [mm] and E [mm] in Gcode,and control the printing process by changing these values.

Extending the capability of a 3D printer is a workflow design,
which allows users to fabricate different and desirable
objects, and it is an important topic in the field of digital
fabrication in HCI. Within the context of HCI, a 3D printercan be considered as an output device such as a display. We
provide a new perspective to a display (e.g., tactile display),
whereas a high-resolution display is sought. Although our

Calculation of material amount

These parameters are especially important for high-quality
printing [2, 3], and the equation to calculate the amount ofmaterials using several parameters, including the height
position of the extruder, has already been defined. As thenumber of parameters increases, this relationship becomes
more complex. Therefore, we prioritize these parameters anduse other parameters as constant values.
We illustrate the condition of the material being extruded
from a nozzle (Figure 2). A linear material (filament) is fed
into the heated nozzle; subsequently, the melted material is
extruded. The extruded material takes a certain size (layerheight and road width) and forms a road on the platform. The
amount of material is calculated based on the relationship inwhich the volume of the extruded material (approximated ina cuboid shape) is equal to the volume of the material fed
into the nozzle. Thus, by letting a cross-sectional area of afilament as Sf [mm2] and its length as Lf [mm] and by lettinga cross-sectional area of a printed road as Sr [mm2] and its
length as Lr [mm], the following relationship holds:
𝑆𝑓 × 𝐿𝑓 = 𝑆𝑟 × 𝐿𝑟 .

(1)

Using Eq. (1), the length of material that should be fed (Lf)to print the desired length of the road (Lr) is calculated. Sf andthe width of the road are constant values determined by thediameter of the filament and the nozzle, respectively. The
layer (road) height is determined by a corresponding
parameter, which is given by the slicer software. Becauseparameter E in G1 is equal to Lf, Eq. (1) can be rearranged asfollows:
𝐸=

𝐿𝑎𝑦𝑒𝑟𝐻𝑒𝑖𝑔ℎ𝑡 × 𝑁𝑜𝑧𝑧𝑙𝑒𝑊𝑖𝑑𝑡ℎ × 𝐿𝑟
𝑆𝑓

(2)

In this paper, we refer to the layer height in Eq. (2) as theheight position of the extruder. We conduct an experimenton the height position of the extruder and the amount ofmaterials using the parameters derived from the extension of
Eq. (2).
EXTENSION OF EQ. (2)Equation (2) can be regarded as a linear function of the layerheight when the length of the printed road Lr is 1 mm (oneunit of distance). Figure 3 shows the relationship between theheight position of the extruder and the amount of materials.
The bold line indicates the relationship of Eq. 2. We note thatthe relationship is calculated using a 1.75-mm filament
diameter and 0.4-mm nozzle width.
We consider the linear function to be in a polar coordinate
form to explore the combination of various parameters basedon this relationship. To express the function, we define twoparameters, namely, θ [°] and r [mm]. First, Eq. 2,
represented by the bold line, is expressed using θ = 45° toconsider the parameter sets given by its relationship as abasis. To perform the calculation according to this basis, we
adjust θ by multiplying the amount of materials by acorrection value, which is the inverse of NozzleWidth×Lr/Sf
in Eq. 2 (approximately 6.013 in this case). We introduce
arbitrary values for θ and r to calculate the height position of
the extruder and the amount of materials as follows:(3)

𝐻 = 𝑟 𝑐𝑜𝑠 𝜃
𝐸 = 𝑟 𝑠𝑖𝑛 𝜃 ×𝑁𝑜𝑧𝑧𝑙𝑒𝑊𝑖𝑑𝑡ℎ
𝑆𝑓

× 𝐿𝑟

(4)

where H is the height position of the extruder [mm] and E isthe amount of extruded materials [mm]. For example, when
the road is printed with a 0.3-mm layer height, this height
position of the extruder and the amount of materials arecalculated using θ = 45° and r = 0.3×√2 = 0.4243 mm.

