Free-form thick layer object manufacturing technology for

large-sized physical models

Johan J. Broek*, Imre Horvath, Bram de Smit, Alex F. Lennings, Zoltan Rusak,Joris S.M. Vergeest

Faculty of Design Engineering and Production, Sub-Faculty of Industrial Design Engineering, Delft University of Technology, Jaffalaan 9,

NL-2628 BX Delft, Netherlands

Abstract

Large-sized free-form objects of different materials are widely used in various industrial applications. Currently, layered

rapid prototyping technologies are not suitable for the fabrication of this kind of objects, due to the necessity of a large number

of layers and the limitations in size. This paper reports a novel approach of layered manufacturing that is more appropriate for

the fabrication of these large objects. A method of thick-layered object manufacturing is presented, which is based on a higher

order approximation of the shape and application of a flexible curved cutting tool.

The method allows the production of physical prototypes, which need little or no finishing. In order to meet the designer’s

intend, as closely as possible, some feasible system characteristics are introduced. The process is ordered in a sequential way

and provides a highly automated process. A hierarchical decomposition of the CAD geometry takes place into components,

segments, layers and sectors, based on morphological analysis. This method enables the manufacturing and the re-assembly of

the parts to produce the physical prototypes without affecting the requested functionality. Due to the possibility of obtaining

multiple solutions in the physical model, much attention must be paid to the efficiency of the process. D 2002 Elsevier Science

B.V. All rights reserved.

Keywords: Rapid prototyping; Free-form thick-layered object manufacturing (FF-TLOM); Higher order approximation; Flexibly curved cutting

tool; Geometric decomposition; Conceptual design

1. Introduction

In the process of industrial design engineering,

testing and reasoning with the help of prototypes or

physical models is commonly accepted among design-

ers and stylists. The material of these objects might

vary considerably and can include plastic foam, paper,

cardboard, plywood, clay, plaster, compound mate-

rials, etc. The applications of these models are often

many-sided.

In the concept phase of the design process, the

physical model (PM) is supportive in the case of

reasoning, communicating with customers, testing

for the functionality and evaluation of the require-

ments of the product. In such cases, the PM is created

and used for only a short period of time. In other cases

the physical model is used for the initiation of the

fabrication of a range of products. Both examples

require different appearances and manufacturing tech-

niques for the PM due to the divergent requirements.

The physical models are mostly generated from com-

0926-5805/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved.

PII: S0926-5805 (00 )00108 -4

* Corresponding author.

Internet address: http://www.io.tudelft.nl/research/ica/.

E-mail address: j.j.broek@io.tudelft.nl (J.J. Broek).

www.elsevier.com/locate/autcon

Automation in Construction 11 (2002) 335–347

puter-based data and produced by a specific Rapid

Prototyping (RP) process.

A distinction can be made between two fundamen-

tal approaches to RP, namely that of incremental and

decremental processes. The decremental process starts

with a solid block of material (stock), which will be

machined or shaped sequentially according to the

geometric CAD data. Characteristic examples of dec-

remental methods are applications like the Sculpturing

Robot [35] and high speed milling [12]. The accessi-

bility check for the machining (avoiding tool interfer-

ence) can be highly calculation intensive and not

always successful.

The second approach is that based upon an incre-

mental fabrication technology. This manufacturing

process is highly or fully automated. A dominant part

of the available RP-processes is based on Layered

Manufacturing Technologies (LMT). The shape is

built up from layers, which are deposited and ma-

nufactured separately. These are stacked onto each

other to create the required shape of a physical mo-

del. Different incremental technologies exist on the

RP-market, e.g. 3D printing, stereolithography, lay-

ered object manufacturing, selective laser sintering

and fused filament deposition. In general, the avail-

able conventional (incremental) LMT are the best

for manufacturing of small and mid-size objects, be-

cause the applicable layer thicknesses in these pro-

cesses are relatively small compared to the dimen-

sions of the model [21,23,24]. More information

about typical technological parameters of these

layer-oriented fabrication methods is presented in

Refs. [4,25,29]. Rapid prototyping in fact can be

considered as an optimization process for productivity

and accuracy [26,27,38,39,41].

