Granular modelling for virtual prototyping in interactive design

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Granular modelling for virtual prototyping ininteractive designKeny Ordaz-Hernandez a b , Xavier Fischer b c & Fouad Bennis aa Nantes Central Engineering School (ECN), IRCCYN–UMR 6597 , Nantes, Franceb Engineering School ESTIA, LIPSI , Bidart, Francec University Bordeaux 1, TREFLE–UMR 8508 , Talence, FrancePublished online: 13 Aug 2007.

To cite this article: Keny Ordaz-Hernandez , Xavier Fischer & Fouad Bennis (2007) Granular modelling for virtual prototypingin interactive design, Virtual and Physical Prototyping, 2:2, 111-126, DOI: 10.1080/17452750701552553

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Granular modelling for virtual prototyping in interactive design

KENY ORDAZ-HERNANDEZ$,%, XAVIER FISCHER%,§* and FOUAD BENNIS$

$Nantes Central Engineering School (ECN), IRCCYN�UMR 6597, Nantes, France

%Engineering School ESTIA, LIPSI, Bidart, France

§University Bordeaux 1, TREFLE�UMR 8508, Talence, France

This paper introduces the concept of granular modelling as a strategy to construct

human-centred virtual prototype and environment models. This approach aims at

providing a granular strategy for virtual prototype models in order to allow the change

from a coarse-grain description to a fine-grain one according to the level of specification

desired. The granular model is built from the aggregation of several component models

and their interaction models, representing the interaction between two components.

Component models must include information not only about themselves but also about

the environmental part related to them. This is important as environmental conditions

may have different effects at different scales/levels. Additionally, it leads to a higher level

of communication, only allowed through the interaction models. This implies that new

different objects might be integrated only by including their component models and their

required interaction. The foreseen advantage is that the human is integrated in a simple

manner: a component model corresponding to a haptic interface and an interaction

model relating it to the virtual product. The first step, identification and organic

description, consists of establishing an interaction graph from the hierarchical structure of

the virtual product and all the objects that will be present in its future environment.

Subsequently, the component and interactions models are constructed. The model is

expected to be implemented into a multi-agent system where every component model

derives into a component agent.

Keywords: Interactive design; Modelling; Virtual prototype; Component model;

Interaction model; Granular model

1. Introduction

Product design research focuses on developing methodolo-

gies that guarantee the reduction in development time

and cost with a complete fulfilment of customers’ require-

ments. Interactive design (ID) emerges as an approach

that integrates user expectations in the product develop-

ment process, allowing the designer to interact with the

virtual product and its environment. It has two main

objectives:

. To identify and model those expectations in order to

include them in the development process.

. To validate a design concept selection, verifying also its

coherence with those expectations.

ID encourages the use of advanced simulation methods and

technology, such as virtual reality (VR), to support

designers’ decision-making. In particular, it aids engineers

to implement realistic virtual prototypes enabling the

interaction between real and virtual elements. Consequently,

virtual prototyping (VP) for interactive design must not

only consider typical product model information (geometry,

materials, etc.) and information from expected use (e.g.

physical behaviour), but also integrate the designer into the

*Corresponding author. Email: [email protected]

Virtual and Physical Prototyping, Vol. 2, No. 2, June 2007, 111�126

Virtual and Physical PrototypingISSN 1745-2759 print/ISSN 1745-2767 online # 2007 Taylor & Francis

http://www.tandf.co.uk/journalsDOI: 10.1080/17452750701552553

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global model. Moreover, it has to model the possible use of

case environment. Within the mechanical design of a

product, VP must clearly include the construction of

mathematical models of physical phenomena. However,

complexity must not be eliminated when there is no need to.

VP must simply emulate the features really relevant to the

application domain. The virtual prototype model represents

not only the virtual product but also its environment, as a

single virtual prototype environment. In the case of virtual

prototyping applications using human-centred virtual rea-

lity, the human being is also a component of the environ-

ment. For this reason, it has an effect on the prototype

being simulated. Consequently, the interaction of real

objects and virtual objects has to be incorporated into the

analysis and design of the virtual prototype.

Thus, a simple modelling approach is desired, integrating

the object-object interactions as well as the object-human

interactions. The possibility of working at different systemic

levels is also important, since the variations of the proto-

type can be directly related to a change in a particular part

of the product. To support this ability, the possibility of

having a coarse-grain description or a fine-grain description

is essential to the virtual prototype environment model.