Figure 3. Relationship between the height position of the
extruder and amount of materials: 0.4-mm nozzle width and1.75-mm filament diameter. The traditional relationship isshown by a bold line. Our parameters (r, θ) and theirrelationship are shown by the red line. (a)–(d) Extrusion stateof each parameter combination shown at the right side.

Using this relationship, we explore the parameter space
while controlling the θ and r values. Figure 3 shows the lines
centered at a 45° line at 10° intervals and the concentric
circles indicating the r values.
The points from a to d in Figure 3 correspond to the figures
at the right side, which show the approximate shape of theroad and the state of extrusion of each parameter. Point a isan ordinary parameter, and 3D printers can print a stable roadaround this point. In Point b, the amount of materials is larger
than the height, and the roads may swell to enclose the nozzle
or beyond the given parameter height. Although Point c is set
as a parameter based on Eq. (2), it indicates printing of a long
lengthwise rectangular parallelepiped due to the constantnozzle diameter. According to the calibration guide1, best
results are obtained when the layer height is 80% or less than
the nozzle diameter and the road width is more than thenozzle diameter. However, results with excessive parametervalues are unclear. Point d is similar to Point c but also lacks
materials. In this case, the 3D printers may not print a roador fail to print at all. In the next section, we present theinvestigation of the behavior of the extruded materials andprinted roads by actually printing various parameters.
EXPERIMENT: PRINTING
PARAMETERS

ROAD

USING

VARIOUS

Design and procedure

We conducted an experiment to explore the parameter space
using Eqs. (3) and (4). We made the 3D printer print a roadusing various parameters. The length of the road along the xaxis was 200 mm, θ was from 1° to 90° with an increment of
1° (90 roads were printed), and r was from 0.1 to 10.0 mm,
which continuously increased by 0.1 mm per printing of a
2.0-mm partial road. We used two materials made of ABS
1

http://reprap.org/wiki/Triffid_Hunter's_Calibration_Guide

Figure 4. (Top) Distribution of the printed structure. (Bottom) Printed objects classified into six categories.

and polylactic acid (PLA): MakerBot True Black ABS andPolymaker PolyMax PLA Black, respectively. We basically
set the printing speed (feed rate) at 300 mm/min in bothmaterials, but we also set it at 600 mm/min in the ABS to
observe the difference in the printing speed.
To generate Gcode for the experiment, we implemented asystem that can generate a road using specific parameters.
Five roads generated with their respective θ values wereplaced side by side at an 8-mm interval, and we repeated theprocess to generate and print roads while changing the θvalues. To minimize involuntary errors and the effect ofoozing, we printed all roads according to the following
procedures.
Slow extrusion (6 mm at 10 mm/s)
Quick retraction (3 mm at 30 mm/s)
Three-second pause (cleaning off the nozzle)
Quick extrusion (3 mm at 30 mm/s)
Printing a 200-mm road while increasing the r value
Quick retraction (3 mm at 30 mm/s)
This process was also performed by the system andintroduced into all roads as pre- and post-processing.
Environment

We used the FDM 3D printer Ninjabot NJB-2002 with a 0.4mm-diameter nozzle and can extrude ABS and PLA. We
23

http://ninjabot.jp/product/fdm-200/
http://www.repetier.com/

rewrote the setting of the maximum extrusion speed, which
was written in a nonvolatile memory (EEPROM), because
the printer firmware originally restricted the maximum
extrusion speed to a small value. This value was used to set
the maximum level and did not affect the amount of materials.
We used Repetier-Host3 software that can edit and print
Gcode to rewrite the above settings and manage the printing.
The temperature of the printer head and the built platform
were 230 and 100 °C for ABS and 190 and 50 °C for the PLA,
respectively. To stabilize the printing, we applied a 50-mmwide washer tape on the built platform and a thin layer ofpaste. All roads were printed on this tape. The laboratory
temperature was regulated to approximately 25 °C, and thehumidity was approximately 60%.
Results

Figure 4 shows the classification of the results as a
distribution. The printed roads are classified into six
categories according to the structural feature (see Figure 4,
bottom). This classification is based on the position
measured using a digital caliper where the structure of theprinted road was varied. We visually recognize suchcharacteristic points. Figure 5 shows example roads printed
at θ = 60°, 45°, and 20°.
Structural feature of printed roads

We describe and analyze the structural feature and material
behavior in each category: stepping out of motor, stable road,zigzag road, coil-like road, frizzy hair-like road, and straight
hair-like road.