Large-sized, free-form PM’s (up to 5 m and

beyond) are made of soft and light materials. Such

models are used in the household appliances manu-

facturing, in the automotive industry, advertisements,

and entertainment industry. Additionally they are used

for scenery pieces in movie film making, for stage sets

in theatres, sculptures, ornaments and for extra-sized

human or animal mannequins. In scientific research

and industry, these models support the visualization of

mathematical models, the testing of human–product

interaction, analyzing aerodynamic and hydrodynamic

behavior, as well as aesthetic and ergonomic impres-

sions.

PM’s of that large size need a large amount of

material for realization. Both decremental and incre-

mental processes are not well equipped for this large-

sized application. The decremental process needs

machining time on very expensive equipment propor-

tional to the volume of the stock. The common LMT

need such a large amount of layers that the fabrication

time exceeds the efficient realization of that kind of

PM [10,30] (also due to the extended area of depos-

ited thin layers). Normally, the dimensions of the ma-

nufacturing equipment put a limitation on the object

dimensions. These conditions need to be addressed by

a different type of technique, like the application of a

thick layer approach.

2. Thick-layered object manufacturing

In recent years, thick layer object manufacturing

(TLOM) has been demonstrated [6,13,36]. The meth-

ods of geometry approximation and machining tech-

nology are based on adaptive slicing and first order

approximation (ruled surface or slanted front faces) of

the nominal shape geometry. Systems like Trusurf,

Charly Robot and Shapemaker offer specific technol-

ogies to fabricate large-sized objects in such a manner.

A survey in the field of TLOM is presented in Ref.

[2]. The fabrication of large-sized free-form PM’s is a

real challenge especially for layered manufacturing.

To come up with practical solutions, the research team

of the authors is deeply involved in the methodolog-

ical and technological issues in order to extend con-

ventional LOM to the large size domain. They propose

the method of free-form thick-layered object manufac-

turing (FF-TLOM) [3,16].

The principle of this new technology is to combine

advantages of both decremental and incremental

methods. This will open up an extension of RP

applications.

2.1. Free-form thick-layered object manufacturing

The principle of the proposed FF-TLOM technol-

ogy is based on the shaping of the front faces of each

layer, which is performed in a free-form way. At a

later stage, the machined layers are assembled or

stacked to obtain the PM. A brief description about

the implications of higher order approximations

J.J. Broek et al. / Automation in Construction 11 (2002) 335–347336

(HOA) is mentioned in Ref. [28] and the idea of a

curved cutting tool is first presented in Ref. [13]. It is

easy to imagine that HOA creates possibilities for the

application of thicker layers under the same or better

accuracy and smoother outside surfaces of a prototype

(a higher layer-thickness/accuracy ratio). HOAapplied,

as circular or free-form approximation of the nominal

shape, however, requires sophisticated shaping techno-

logies.

The tool applications of a fixed curved shape or a

flexible curved shape are considered for the manufac-

ture of the front faces of the layers. The shaping itself

might take place by smearing of hardening plaster or

by cutting light and soft materials like foam. Fixed

curved spherical or conicoid cutting tools [34] can be

applied using the best fitting part of the cutting tool in

order to approximate locally the best nominal shape.

The result will be a layer with a cusped front face,

which might need finishing actions.

The PM fabrication with the FF-TLOM technology

is achieved in such a way that possibly little or no

finishing effort is needed for a proper functional

usage. The proposed technology uses thick high-

density polystyrene foam layers, whose front faces

are shaped according to the principle of free-form

cutting. This lightweight material (ranging from 28 to

40 kg/m3) is cheap, and readily available on the

market in standardized sizes and layer thicknesses.

In the proposed method, the foam layers are shaped

with a flexible hot knife, which is heated by electrical

current. The cutting blade is flexible and its curvature

is adjusted according to the local shape requirements

set by the nominal shape of the CAD-model. The

cutting of the layers is a newly developed technology

and will be explained in more detail in the next

paragraph. Current applicable shaping techniques are

discussed in the following.

3. Flexible blade cutting

In current thick-layered object manufacturing

(TLOM), well-known cutting technologies are ap-

plied, such as hot-wire cutting, water jet cutting, side

face milling, hot knife cutting, filing, milling, and

sanding. Those techniques are related to the chosen

shape approximation based on slanted front layer faces

or ruled surfaces. The thickness of each layer depends,

in case of adaptive slicing, on the maximum allowed

approximation error and the standard slab thicknesses

available in store. Therefore, the applied layer thick-

ness can vary dependent upon each change in local

curvature of the nominal shape.

