Function Modeling:
Con uence of Process Modeling and Object Modeling
Hideaki Takeda
Nara Institute of Science and Technology3
Yoshiki Shimomura yMita Industrial Co., Ltd.
Yasushi Umeda and Tetsuo Tomiyamaz
The University of TokyoAbstractin Section 3. Then we will show a result of analysis ofdesign process by FEP modeling.

Function is a key concept to integrate object modelingand process modeling in design. In this paper function is de ned as a part of FBS (Function-BehaviorStructure) Diagram, where function is a description ofbehavior abstracted through recognition of behavior
for utilization. Function de ned above is then usedin FEP (Functional Evolution Process) to represent
design processes. In FEP, function can be evolved inthree ways, i.e., decomposition evolution, causal evolution, and \patch" evolution. We show a FEP model ofdesign of a weighing scale to illustrate our approach.

2 Function-Behavior-Structure
Modeling
There are many approaches to represent function, butthere is a common problem, i.e., function and behavior
are confused and mixed. Behavior can be directly derived from structure and environment of object, while
function is related to not only structure and environment of object but also related to perception of object by designers. For example, suppose function ofa car. Some people may say one of its function is\moving", others \carrying", and others \trampling",
even if they observe the same behavior. We distinguishfunction, behavior, and structure levels in object representation (see Figure 1).
Structure level is represented by entities and relations among entities. Entities are identi ers of objects, and relations represent attributes of entities,
structures composed by entities, and states of entities. Then behavior is de ned as \sequential changeof states of objects." In the physical world, changesof states of objects are governed by physical laws.
We call this set of de nitions of structure and behavior aspect which is a basic unit of object representation. Aspect consists of de nition of terms and entities(structure) and rules (physical laws). Designers have
many kinds of aspects from well-de ned aspects (e.g.,
rigid body dynamics) to ill- or vaguely- de ned aspects(e.g., manufacturability).
While behavior is grounded on structure and within
the scope of aspect, function is indirectly related tostructure and not in the scope of aspect. We de ne
function \a description of behavior abstracted throughrecognition of behavior for utilization." Function isde ned on a chunk of behavior (or behavior itself).
There are a lot of possible chunk of behavior. But1 Introduction
Function is a key concept in design because ideallydesign is a process in which object is realized fromits functionality (see [4]). Although it is well known
concept, its de nition has been vague yet. In our approach, function is de ned using structure and behavior (FBS: Function-Behavior-Structure modeling)[5].
Then it is used in design process where function isgradually evolved (FEP: Functional Evolution Process). In the designers' standpoint of view, function isused rstly as modeling language by which they cancompose and develop their requirements. It also serves
as object representation which can connect requirements and objects in the middle stage of design. After
construction and deliberation of object representation,function representation is again used to evaluate object representation.
In the following section, we will show our model offunction and a test case of its application. We will
explain FBS modeling in Section 2 and FEP modeling
3 8916-5, Takayama, Ikoma, Nara 630-01, Japan, Fax: +817437-2-5269, Email: takeda@is.aist-nara.ac.jp
yTamatsukuri 1-2-28, Chuo-ku, Osaka, Japan, Fax: +81-6764-3309, simomura@mita.co.jp
zYayoi 2-11-16, Bunkyo-ku, Tokyo 113, Japan, Fax: +81-33813-5772, fumeda, tomiyamag@zzz.pe.u-tokyo.ac.jp

1

Function Set: functionF-B Relationship

Behavior Set: behavior: behavior sequence
B-S RelationshipPhysical Laws
Structure Set: state: state change

ASPECT

Figure 1: Relationship among Function, Behavior, and Structure
only some of them are meaningful for designers whenshould be transferred to behavior and structure
they recognize and design objects.
level.
Although function is not included in aspect, most offunctions are associated to aspects, because behaviors be-caused-by It means that new function B isneeded to exist in order to realize function A. B
which a function is based on, are in a single aspect. Inisnecessary condition for A. This relation should
other words, an aspect has a set of associated functions
besupported causal relation in behavior level.
which is a description of the aspect in the view pointof utilization.
be-reinforced-by It means that new function B isrecommended to exist in order to realize function
A properly. Since B is not necessary condition
for A, A alone can exist. But A with B would
accomplish its functionality more properly. ThisIn this section, we show function representation in derelation would be generated as a result of intersign processes.
pretation of functional modi ers.
Function in the early stage of design is a language
to describe requirements. Requirement is not comFunctional evolution is to generate functions andplete in the most of design. Detail of requirement is relations among functions. According to these three
realized according to detailing of object description, types of functional relations, functional evolution hasi.e., function is also detailed in design processes. We three di erent ways.
call it functional evolution process.
In order to represent functional evolution process, decomposition evolution Designers try to nd
sub-functions from a function. Then they try to
we provide description of function and its relationship.
nd either sub-sub-functions or behaviors associA function is represented as combination of a funcatedto sub-functions (see Figure 2). For example,
tion body objective entities and functional modi ers.
Function\to visualize weight" is decomposed into
A function body is a symbol which carries meaning ofFunction\to make weight into displacement" andthe function. A typical function body is a verb word inFunction\to convert weight and visualize".
sentences like \move" and \carry." An objective entity
is an entity which function occurs on or to. It should causal evolution Designers try to nd functions
be realized as an object in structure level until the end
linked by causal relation. This relation is foundof design. A functional modi er is a symbol which rethroughbehavior level. First they would nd bestricts functionality in order to match functionality
haviorassociatedto the given function. Thenwith designers' intention. A typical functional modithey
wouldndcausal
behaviors to the behaver is an adverb word like \precisely" or \ rmly."
iorbyusing
causalsimulation(e.g., Qualitative
We provide three types of relations among functions.
Simulation[1]). Finally they would obtain funcdecompose It is a typical process for designers totions associated to these behaviors (see Figure 3).
divide a function into sub-functions. This relation
For example, Function \to translate weight into