Figure 5. Variation in the road structure (ABS at 300 mm/min). Red lines indicate the change points of the structural feature.
Stepping out of motor

The 3D printer can stably extrude materials even if theparameters exceed their ordinary values. An exception to thisperformance is when the amount of materials is extremely
large. In this case, the stepping motor, which consists of the
extruder, frequently steps out, and the road becomes partiallythin or disconnected fragments due to unstable extrusion.
Printing speed also affects this phenomenon, and this area inthe distribution becomes larger as the speed increases (seeFigure 4; ABS at 600 mm/min). In PLA, although this area
is also large, the cause could be due to the nozzle temperature.
PLA was printed at 190 °C. By taking the average amount ofmaterials when stepping out occurs, the limit of the extrusion
speed can be estimated. The printer used in this experimentcan extrude ABS of up to 11 mm3/s.
Stable road

When stepping out does not occur, a road is printed at a stablestate. We classify the road with traditional parameters into
this category. The road becomes thicker as the amount ofmaterials increases. However, some thicker roads with ABS
have a rough surface. Figure 4 shows relatively thick roads.
This roughness may be caused by changes in temperatureand distortion of the road [5]. Materials that have just been
extruded have high temperature and are deformed as they are
gradually pushed up by other materials extruded later. A roadpart that cannot stand this deformation hardens and remains
distorted or show traces of exploding air bubbles. In PLA,
this distortion is not observed.
Zigzag roadAs the height increases, materials are extruded with anuneven structure. We call this as a zigzag road. The road also
becomes thicker and rougher as the amount of materials
increases. This road cannot be printed with traditionalparameters and obviously looks like a printing error.
However, we focus on the appearance and rough texture,
which is difficult to print even by high-resolution 3D printers.

directions (clockwise and counterclockwise). The directionof rotation is basically maintained during printing. However,entanglement in the middle of the road or reversal in the
direction is seldom observed.
Frizzy hair-like roadAs the amount of materials decreases, a coil-like road
becomes a hair-like road. Distinguishing this road from theother will be described later. We classified this case as frizzy
hair-like road. This road is created depending on the amountof materials because this category covers a rectangular areain every distribution (see Figure 4).
Straight hair-like road

Finally, a small amount of materials is extruded and pulledby the nozzle, and a straight hair-like road is printed. Thiscondition can be considered to be the same as a structure
printed in 3D printed hair [16]. When this road is printed, thewhole road floats in midair. Thus, the starting point of theroad must be fixed on the platform or the extruded materials
are wiped out by the extruder movement. Moreover, when theprinting speed is slow, the material tends to be burned out by theheat of the nozzle. The blank space, which is especially thelower part of ABS at 300 mm/min, indicates thisphenomenon, and we were not able to obtain a road with thisparameter (θ < 7°). Although this phenomenon was alreadydiscussed in [16], we reproduce it using our approach.
DESIGN SYSTEM

We implement three design systems that enable users toutilize our results. The systems are implemented with vvvv4,
which is a visual programming language and renders
graphical objects using DirectX, and we developed plugins
with C#. To implement the design system, additionalparameters are needed beforehand to stack up or align eachroad (Figure 6). In the current system, users have to
beforehand measure these properties according to each

Coil-like road

When θ is less than 60°, a coil-like road is printed. This
category widely spreads out in terms of distribution, and thisstructure differs depending on the combination of parameters,e.g., a spiral with θ = 20° has a sparser structure (see Figure5). This structure is printed by extruding materials from ahigh position similar to the zigzag road. This condition
occurs because the parameter may have met several
requirements to print this road. This road is not broken by thematerials being extruded and can maintain its structure until
it becomes stiff. In addition, the road is twisted in two