With this purpose in mind, granular modelling is intro-

duced as a strategy for virtual prototype modelling to allow

change according to the level of the desired specification, by

including only the features relevant to the use case.

This paper presents an ongoing approach for virtual

prototype modelling with a granular description.

The next section provides an extended statement of the

problem studied in this paper. Section 3 introduces the

related work found in modelling virtual environments and

virtual prototypes. The following section, section 4, intro-

duces the proposed approach for modelling. Section 5

presents the mechanical and computational specification

aspects of the granular model. Section 6 exhibits the current

state of the methodology to construct models for virtual

prototyping. The component modelling and the interaction

modelling are also introduced. Section 7 shows the applica-

tion of this approach to a simple problem: a cantilever

beam under the action of a human hand, for illustration

purposes. Section 8 discusses the results and their implica-

tion to virtual prototyping. Finally, conclusions and

perspectives are presented in section 9.

2. Problem statement

A recent trend in the creation of virtual prototypes for

product design is the inclusion of interactivity. Virtual

prototypes are digital representations or simulations of the

product concept. Simulation of interactive prototypes (or

interactive simulations) can be used to explore and experi-

ment with product concepts according to the expertise and

intuition of the designer (Cartwright 1997) and the future

user. Similarly, it has been suggested that the use of

interactive simulation will speed up the findings and

concept design reviewing at the early stages of the devel-

opment process (Bao et al. 2002). Virtual prototyping

interactivity is the capability to simulate the human’s

interaction with the design. In the past, the effectiveness

of an interactive virtual prototype was limited to the

following features: realistic visualization, geometry-related

constrains, and realistic simulation of physical behaviour

(Thompson et al. 1998). However, human-product interac-

tion should be included (Song et al. 1999) as well as real-

time processing and rendering (Leon 2003, Bao et al. 2002)

to maintain the illusion of realism in the simulation

(Zachmann 1998). In fact, as stated by Liu et al. (2004),

the key problem of virtual prototyping is how to build

credible VP models. Today, virtual prototyping for product

design must provide interactive simulation that ensures:

realism (visual and behavioural), fast processing (computa-

tion of models), and integration of the human-object

interaction. Also, extensible and reusable models are

desired to simulate different design alternatives with a

minimal effort. Therefore, the interactive simulation must

reflect the following features:

. Accuracy and appropriate speed. Visualization and

simulation of physical behaviour must be accurate to

provide a realistic reliable experience to the user

(Thompson et al. 1998), and fast enough to maintain

the sensation of immersion (Zachmann 1998).

. Human integration. Object-object interactions as well as

also human-object interaction must be integrated (Zach-

mann 1998), so that the designer is able to explore and

experiment with the future user reaction with the design

alternatives.

. Extensibility and reusability. Quick integration of

changes in the virtual prototype (Thompson et al.

1998) and easy derivation of virtual prototype variations

(Fok et al. 2001) allowing the creation of prototypes for

the different design alternatives.

In the current research, exploration of the interactive

simulation models is performed. It aims to develop a

modelling methodology with the features mentioned above,

except for the realistic visualization.

In this study, an extensible and human-aware model of

interactive simulation is addressed.

3. Background of modelling in virtual prototyping

Virtual prototyping is a trend that suggests the use of virtual

prototypes and simulation results in order to reduce the

number and role of physical prototypes (Fontana et al. 2005).

112 Ordaz-Hernandez et al.

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Many definitions exist of what avirtual prototype is (Wang

2002, Zorriassatine et al. 2003), with quite different model-

ling methodology. In this work, a particular type of virtual

prototype is addressed: a hybrid immersive analytical virtual

prototype. This type of prototype is characterized by the use

of virtual reality technologies and accurate physical-based

models. For further explanation see Tseng et al. (1998).

Some papers describe strategies to use a CAD model,

first as a digital mock-up (DMU) and later in virtual

prototyping (Bullinger et al., 1999; Lee 2001). Nevertheless,

the important issue is the inclusion of interactivity in the

virtual prototype simulation environment as described by

Cartwright (1997) and Thompson et al. (1998). Moreover,

the use of haptic force feedback in virtual prototyping has

been suggested as a way to improve the design process (Ren

et al. 2006). The use of haptic feedback in virtual reality

(Burdea 2000) has shown that modelling the haptic inter-

action is an essential tool. The creation of haptic interaction

models is particularly important, since they are an essential

type of object-human interaction (Bordegoni and Cugini

2006, Bao et al. 2002, Jayaram et al. 2000).