The approach of TLOM is to find an orientation,

which will need the minimal number of slices and

then orientating the model to keep the slicing of the

complete object in the same direction. It is obvious

that this method can be improved by considering a

different treatment for thin layers due to very local

curvature changes and degenerated layers like the first

and last layer of an object. More about these issues is

presented in the section about decomposition.

A valuable extension of the TLOM method is the

application of a cutting technology, which is based on

a cutting device able to adapt to the local curvature

requirements and hereby offers the possibilities of

increased applied layer thickness.

Fig. 1. FF-TLOM cutting head.

J.J. Broek et al. / Automation in Construction 11 (2002) 335–347 337

The fabricating technology under development in

our group is based on the cutting of polystyrene foam

with a flexible cutter. Polystyrene is a cheap and com-

monly available material, which is also commonly

applied in creating physical models. The foam is melt-

able and can be shaped easily with hot wire cutting,

filing, sawing, sanding, etc.

The cutting is performed with a cutter, which

consist of a flexible cutting blade supported at both

ends. This is shown in Fig. 1 where the supports are

rotatable and introduce an inclination at both blade

ends in respect to the U-shaped support structure. In

Fig. 2, a typical layout of the layer cutting is pre-

sented. The shape and curvature of the blade are

defined by the inclination of the blade at both support-

ing ends, the length of the blade, the endpoints and the

assumption that the blade will take up a shape related

to the minimal strain energy inside the blade.

The cutting blade is electrically heated. Due to heat

radiation towards the foam, the foam melts locally and

creates a gap in which the cutting blade can proceed.

This is a continuous process, which require continu-

ous energy input into the cutting blade to prevent the

blade cooling down. The amount of power required

depends, amongst other things, on the cutting speed

and the electrical properties of the cutting blade.

When the applied cutter speed is too high the melting

does not have proper time to have effect, the gap is not

sufficiently shaped and the foam material opposes the

blade. This will create higher cutting forces, which

will deform the blade shape. On the other hand, when

the speed is too low the foam melts away in a wide

gap, which will have also a negative effect on the

cutting accuracy. Cutting speed, surface quality and

provided heat are important items and need thorough

investigations to achieve a feasible cutting technology.

Fig. 2. FF-TLOM process simulation.

J.J. Broek et al. / Automation in Construction 11 (2002) 335–347338

Preliminary results indicate that the technology is able

to give feasible results in a reasonable application

domain Ref. [7]. The cross-section of the blade is

considered constant having a high aspect ratio (thick-

ness/width ratio). The cutting blade is applied as a

circumferential cutting tool. So the cutting direction of

the blade is tangential to the slicing contour of the

layer front face and the blade-bending plane is kept

perpendicular to the front surface of the layer. The

blade cross-section introduces some limitations in the

cutting of high curvature regions in the cutting direc-

tion and regions, which need a large change in pitch of

the cutter. Also due to the tangential cutting direction,

the movements of the cutting head and the slab will

introduce acceleration movements, which will expose

a high dynamic load on the cutting manipulator. A

kinematic concept of the blade and its support is

presented in Ref. [33]. The related cutting and han-

dling manipulation is analyzed and presented in Refs.

[8,11].

As previously explained, the blade is heated elec-

trically and must be bent during heating in a flexible

manner. The cutting blade has to be flexible enough to

take up the requested tool profile, referred to as tool

shape, in order to give the required shape curve

(nominal shape). It must also be rigid enough to

sustain that tool shape during cutting. These condi-

tions of flexibility at high temperature bring their own

specific material requirements. At the same time, the

blade material must have electrical resistance in order

to be heated up and also have good dynamic heating

characteristics. The blade material is thus very impor-

tant and it seems to be most likely that the requested

material properties cannot be achieved in one specific

type of material [40] and the application of compound

material for the blade will thus be considered.

In order to control the blade shape of the actual

cutter and to define the blade shape for the approx-

imation of the local nominal shape, a mathematical

model of the blade mechanics is necessary. From a

mechanical standpoint, the blade is in fact a very

slender bar with a small cross-section to length ratio

[9] and thus behaves like a ‘‘physical spline’’, which

takes up its shape by following the law of ‘‘minimum

strain energy’’. Since the deformation is comparable

to the nominal size of the blade, the linear theory is

not applicable, therefore, a higher order theory has

been developed to describe the blade behavior. The

shape of the blade is derived as a function of mechan-

ical property and degrees of freedom mentioned

Fig. 3. Minimum strain curve calculation.