Figure 6. Additional parameters required to implement a
design system.
4

https://vvvv.org/

combination of parameters using a digital caliper and input
its measurement result to each design system. For example,
the height position of the extruder for the first layer isobtained from Eq. (3), and all subsequent layers are sorted
according to the road height, which is obtained bymeasurement. Thus, we focus on several combinations ofparameters in the following section.
#1 Slicer using zigzag road

First, we implement the slicer software that can be used in
the same manner as a traditional one. This slicer analyze
whether a support structure is needed or not and slice a 3Dmodel into the contour and the inner structure according to
the road height. If the support structure is needed, the slicer
generates it around the 3D model. Overhang angle and bridge
length are used to generate a support structure. Figure 7
shows the analysis process, a preview, and a printed result.
To print the Stanford Bunny with a zigzag road, we used aparameter set (θ = 65° and r = 7.0 mm), ABS, and additionalparameters measured before slicing.

Figure 8. Design system for emboss processing (see Figure 10).
#3 Wavy sheets

Wavy sheets also use two parameters to express the smoothsurface. To generate wavy paths, this system generates
numerous micro movements and assigns parameters to every
path. Figure 9 shows the wavy paths divided into micro
movements. The system requires two parameters (top andbottom) and complements the path between these according
to the height position of the extruder.

Figure 9. Design system for wavy sheets (see Figure 10).
EXAMPLES

Figure 7. Slicer software with a zigzag road.
#2 Emboss processing

Figure 8 shows the system for emboss processing. Thissystem uses two parameters to generate bumps on the surface
of printed objects; we intend to print a simple embossed wallin the current system. Users create and import a binary image,and the system then generates Gcode with different
parameters according to its tone. To print the embossed
object, we used two parameters (see Figure 8) and measured
the road width of each parameter. Because these parameters
have the same height, we can only change the width toexpress bumps.

We show 2D and 3D examples with various materials andparameters (Figure 10). A part of these examples is printed
using the above design systems. Note that we adjusted theprinting speed to prevent stepping out of motor and used therecommended temperature for each material.
Staircase effect represents an example constructed with thickroads. The staircase effect is one of the notable printing
errors, which means that a stair is created on the surface ofobjects due to the thick layers. On the other hand, thisroughness can provide a sense of stroking bellows, and we
can easily control its condition using our method.
Weaver-nest-like objects are constructed by the zigzag roadand have a quite rough surface. However, the whole structureis stable, and the printed object resembles a nest of a weaver

Figure 10. Example objects with new expressions. The materials and parameters used in each example are shown.

bird. In PLA and Polywood, we decrease the r value to obtaina zigzag road. When r has the same value as that in ABS (r= 8.0 mm), the printed road partially becomes a coil-like road.
Hamper-like objects are constructed by coil-like roads andhave a flowery structure. Stacking this road is comparatively
difficult. In particular, it becomes unstable around the startand end points of each layer, and the rotation direction of thecoil varies in several layers.
Emboss processing is an expression using thickness control.
We used the design system and two parameters to control theamount of materials with the same layer height. The overextruded material draws patterns and characters on the wallof the objects. Although this printing technique is not novel[14], we quantitatively show a method of setting theparameters as well as the relationship between the overextrusion and the parameters.
Wavy sheet is an object that is tactile and has a smooth
pattern, and we print it using the design system thatdynamically changes the parameters according to its shape.
Using a flexible material and attaching it to a watch strap, we
can change the sense similar to touching something that
resembles an alligator hide. To print a larger bump, we also
used an extremely large r value (r = 17.0 mm). Although thisvalue exceeded the range in our experiment, the 3D printerwas able to print the thicker part by reducing the printing
speed to avoid stepping out of the motor. This printing
technique can be applied to adaptive slicing [20], which
controls the road thickness to minimize volumetric error.
By combining these expressions, we created miniaturemodels and a diorama. In this example, we used our method
to express all objects, which were a fluffy lawn, hair of a bear,a water surface, and a wall and roof of a house. An expressive
printing technique enables users to print the delicate features.
DISCUSSION