4. Proposed approach for modelling virtual prototypes

Interactive simulation, or the simulation of interactive

virtual prototypes, depends on certain characteristics to

be fully exploitable in product design. In particular,

extensibility and human integration are key features for

interactive design. It is desired to have a model that is easily

extendible to facilitate the variation of a virtual prototype,

integrating the human (user/designer).

The proposed approach consists of providing a virtual

prototype model with a granular description. The granular

model of a virtual prototype is a collection of two different

elements: components and interactions. Every element of the

environment must be classified as component (if it is an

entity of the virtual prototype environment) or as interac-

tion (if it relates two entities of the virtual prototype

environment). The granular model can be created as a

coarse-grain description or a fine-grain description (or a

mixture) by taking all the parts of an object as separate

entities, according to the choice of the engineer.

An entity in the virtual prototype environment is an

object that has a distinct, separate existence, even if it is

virtual. In the environment, the virtual product (i.e. its

prototype) and the human are entities. As every entity has

an existence, it is characterized by performing a specific

behaviour under certain circumstances of the environment.

In consequence, an entity model integrates at least one

behavioural model and its corresponding validity domain,

which is the extent or the circumstances where the

behavioural model is valid. Behavioural models and validity

domains are represented as follows:

(B;D) where

B is a behavioural model; and

D is the validity domain of existence ofthe corresponding behavioural model:

8<: (1)

The elements of the granular model are:

. The component models. A component model is an entity

of a virtual environment with one or several possible

behaviours that contingently depends on the nature and

intensity of the external actions upon it. Commonly,

these models are different in form, density and typology,

all being characterized by the inclusion of a series of

(B;D) pairs.

. The interaction models. An interaction model refers to

the interaction among the components, mostly energy

transfers that allow elements of the environment to react

to the transmitted solicitations. Interaction models serve

to activate the behavioural models of the related

components.

In general, both groups of models are required in a

virtual prototype simulation. Component models are ob-

viously used to simulate the behaviour of the component.

Interaction models are the reciprocal manipulation of

components, in an action-reaction situation. Hence, inter-

action models can be considered as some sort of simulation

control. The use of the abovementioned models in virtual

prototyping is shown in figure 1.

Even if the granular model is a collection of component

models and interaction models, it defines the level of

abstraction of specification corresponding to the granular

description. The granular modelling is introduced as a

strategy for virtual prototype modelling to allow the change

from a coarse-grain description to a fine-grain description,

according to the level of desired specification, by including

only the features relevant to the use case.

4.1 Coarse-grain description and fine-grain description

Typically, these descriptions refer to the size of the grain in

a system’s description. In addition, the description also

refers to the systemic level or specialization level of a virtual

prototype system (figure 2). These levels correspond well to

several products in the mechanical design field. In this

figure, five specialization levels are shown: system, sub-

system, assembly, sub-assembly, component, and sub-com-

ponent. Obviously, the number of elements at each level is

different. For the example illustrated in figure 2, it is

possible to observe the following:

. Sub-system: two elements {B1,B2}(1)

. Assembly: three {C1,C2,C3}(2)

. Sub-assembly: four {D1,D2,D3,D4}(3)

. Component: eight {E1,E2,E3,E4,E5,E6,E7,E8}(4)

113Granular modelling for virtual prototyping

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where { �}(i) is a discrete set of entities at systemic level i.

For modelling interactive virtual prototypes, having the

option of establishing a coarse-grain description or a fine-

grain description is essential to allow working at different

systemic levels, since the variations of the prototype can be

directly related to a change in a particular part of the

product. Hence, for the example of figure 2, a coarse-

grain description and a fine-grain description can be

extracted. On one hand, a possible coarse-grain model

would include elements at the Assembly level {C1,C2,C3}(2)

and provide a series of behavioural models (B, D) for

each element. On the other hand, a possible fine-grain

model would include elements at the Component

level {E1,E2,E3,E4,E5,E6,E7,E8}(4). See figure 3 for a sche-

matic representation of both descriptions for the given

example.