J.J. Broek et al. / Automation in Construction 11 (2002) 335–347 339

before. The higher order mechanical model consists of

a non-linear differential equation, for which no exact

analytical solutions are provided [14]. Geometric

based modelling of the blade curve can help to solve

the problem during approximation calculations of the

blade shape and the nominal object shape. The

assumption is that, irrespective of the blade cross-

section, the curved blade can be substituted by its two-

dimensional profile curve of ‘‘least strain energy’’ and

prescribed length [16,17]. Kallay [22] presents an

algorithm, which allows the calculation of a least

strain energy curve and the applied method of calcu-

lation is presented in Ref. [18]. The calculation of the

smoothest curve of prescribed length, endpoints and

tangent vectors starts with a poly-line, which is

represented as a saw-tooth curve in Fig. 3. The other

curve in Fig. 3 represents the calculated curve of least

strain energy. This computed curve is used for the

shape approximation and for visualization of the

cutting process. However, the calculation of each

curve has a tendency to become very time-consuming.

A complete set of parametric curves is computed

offline in order to solve the problem of representing

a bent blade, indexed and put into a database, since

the tool profile has to be adjusted continuously at

sufficiently small increments. Practical measurements

are needed to calibrate the bending characteristics of

the cutting blade in order to develop and to apply an

accurate and reliable cutting tool. The challenge is the

development of this cutting tool, together with the

application methodology in a FF-TLOM system.

4. Decomposition of CAD geometry

First step in the RP process is the transfer and input

of geometry into the RP system. The computer

generated geometry, a CAD model or here referred

to as nominal shape is transferred into the analyzing

and decomposition section of the RP-system in a

standard geometric transfer format. Different standard

formats are available. An overview of these is pre-

sented in Refs. [5a,b]. A commonly applied transfer

standard is the STL-format, which contains only

information about triangular shaped elements defined

by corner points and orientation. Nowadays, all solid

modellers deliver correct STL transfer data. Funda-

mentally, surface modellers have difficulty in produc-

ing correct STL files. Special software is available on

the market that is able to repair the inconsistencies of

the STL data.

Special shape details, not covered by the chosen RP

method, will require special treatment during the pre-

paration of the geometric data. The information trans-

fer of object and application related data of the phy-

sical model towards the RP system will facilitate the

analysis and decomposition of the geometry. NURBS

[31] representations are elegant in terms of the amount

of data to be transferred and the exact representation

of the nominal shape. Practically, a STEP transfer

format, combined with the geometric representation

of NURBS, is used for the input of the FF-TLOM

preparation process [32].

According to the needs and intentions, PM’s sup-

port his endeavors of the designer during an efficient

design process, in order to obtain as early as possible

the correct and supportive information. This approach

reflects the need of having PM’s, virtual models, etc.,

which are suited for only one or a few more specific

aspects of reasoning or functionality testing. In turn

these aspects will have an impact on the extent and

structure of the PM. The intention of the designer

during conceptual design is to test one single or a

restricted group of functional properties, rather than

the preparing and manufacturing of a complete and

expensive PM. It often takes too much time and effort

to realize such a PM that may be used for a very short

period. As a result of the testing, the design might be

changed and the PM produced may be scrapped. The

full PM might thus not provide any more information

than a simplified version. At this moment, none of the

geometry transfer formats, like STEP, IGES, etc.,

support such kind of functionality transfer.

Next step in the RP process is the conversion of the

geometry data into an internal representation, that will

facilitate the storage and manipulation of the data

during the total process of calculations and geometric

reasoning.

In common LMT, the word ‘‘decomposition’’ is

used for the slicing of the nominal model in an ad-

vantageous orientation. The slicing criteria are related

to manufacturability, minimum number of deposited

layers, accuracy and finishing effort. When the ap-

plied layers become thicker, the appearance and

accuracy of the PM is affected and the finally as-

sembled product will need much finishing effort.

J.J. Broek et al. / Automation in Construction 11 (2002) 335–347340

When creating a part from thin layers with conven-

tional LOM technologies, the morphological com-

plexity and geometric complexity of the part has

significantly less impact on the fabrication process,

but for the production of a PM much manufacturing

time is needed. In the case of large-sized free-form

physical models, the application of thick layers

reduces the manufacturing time. If the above-men-

tioned characteristics coexist at the same time, phys-

ical model fabrication results in a complex manu-

facturability problem (even when the FF-TLOM

technology is applied). A way of reducing the manu-

facturing and handling problems is thought the intro-

duction of a form of artifact decomposition.