Using the distribution, users can control the structure, and thedesign systems contribute to the utilization of our results. We
received favorable responses from people who physicallyhandled our examples; they described that the printed objects
have a handmade feeling. We believe this comment implies
the important aspect of personal fabrication.
However, an obscure area exists around the boundary of
every category because each structure can be affected by thepreceding and immediately following structures. Therefore,
when the parameter is extremely varied or curved andpolygonal roads are printed, the printed structure may bedifferent from that in our result. In the experiment, we used
several parameters as constant, and the effect of theenvironment is still significant. We applied the same
parameters to other printers: Genkei Atom5 and Bonsai Lab.
BS01+6 (Figure 11). When we printed examples using
different printers and materials, we had to adjust θ, r, and the56

http:/genkei.jp/
http://www.bonsailab.asia/

Figure 11. Application to other 3D printers.

printing speed once or twice. On the other hand, even if such
constant is varied, the distribution of the parameters can beeffectively utilized. For example, we reduced the printing
speed to prevent stepping out in accordance with the
distribution. Moreover, we could create the distribution ofother materials in the same manner. If users want to control
the printed structure in detail in their own environment, theyneed to clarify the features of the environment by conducting
a similar experiment.
In our future work, we will investigate and provide therequirements to correctly print each structure. Although weclassified the structures into six categories, each structure has
different thickness and texture depending on the combinationof parameters. For example, the stable road becomes thicker
as the amount of materials increases. Some roads require a
support structure similar to that of traditional printing to printin midair. On the other hand, several roads constructed witha complex structure (e.g., coil-like road) are difficult to print
even with the support structure. We will also sensitively
evaluate the objects printed with expressive FDM. Wang etal. conducted a user study to assess their objects in terms ofboth haptic and visual quality [32].
We provided the understanding related to the parameters,
and it can open up a new interaction between human and 3D
printers. We intentionally used descriptive and metaphoricalwords because we believe these are warranted by our result.
Moreover, these can be used for designing textures (e.g.,using natural language as input). Our work contributes to thedevelopment of the digital fabrication field in HCI.
CONCLUSION

In this work, we focused on the height position of the
extruder and the amount of materials to extend theexpression of FDM. We presented equations to explore theparameter space and conducted an experiment to investigate
the combination of the parameters. The printed roads wereclassified into six categories according to the structuralfeature and were shown as a distribution of parameters. We
implemented the design systems and printed example objects
with our result to demonstrate new expressions.
Although many researchers and manufacturers pursue highquality printing using high-resolution and expensive printers,true high-quality objects are results that should satisfy theneeds of users. To achieve such objects, users need toprovide various expressions. We exploited even the printing
errors to extend the capability of FDM 3D printers andallowed users to express the texture, surface condition, andappearance using a 3D printer.
ACKNOWLEDGEMENTS

This work was supported by COI, JST.

REFERENCES

1.

2.

3.

Mukesh K. Agarwala, Vikram R. Jamalabad, Noshir A.
Langrana, Ahmad Safari, Philip J. Whalen, andStephen C. Danforth. 1996. Structural quality of parts
processed by fused deposition. Rapid Prototyping
Journal, Vol. 2, No. 4, 4–19.
http://dx.doi.org/10.1108/13552549610732034
Daekeon Ahn, Jin-Hwe Kweon, Soonman Kwon,
Jungil Song, and Seokhee Lee. 2009. Representation of
surface roughness in fused deposition modeling.
Journal of Materials Processing Technology, Vol. 209,
No. 15–16, 5593–5600.
http://dx.doi.org/10.1016/j.jmatprotec.2009.05.016
R. Anitha, S. Arunachalam, and P. Radhakrishnan.
2001. Critical parameters influencing the quality of
prototypes in fused deposition modelling. Journal of
Materials Processing Technology, Vol. 118, No. 1–3,
385–388.
http://dx.doi.org/10.1016/S0924-0136(01)00980-3

4.

Blit it.
https://blitit.com/(Retrieved January 6, 2017)5.