The granular description is also important as a means of

passing from a conceptual mechanical domain to a

implementation computational domain.

4.2 Mechanical and computational domains

It is important to remember that, in mechanical engineer-

ing, the simulation of virtual prototypes must include the

mechanical problems in terms of computational representa-

tion. That is, the virtual prototype model is conceived in a

mechanical domain, but it has to be implemented in the

computational domain of the virtual prototype environ-

ment. Two separate visions of the problem domain must be

accounted for, the mechanical and the computational one,

in a complementary way as together they define the model.

A vision of the mechanical and computational spaces is

given in figures 4 and 5.

Agents have already been employed in both mechanical

design (Capera et al. 2004) and collaborative design

(Rosenman and Wang 1999) for the creation of a compo-

nent agent-based design-oriented model.

Intelligent agents have been chosen as a modelling

paradigm since this provides a good mapping between the

Figure 1. Modules collaboration for virtual prototyping: adapted from Salmela and Pulli (1997).

Figure 2. Organic description with systemic levels.


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software and the world (Yu 2002). The definition of agent

given by Jennings and Wooldridge (1998) is appropriate to

this work: an agent is a software element that is situated in

some environment, capable of autonomous action in this

environment in order to meet its design objectives.

Hence, a component agent is an element of the extended

virtual prototype (EVP), situated in the virtual prototype

environment, and capable of autonomous action in this

environment. An interaction agent is an element of the

EVP, capable of transmitting the action of one component

to another.

In the classification of Wooldridge (2002), the interaction

agents can be seen as reactive agents (they correspond to

the interaction of a component agent with the environ-

ment), while the component agents behave as pro-active

agents that adapt their behaviour correspondingly to the

status of the environment, while trying to maintain a good

performance in terms of both accuracy and speed. In this

work, the notation employed corresponds to the formal

framework for multi-agent environments introduced by

Helleboogh et al. (2007).

5. Granular model of the virtual prototype

This section introduces the concept of granular model of

the virtual prototype. Granular modelling is a strategy for

virtual prototype modelling to allow the change from a

coarse-grain description to a fine-grain description, accord-

ing to the level of specification desired, by including only

Figure 3. Entities of a virtual prototype environment.

Figure 4. Mechanical domain of the virtual prototype environment.


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the features relevant to the use case. Hence, the granular

model allows the creation of a new variation of the virtual

prototype model by:

. changing a particular part (or component)

. reusing the remaining elements of the model, and

. extending the model by the inclusion of new parts.

It is important to simplify the model by including only the

relevant parts of the entities of the intended environment.

In this work, the concept EVP is considered as a modelling

artefact. EVP is defined as the inclusion of all parts of the

virtual prototype, i.e., VPƒE; and of certain parts of the

other objects that interact with it HƒE; OƒE; Hpƒ

H; Op �O: This way (see also figure 6)

Figure 6. Extended virtual prototype.

Figure 5. Computational domain of the virtual prototype environment.


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EVP�VP@Hp@Op: (2)

As a consequence of equation , the EVP is a subset of the

environment:

EVPƒE: (3)

From now on, the term VP environment will be used

interchangeably with the term extended virtual prototype to

refer to this subset of the environment.

The model of the virtual prototype environment is

defined as a collection of components and interactions.

An organic description of that collection is required. Its

granular model is specified in two diagrams: the conceptual

diagram and the implementation diagram. The conceptual

diagram provides an organic description in the mechanical

domain without making any distinction regarding the

virtual or real existence of entities, while the implementa-

tion diagram provides an organic description in the

computational domain, including the nature of the entities’

existence. This inclusion is more relevant for implementa-

tion, since human-computer interfaces are required for

human-object (real-to-virtual) interactions.

5.1 Conceptual and implementation diagrams

The conceptual diagram corresponds to a vertex-edge graph

that represents an organic structure of the VP environment

in terms of components and their interactions. A vertex-

edge graph G(V, E), in mathematics, is a tuple (V, E)

where V is the set of nodes and E is a subset of V�V that

denotes the edges. Here, the created graph is called the

component-interaction graph (C-I graph), which represents

an organisational mechanical view of the environment

showing that:

. the components of the VP environment, without defin-

ing the systemic level; and

. the interactions are the actual relationships between

those components.