The RP preprocessing and preparation phase is

based on FF-TLOM technology, on geometric analy-

sis of the CAD model and depends on functionality of

the prototype and type of physical prototype realiza-

tion. This phase might be realized successfully apply-

ing a decomposition of the geometry into elements

that are efficiently manufactured, assembled, stacked

and finished.

Geometric models are generated and adapted dur-

ing a product development process and commonly

complete assemblies are under development and are to

be prototyped. The expression assembly is related to a

system of parts, units or components that is in a

specific relational, functional and morphological con-

nection to each other. For the purpose of RP, an as-

sembly is decomposed for reasons of structure, shape,

size, materialization, fabrication, handling and/or

functioning. In Fig. 4, the decomposition related to

the FF-TLOM technology is subdivided into four

hierarchical levels and is represented at the right side

of the figure. In the same figure at the left side the

hierarchical manufacturing or recombining levels of

the physical prototype are represented. It will be ob-

vious that decomposition must support an efficient

and competitive RP-fabrication process and has to

deliver a functional prototype.

A functional decomposition of assemblies is

defined by the following actions: the assembly is

subdivided in single parts, each part has a known

relationship to the complete assembly in terms of

kinematic mobility to the other parts. The complete

collection of assembly parts is analyzed for required

functionality and inserts. An insert is defined as a part,

which is not manufactured by the FF-TLOM technol-

ogy and will become available from other manufactur-

ing processes, RP-technologies or standard parts.

Some examples of inserts are parts that are embedded

inside the foam structure, e.g. a metal part for weight

simulation or a skeleton for mechanical strength.

Those inserts are considered as alien parts and are left

out of the FF-TLOM manufacturing stream, but are

included into the logistic support of the system,

because they are needed for a successful assembly

and might possibly influence the assembly sequence of

the PM.

As a result of functional testing of one single or a

few functional issues and allowing only those char-

acteristics for the restricted functionality test, might,

for efficiency reasons, result in an analysis of the

minimal functionality of the PM for that specific

situation. Until that moment, only the designer is

aware of the extent of the tests and only he can decide

on the details of the tests and so, on the materializa-

tion of the required PM, e.g. parts which are inter-

connected rigidly are considered to be one rigid

subassembly and will be manufactured likewise.

Another decision can be made about the needed

kinematic freedom of the parts for testing purpose

only. The decision about which combination of

assembly parts have kinematic freedom or are sup-

posed rigidly interconnected, cannot be automated

because the functional decomposition depends on

Fig. 4. Decomposition and assembly process.

J.J. Broek et al. / Automation in Construction 11 (2002) 335–347 341

the designer’s personal intent and his knowledge

about the functioning of the prototype during testing.

A positive influence on the efficiency of a PM pro-

duction process is obtained when the number of ri-

gid connected parts or subassemblies are minimized.

Parts, set of parts, units, subassemblies, which are

manufactured in one single piece without loosing

any requested functionality are referred to as compo-

nents. When the components are decided on, gener-

ation of an enclosing boundary of the set of parts

(component) is performed in an automatically way.

The components are elaborated and decomposed at the

next hierarchical level.

A morphological decomposition of the components

into technological advantageous segments is based on

partly morphological and partly technological issues.

By means of morphological considerations, compo-

nents can be subdivided into smaller parts. The process

is called segmentation, and the aim to reduce the

dimensional and morphological complexities. It will

provide better conditions for the manufacturing of the

physical model. The morphological issues are related

to the detection of shape characteristics that need

special care in the FF-TLOM technology. Attention

must be paid to discontinuities in curvature and tan-

gency, the so-called singularities [15], regions of high

and moderate change of curvature and flat regions. The

technological issues are related to the choice of an

optimal segment orientation for slicing and stacking,

the applied layer manufacturing technology and the

manufacturing efficiency in time and costs. The com-

plex task is to decompose each of the component into

segments, taking into account the special shape char-

acteristics in such a manner that it supports optimally

the efficient PM production and in the same time

satisfying the requirements.