3 Functional Evolution Process2displacement" invokes Structure \spring". Butby mental simulation designers nd that a newstructure like \plate spring" is needed \to guide"
spring. Function \to guide" is found through behavior and structure levels.

be-reinforced-byfunction Bbehavior B
structure B\patch" evolution Designers would nd new functions by consulting functional modi ers. Then
designers would combine and test behaviors associated to the given function and derived functionin order to know whether the derived function
would support the given function according to themodi er (see Figure 4). For example, Function\to enumerate rotation" invokes Structure \rotation plate". Then designers examine how rotation plate can realize Function \to enumerate rotation" with modi er \as large as possible", here
the modi er is criteria to evaluate realized function. Then designers nd another function \to enlarge indicator" is needed to accomplish the function properly. This function can not be derived inbehavior and structure levels only, but functional
evaluation can generate it.

decomposefunction B
behavior B
structure B

modifier A1function A
behavior A
structure A

Figure 4: \Patch" Evolution

4 Applicability
We are now testing our representation with some examples. Figure 4 shows a functional evolution process
in design of a weighing scale1 .
This gure explains how both function and structure of a weighing scale are developed in this design.
At the beginning of the design process, there are a few
functions like \to visualize weight" which are directly
derived from the given speci cations. But as design
proceeds, there appeared other functions which arederived as evolution of the given functions. Some ofthem are internal functions for a scale, but others areexternal, that is, more detail speci cations of a scale.
It is an advantage of our approach, because functionand structure are developed separately in traditionalapproaches (for example [2]).
We are also analyzing design processes of PPC
copiers with the same method.

function A
function C

References

behavior Cstructure C[1] K.D. Forbus. Qualitative process theory. Arti cialIntelligence, 24:85{168, 1984.
[2] G. Pahl and W. Beitz. Engineering Design. The
Figure 2: Decomposition Evolution
Design Council, London, 1984.
[3] H. Takeda, S. Hamada, T. Tomiyama, andH. Yoshikawa. A cognitive approach of the analysisof design processes. In Design Theory and Methodbe-caused-byology { DTM '90 {, pages 153{160. The American
Society of Mechanical Engineers (ASME), 1990.
function B
function A[4] H. Takeda, P. Veerkamp, T. Tomiyama, andH. Yoshikawa. Modeling design processes. AIbehavior B
behavior A
Magazine, 11(4):37{48, 1990.
structure B
structure A[5] Y. Umeda, H. Takeda, T. Tomiyama, andY. Yoshikawa. Function, behaviour, and structure.
In J.S. Gero, editor, Applications of Arti cial InFigure 3: Causal Evolution
telligence in Engineering V, volume 1, pages 177{
194, Berlin, 1990. Springer-Verlag.
Through these processes, functional representation
1 Detail of the design process is shown in [3].
is gradually detailized.
3

4

cradleresin

springstrucutreC

plate
springto guideto translate liner disp.
into rotation displacement

M6: as large as possible
M7: tightly
M8: along with looking direction

leverRR(M7)

M6: as large as possible

rotation
platelensto numeraterotationto enlarge
Rindicator(M6)

to control backlashD

to enlarge and numerate
displacement

to enlarge rotation

helicalgear

Figure 5: Functional evolution in design of a weighing scalerack &spiralgearR(M6)to translate vertical disp.
into horizontal disp.

into liner displacemnet(M8)

D

to convert weightand visualize

C to translate spring disp.

DR(Mn): be-reinforced-by(related modifier)

D: decompose

C: be-caused-byrelation typefunction nameMn: modefier nameto make foottouch better

R (M5)

to receive vertical weight

M5: confortably

DDD

to visualize weight

to return
initial state
R (M9)
to translate weight
into displacement

M9: repeatedly

to make displacement
into weight

DM1: comfortably
M2: easy to see
M3: precisely
M4 : continually