Then, the implementation diagram is constructed from the

information contained in the conceptual diagram, but

oriented to a computational domain where the virtual

prototype would exist. An important difference is that the

implementation diagram requires that the set of entities is

partitioned by type of components (virtual, real) and by

type of interaction (object-object, human-object). Multi-

agent systems modelling has been chosen as implementa-

tion technique. Examples of C-I graph and implementation

diagram are given in figure 7 and figure 8.

Figure 7. Conceptual diagram represented by a compo-

nent-interaction graph.


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The proposed methodology for granular modelling of

virtual prototypes is described in the next section.

6. Methodology of granular modelling

The environment is modelled as a collection of components

and interactions where each component’s properties and

behaviour are encapsulated in a single element. The compo-

nent integrates a series of behavioural models along with

their validity domains, and it is able to choose (in terms of

speed and accuracy) which one to use according to the

interactions from the related components. Modelling is

performed at two stages. First, the component and interac-

tion identification is performed by using specific design tools

(e.g. technical chart, substance-field graph) and a compo-

nent-interaction graph is then constructed. Then, an im-

plementation diagram is constructed to represent the

computational view of the granular model in terms of a

multi-agent system.

The steps of the methodology for constructing the

conceptual diagram (figure 9) and the implementation

diagram (figure 10) are presented next.

Figure 8. Implementation diagram for virtual prototyping.

Figure 9. Steps to build a conceptual diagram in the

granular modelling methodology.


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6.1 Conceptual diagram

6.1.1. Entity identification. This stage consists in the ana-

lysis of schematics or any kind of representation of the

expected environment. The elements that seem to partici-

pate in the simulation are identified. In many cases, a

technical chart resulting from the design process is a good

start.

6.1.2. Interaction identification. A substance-field graph is

a tool that serves to analyse the relation between objects

with non-zero volume or mass, called substances; and the

action of one substance on another, called fields. Usually a

pictorial representation is used, but a tabular representation

is occasionally employed. It is possible to observe that

substances are nouns, while fields are verbs.

6.1.3. Organic decomposition. The environment is now

represented in an organic view where all its components

are identified (corresponding to the substances of the

previous stage) as well as the interactions (concrete nouns

from the fields of the previous stage). The pictorial

representation is similar to the technical chart, blocks

representing the components; but interactions are now

represented by interconnecting arrows. This allows compo-

nents to be arranged in a vertex-edge graph where

components correspond to the graph vertices, and interac-

tions correspond to the graph edges. This abstraction

corresponds to a simple view of the environment where

either the coherence of the interactions can be studied or

generic or basic object-object interactions or human-

object interactions can be detected. This corresponds

to the component-interaction graph (C-I graph) intro-

duced in the previous section, which is a high level

diagram representing a partial action-reaction sequence

(figure 11).

6.2 Implementation diagram

6.2.1. Multi-agent system modelling. A dynamically adap-

table environment is desired to ensure interaction coher-

ence, so multi-agent system (MAS) modelling appears as an

appropriate solution since it helps to eliminate complexity

by the divide and conquer strategy. Intelligent agents can

provide a great level of adaptability as they perform their

tasks. For VP in ID, MAS modelling considers the

environment as an ensemble of component agents and

interaction agents, each one corresponding to an element

found in the conceptual diagram (see section 6.1). A

component agent comprises all the characteristics of a

component entity: material definition, geometric definition,

temporal definition, boundary conditions, and the series of

the component’s local behaviours. An interaction agent

works as the link between two component agents. It serves

as a boundary condition transmitter, and helps to adjust the

components agents’ models with the applicable laws,

according to the environment status. It is the implementa-

tion of an interaction model.

Two concepts represent the parts that constitute the

simulated environment: components and interactions.

6.2.2. Structure of the simulated environment. The basic

concepts that are used to represent the structure of the

environment are introduced here. This part of the formal-

ism is described in a simplified way only to discuss the link

between the component-interaction graph and the multi-

agent system for the virtual prototype simulation.

Environmental entities. Environmental entities are, as the

name suggests, all the entities of the virtual prototype

environment.

/ E�fe1; e2; � � � ; eng ½ the set of environmental entities.