For the automation of the process, an algorithm

might perform the decomposition of components into

segments. In Ref. [19], a segmentation method based

on the FF-TLOM technology is described. The

assumptions are:

� the nominal shape are morphological well

behaved objects,� the need for an extreme long blade and extreme

arm positions are avoided and the range of

movement is kept in between + 45� and � 45�(total range 90�) measured from the basic tool

access plane. The tool access restriction will be

called pitch constraint,� Support structures for assembly are considered

to be external devices,� Depending on the requirements, different

efficient segmentation solutions are possible.

The object segmentation starts with the selection of

a segmenting orientation, which depends on efficiency

factors like fabrication time and cost, complexity of

tasks, minimal cutting length for manufacturing of a

complete PM, etc. When an orientation is selected, the

calculation and morphological interrogation can start.

A normal distribution across the component surface is

calculated and cases where the surface normal is

collinear or almost collinear with the segmentation

orientation are detected and defined as feature points.

In Ref. [19], different feature point configurations are

classified. Near these feature points positions of

Fig. 5. Regions of maximum cutter pitch.

J.J. Broek et al. / Automation in Construction 11 (2002) 335–347342

maximum pitch of the cutting tool are calculated.

Next step is more deeply investigation of these

regions in order to create feasible segments (Fig. 5).

The method of shape analysis for segmenting purpo-

ses is very effective and appears to be not computing

intensive.

A geometric decomposition of the segments into

thick layers is called slicing. The slicing process can

be automated on the basis of a slicing algorithm. This

method applies higher order approximation and adap-

tive layers and is discussed in Ref. [16]. The flexible

hot knife cutting is performed tangential to the slicing

contour. The local nominal shape curve is derived

from the intersection of a plane perpendicular to the

slicing contour and the nominal shape. The curve

representing a section of the tool shape curve is

subsequently matched under tolerance constraint

[17] against the nominal shape. In order to speed up

the matching process and to minimize the computing

effort a library of pre-calculated tool profile curves is

available (Fig. 6). All the curves in the library satisfy

the requirement of being planar least energy curves.

All the available tool shape curves in the library are

applied for matching. For each successful match, the

relevant tool data is stored. However, when the match

fails, another tool shape curve from the library or

another section of the same tool curve is considered.

When no match is found against all the curves of

the tool shape library, then the section length of the

tool shape curve is decreased and correspondingly

the thickness of the applied layer will be reduced,

until matching is achieved. This procedure is repeated

along the slicing contour at all positions. The final

result is a set of successful matched tool curves at

each selected position at the base contour of a layer.

The minimal section height is selected and the layer

thickness is chosen. Next, a standard layer thickness,

which is the maximum slab thickness fitting inside

the calculated layer thickness, is selected from the

foam stock. The tool shape data at the periphery is

analyzed and a family of tool shape curves and tool

control data is selected. The selection is based on

principles of minimal tool adaptation, adjustments

and movements during the cutting of the specific

contour.

For a good appearance, a prototype must at least

have a first order continuity in the transient regions of

the layers. This principle requires the same contours at

the contact planes of the layers. In order to satisfy

these requirements, an error compensation d in pitch

of the cutting tool and a related tolerance check is

performed (Fig. 7). Finally, the tool data of the sliced

layer is prepared for tool path calculations. Subse-

quently, the top of the calculated layer becomes the

basis of the slicing procedure of the next layer. The

choice of slicing positions will be influenced by the

achievable preciseness of the shape approximation.

An extended description of this issue is presented in

Ref. [16].

In Ref. [6], specific TLOM problems using one

single slicing orientation for the complete PM are the

branching problem, the correspondence problem and

the difficulty to manufacture degenerated layers. The

branching problem occurs when during slicing in

successive positions, the number of closed contours

(loops) changes. When the next slicing positions

contain more closed slicing contours, then locally,

Fig. 6. Examples of tool shape library.

J.J. Broek et al. / Automation in Construction 11 (2002) 335–347 343

the shape is branched in more branches. In this case,

the geometric information of the shape in between

both cross-section levels is not properly defined and a

segmentation of the nominal shape is proposed. In

some circumstances, the branching problem can be

avoided, e.g. when the slicing orientation is changed.

The correspondence problem occurs when adjacent

slicing levels contain multiple contours and intercon-

nection of the individual slicing contours is subject to

multiple interpretations.

During slicing, some regions of the layers might

become very thin and also the front face inclination

is so extreme that manufacturing of that layers

cannot be achieved with normal TLOM techniques.

These layers are referred to as degenerated layers.