Anna Bellini. 2002. Fused deposition of ceramics: acomprehensive experimental, analytical andcomputational study of material behavior, fabrication
process and equipment design. Ph.D. dissertation,
Drexel University, Philadelphia, PA.
http://hdl.handle.net/1860/22

6.

Robert S. Crockett and Paul D. Calvert. 1996. The
liquid-to-solid transition in stereodeposition
techniques. In Proceedings of Solid Freeform
Fabrication Symposium, 257–264.

7.

André Dolenc and Ismo Mäkelä. 1994. Slicing
procedures for layered manufacturing techniques.
Computer-Aided Design, Vol. 26, No. 2, 119–126.
http://dx.doi.org/10.1016/0010-4485(94)90032-9

8.

Epic 3D printing fail.
http://epic3dprintingfail.tumblr.com/(Retrieved January 6, 2017)

9.

L.M. Galantucci, I. Bodi, J. Kacani, and F. Lavecchia.
2015. Analysis of dimensional performance for a 3D
open-source printer based on fused deposition
modeling technique, Procedia CIRP, Vol. 28, 82–87.
http://dx.doi.org/10.1016/j.procir.2015.04.014

10. Madeline Gannon, Tovi Grossman, and George
Fitzmaurice. 2015. Tactum: a skin-centric approach todigital design and fabrication. In Proceedings of the
SIGCHI Conference on Human Factors in Computing
Systems (CHI '15), 1779–1788.
http://dx.doi.org/10.1145/2702123.2702581
11. Wenbiao Han, Mohsen A. Jafari, Stephen C. Danforth,and Ahmad Safari. 2002. Tool path-based deposition
planning in fused deposition processes. Journal of

Manufacturing Science and Engineering, Vol. 124, No.
2, 462–472.
http://dx.doi.org/10.1115/1.1455026
12. Olivier van Herpt. Solid Vibrations.
http://oliviervanherpt.com/solid-vibrations/(Retrieved January 6, 2017)
13. Rhys Jones, Patrick Haufe, Edward Sells, Pejman
Iravani, Vik Olliver, Chris Palmer, and Adrian Bowyer.
2011. RepRap - the replicating rapid prototype.
Robotica, Vol. 29, No. 1, 177–191.
http://dx.doi.org/10.1017/S026357471000069X
14. Yasushi Kanada. 2016. 3D printing of generative art
using the assembly and deformation of directionspecified parts. Rapid Prototyping Journal, Vol. 22,
No. 4, 636–644.
http://dx.doi.org/10.1108/RPJ-01-2015-0009
15. Antonio Lanzotti, Marzio Grasso, Gabriele Staiano,and Massimo Martorelli. 2015. The impact of processparameters on mechanical properties of parts fabricatedin PLA with an open-source 3-D printer. Rapid
Prototyping Journal, Vol. 21, No. 5, 604–617.
http://dx.doi.org/10.1108/RPJ-09-2014-0135
16. Gierad Laput, Xiang 'Anthony' Chen, and Chris
Harrison. 2015. 3D printed hair: fused deposition
modeling of soft strands, fibers and bristles. In
Proceedings of the ACM Symposium on User Interface
Software and Technology (UIST '15), 593–597.
http://dx.doi.org/10.1145/2807442.2807484
17. LIA. Filament sculptures.
http://www.liaworks.com/(Retrieved January 6, 2017)18. Stefanie Mueller, Sangha Im, Serafima Gurevich,Alexander Teibrich, Lisa Pfisterer, François
Guimbretière, and Patrick Baudisch. 2014. WirePrint:
3D printed previews for fast prototyping. In
Proceedings of the ACM Symposium on User Interface
Software and Technology (UIST '14), 273–280.
http://dx.doi.org/10.1145/2642918.2647359
19. Jifei Ou, Gershon Dublon, Chin-Yi Cheng, Felix
Heibeck, Karl Willis, and Hiroshi Ishii. 2016. Cilllia:
3D printed micro-pillar structures for surface texture,
actuation and sensing. In Proceedings of the SIGCHI
Conference on Human Factors in Computing Systems(CHI '16), 5753–5764.
http://dx.doi.org/10.1145/2858036.2858257
20. Pulak Mohan Pandey, N. Venkata Reddy, and Sanjay
G. Dhande. 2003. Slicing procedures in layered
manufacturing: a review. Rapid Prototyping Journal,
Vol. 9, No. 5, 274–288.
http://dx.doi.org/10.1108/13552540310502185
21. Tim Reiner, Nathan Carr, Radomír Měch, Ondřej
Št'ava, Carsten Dachsbacher, and Gavin Miller. 2014.
Dual-color mixing for fused deposition modelingprinters. Computer Graphics Forum. Vol. 33, No. 2,
479–486.
http://dx.doi.org/10.1111/cgf.12319
22. Christian Schüller, Daniele Panozzo, and Olga
Sorkine-Hornung. 2014. Appearance-mimicking
surfaces. ACM Transactions on Graphics, Vol. 33, No.
6, Article 216.
http://dx.doi.org/10.1145/2661229.2661267
23. Christian Schumacher, Bernd Bickel, Jan Rys, Steve
Marschner, Chiara Daraio, and Markus Gross. 2015.
Microstructures to control elasticity in 3D printing.
ACM Transactions on Graphics, Vol. 34, No. 4, Article
136.
http://dx.doi.org/10.1145/2766926
24. Simplify3D. Print Quality Troubleshooting Guide.
https://www.simplify3d.com/support/print-qualitytroubleshooting/(Retrieved January 6, 2017)
25. Q. Sun, G. M. Rizvi, C. T. Bellehumeur, and P. Gu.
2008. Effect of processing conditions on the bonding
quality of FDM polymer filaments. Rapid Prototyping
Journal, Vol. 14, No. 2, 72–80.
http://dx.doi.org/10.1108/13552540810862028
26. Cesar Torres, Tim Campbell, Neil Kumar, and Eric
Paulos. 2015. HapticPrint: Designing Feel Aesthetics
for Digital Fabrication. In Proceedings of the ACM
Symposium on User Interface Software andTechnology (UIST '15), 583–591.
http://dx.doi.org/10.1145/2807442.2807492
27. Brian N. Turner, Robert Strong, and Scott A. Gold.
2014. A review of melt extrusion additive