Environmental entities can be partitioned into a set of

disjoint subsets, with each subset grouping entities of the

same kind. Formally

/PartE �fE1;E2; � � � ;Ekg��

a partition of environmental entities

with

EiƒE

E�@ i�1...kEi

EiSEj �¥;� i" j

The set of environmental entities can be partitioned to

provide a structure that corresponds to elements in a higher

systemic level. An example of a partitioned set of environ-

mental entities:

Figure 10. Steps to build an implementation diagram in the

granular modelling methodology.


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E�fproduct;designer; support; temperature;humidity;airg (4)

PartE �fPrototype;Human;Otherg (5)

Prototype�fproductg (6)

Human�fdesignerg (7)

Other�fsupport; temperature; humidity; airg (8)

Component partition. The components are basically the

entities found in E: In consequence, components take a

similar form to the environmental entities.

/C�{c1,c2,. . .cq}½ the set of EVP components.

Partitioning the EVP components C; PartC; is useful for

defining interactions. Examples of components partitioned

by their kind of existence (virtual or real):

C�fproduct; designer; support; temperature; humidityg (9)

PartC�fVirtual;Realg (10)

Virtual�fproduct; support; temperature; humidityg (11)

Real�fdesignerg (12)

Interaction partition. An interaction in the environment was

already defined as an exchange of energy between two

components (see section 4). To formalize the definition of an

interaction, the existing relations between components of

the conceptual diagram are formally described as follows:

ck R cj U(ck; cj) � G ½ G�f(ck; cj) � C2 ½ ck R cjg (13)

where:

R is a relation of the Conceptual Diagram (C-I graph);

/G is the relation graph equivalent to the C-I graph;

/C2 is the Cartesian Product C�C; C is the set of components.

If R exists then there is a application Ikjthat relates the

components ck and cj (/Ikjis bijective and also its inverse I�1

kj):

ek R cj [ Ikj: Ek 0 Ej

pk � Ikj(pk)�pj

; Ek; E j ƒ´ (14)

where: Ek; E j are the sets of the emitted or received energy by

the components ck or cj;

/pk; pj emitted or received energy by the components ck

and cj, respectively;

/Ikjis an application that is called an interaction when:

Ikj�Ijk

�I�1kj

�Ijk(15)

Figure 11. Conceptual diagram for virtual prototyping.


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For the definition of interactions, a prefix notation would

be used instead of the infix notation of the relations. That is,

ck R cj �R(ck; cj) (16)

Then the set of interactions for the virtual prototype

environment can be defined as

I�fIkj½ R(ck; cj)fflIkj

:Ek 0 E jg (17)

Examples of interactions partitioned by the type to which

they belong:

I�fIdesigner; product; Iother; productg (18)

PartI �fHumObj;ObjObjg (19)

HumObj�fIdesigner; productg (20)

ObjObj�fIother; productg (21)

with pproduct�Idesigner; product(pdesigner) is a mechanical energy

that could be obtained by

pproduct�WF �gl

Fdx; if F is a force (22)

The implementation diagram (figure 8) shows the compo-

nents grouped by their real or virtual existence and the

interactions grouped by their type: object-object, human-

object.

7. Virtual prototyping of a cantilever beam-like object

A long thin cantilever beam, under human action at the free

end, is to be modelled for interactive simulation (figure 12).

The cantilever beam is considered to be of uniform

rectangular cross-section made of a homogeneous and

isotropous elastic material that follows a linear elastic

constitutive law. Only small deformations are accepted,

but large deflections may appear. Since large rotations move

the current configuration (/CD) away from the base config-

uration (/C0); a linear model cannot be used except for small

rotations. A total lagrangian (TL) formulation model is

accurate and precise enough; but the computing time

exceeds the acceptable threshold for an interactive simula-

tion since it requires an iterative solution process (usually a

variant of the Newton-Raphson is used).

Table 1 summarizes the data of the cantilever beam used

as the test case. It is analogous to the problem experimented

in Belendez et al. (2002). Their results were validated

experimentally. Table 2 presents the resulting displacements

at the free end of the beam, which correspond to the

maximal values.

In this case, the beam is subjected to the action of a

human hand, as depicted in figure 12.

The methodology presented in the previous section is

applied to model the environment, the components and the

interactions.

7.1 Beam environment model

The beam environment model is built following the

granular model methodology.

7.1.1. Entity identification. As a cantilever beam is de-

formed by a human, it is possible to detect three objects: a

beam, a human and a support. Since the complete

modelling of a human is not practical, only the hand that

is the part interacting with the beam is considered. The

identified elements are: beam, hand and frame (figure 12).