Application of a combination of morphological and

geometrical decomposition may solve these problems

(Fig. 8).

A technological decomposition of layers into sec-

tors is completely a technological issue. The cutting

tool interference with a foam slab, the hollowing of a

layer, the maximum working space of the flexible

cutting machine, the transportation and handling of

the layers (e.g. weight, dimensions), the stacking

provisions, the rigidity of the slab during manipula-

tion, stacking of the sectors and the complete model

are considered in this decomposition. Each of the

enumerated issues will introduce their own decom-

position in sectors. Some issues are strongly related to

a precise geometric subdivision (due to curvature,

undercutting, tool holder interference) while others

allow a more general subdivision (due to hollowing

and dimensions). In order to perform the decomposi-

tion in an efficient way, the decomposition sequence

must start with the precise position related sectoring.

This sectoring might already satisfy the remaining

sectoring requirements. When sectoring is completed,

the created sectors are geometrically closed in order to

create consistently closed objects. The sectors are

individually marked for logistic reasons, and accord-

ing to the sequence of stacking.

When the decomposition of the object is com-

pleted, the next step is to generate for each single

part the tool paths along the contour of that part.

Minimization of tool and slab movements is needed to

obtain minimal dynamic effects on the cutting equip-

ment. In Fig. 9, a typical tool path for FF-TLOM is

Fig. 8. Example of segmented object.

Fig. 7. Cutting tool correction.

J.J. Broek et al. / Automation in Construction 11 (2002) 335–347344

presented. In order to avoid extreme dynamic effects,

the resulting tool path will be smoothed.

5. The physical model

When all parts are produced according to the FF-

TLOM technology, the model can be re-assembled.

Each part is marked for the re-assembly sequence and

stored dependent upon manual or automatic stacking.

The stacking of the sectors, layers, segments, sub-

assemblies and assemblies takes place into reverse

direction of the decomposition action. However, when

inserts are defined inside the PM, this sequence has to

be adapted to that situation. During stacking stability

of the stacked object in progress is an issue and must

be checked and analyzed during stacking [37]. In

general, unstable situations must be avoided, while

extra provisions to perform the re-assembly in a

proper way will worsen the efficiency of the FF-

TLOM process. Stability can be guaranteed by sup-

porting structures [1]. Creating these structures needs

also manufacturing efforts (time, material, etc.). A

different approach might be another sequence of

stacking by creating stable clusters of assembled parts

Fig. 9. Calculated tool path.

Fig. 10. Example of a stacked physical foam model.

J.J. Broek et al. / Automation in Construction 11 (2002) 335–347 345

and at a later stage to interconnect these subassem-

blies. The accuracy and rigidity of the PM will depend

on the way the stacking is performed, e.g. the inter-

connection of the parts by dowels in center holes and

glueing the layers together. When a subassembly is

applicable for more than one PM (family of PM’s),

then it must be possible to decide about a detachable

interconnection [20]. Finally, a PM is finished and

conserved according to the needs of the designer.

A typical example of a physical model of the FF-

TLOM process is an object, which consists of four

stacked layers of 5 cm thick each (Fig. 10).

6. Conclusions

This paper describes the proposed FF-TLOM

method, which is very well suited for large-sized

monolithic doubly curved objects. The process is

based on higher order approximation of the nominal

shape, decomposition of this shape into easy to manu-

facture parts, stacking the parts in order to obtain a

large-sized physical model and finally, finishing it.

The higher order approximation is supported by a

technology of a flexible hot knife cutting. The geom-

etry decomposition is subdivided into a few hierarch-

ical levels, each with its specific input and result

(functionality, shape representation, accuracy, applied

technology, etc.). The stacking of the parts is per-

formed in the opposite direction of the decomposition.

The process of creating a physical model is feasible

and allows the designer to apply functional physical

models in an early stage of a design process and to

perform it in an optimal way (dedicated to pinpoint

functionality). The amount of effort to finish the object

is minimal and is, in many cases, restricted only to

painting. The FF-TLOM process, however, show a

tendency to become very complicated and care must

be taken to efficiency of the process in order to remain

competitive against other RP methods. Special features

like hollowing, inserts and dedicated tool path gener-

ation might improve the applicability of the process.

Acknowledgements

The research work reported in this paper is a part of

the Integrated Concept Advancement (ICA) project of

the Sub-Faculty of Industrial Design Engineering,

FDEP, of the Delft University of Technology.

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