manufacturing processes: I. Process design andmodeling. Rapid Prototyping Journal, Vol. 20, No. 3,
192–204.
http://dx.doi.org/10.1108/RPJ-01-2013-0012
28. Brian N. Turner and Scott A. Gold. 2015. A review ofmelt extrusion additive manufacturing processes: II.
Materials, dimensional accuracy, and surface
roughness. Rapid Prototyping Journal, Vol. 21, No. 3,
250–261.
http://dx.doi.org/10.1108/RPJ-02-2013-0017
29. N. Venkataraman, S. Rangarajan, M. J. Matthewson, B.
Harper, A. Safari, S. C. Danforth, G. Wu, N. Langrana,
S. Guceri, and A. Yardimci. 2000. Feedstock material
property - process relationships in fused deposition ofceramics (FDC). Rapid Prototyping Journal, Vol. 6,
No. 4, 244–253.
http://dx.doi.org/10.1108/13552540010373344
30. W. Walters. 1992. Rapid prototyping using FDM: afast, precise, safe technology. In Proceedings of Solid
Freeform Fabrication Symposium, 301–308.
31. Tian-Ming Wang, Jun-Tong Xi, and Ye Jin. 2007. A
model research for prototype warp deformation in the
FDM process. The International Journal of Advanced
Manufacturing Technology, Vol. 33, No. 11, 1087–
1096.
http://dx.doi.org/10.1007/s00170-006-0556-9
32. Weiming Wang, Cédric Zanni, and Leif Kobbelt. 2016.
Improved Surface Quality in 3D Printing by
Optimizing the Printing Direction. Computer Graphics
Forum, Vol. 35, No. 2, 59–70.
http://dx.doi.org/10.1111/cgf.12811