7.1.2. Interaction identification. The substances are: beam,

hand and frame; and the relations between the substances

are: (i) the hand deforms the beam, and (ii) the frame

supports the beam. A representation of the graph is shown

in figure 13.

7.1.3. Organic description. The above-mentioned sub-

stances (beam, hand, frame) and fields (deforms, supports)

can be established as the components of the environment

(the substances) and the interactions: force (from the field

Figure 12. Long deflection cantilever beam problem for

flexible modeling.

Table 1. Data for the cantilever beam (Belendez et al. 2002).

Description Value

Length L 300 mm

Width b 30.4 mm

Height h 0.78 mm

Moment of inertia I 1.20�10�12 m4

Young’s modulus E 200 GPa

External force F 3.92 N

Table 2. Displacements at the free end of the cantilever beam.Numerical results of the reference model, validated experi-

mentally (Belendez et al. 2002).

Displacements Response of the reference model

dx /31:4 mm

dy /121:6 mm

ux 36.098


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deforms) and clamping (from the field supports). Both

groups represent the organic decomposition of the environ-

ment, and they are presented in the form of a technical

chart, as illustrated in figure 14.

From the organic decomposition of the environment, the

components (beam, hand, frame) are arranged in a vertex-

edge graph where components correspond to the graph

vertices, and interactions (force, clamping) correspond to

the graph edges (figure 15a). According to the use of the C-I

graph, it can be alternatively represented with a vertex-edge

graph, where components and interactions correspond to

the graph vertices. The two component vertices are only

connected indirectly by an interaction vertex that relates

them (figure 15b).

7.1.4. Implementation diagram. Components and interac-

tions are extracted from figure 15 and grouped in the

following equations

C�fbeam; hand; frameg (23)

I�fIhand;beam; Iframe;beamg (24)

where:

/Ihand;beam is the interaction model that applies the energy Ehand

to the energy Ebeam; by means of a force;

/Iframe;beam is the interaction model that applies the energy Eframe

to the energy Ebeam; by means of a clamping;

Then, the component set C is partitioned into Virtual and

Real components,

PartC �fVirtual;Realg (25)

Virtual�fbeam; frameg (26)

Real�fhandg (27)

Also, the interactions set I is partitioned in HumObj

(human-object) and ObjObj (object-object) interaction

models.

PartI �fHumObj;ObjObjg (28)

HumObj�fIhand;beamg (29)

ObjObj�fIframe;beamg (30)

Finally, all partitions are represented in the resulting

implementation diagram, as shown in figure 16. Only a

relationship is marked for simplicity.

7.2 Beam component and interaction models

7.2.1. Interaction models. In the beam environment, two

interactions were found: clamping and force. These are

modeled as simple boundary conditions: the support at

the fixed end (displacements and rotation are equal to

zero) and the varying force transmitted from the hand to

the beam.

7.2.2. Component models. The components of the envir-

onment are three: beam, human hand and frame. As the

beam presents a more interesting series of behaviours, this

section is focused on its modelling. First, two beam

models are studied: a linear formulation model and a

total lagrangian formulation model (see Bathe 1996). As

the linear model is known to be valid only under small

displacements, the non-linear model is used to model the

beam behaviour under great displacements. However, this

model uses an iterative method to solve its governing

equations. As a consequence, it is known that it is not

capable of responding in real time.

The solution is to apply a model reduction technique to

the non-linear model. The reduced non-linear model is

Figure 13. Substance-field graph of the beam environment.

Figure 14. Organic decomposition of the beam environ-

ment.

Figure 15. Component-Interaction graph.


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more accurate that the linear model and it is suitable for

real-time simulation. Unfortunately, the technique used

(neural networks) has induced a shortening of the validity

domain. Now, the neural network-based model is not

capable of simulating the beam response under small

displacements.

At this point, there are two available models: the linear

model which is fast and valid under small displacements,

and the reduced non-linear model which is also fast but

valid only under great displacements.

An aggregation scheme that uses both models at different

statuses of the environment (small displacements, great

displacements) is introduced. This aggregation scheme

corresponds to a behaviour selector and it is based on fuzzy

logic. It considers two indicators: the size of the maximal

rotation uz and the temporal derivative of the rotation uz:

8. Discussion

The environment modelling methodology does not present

any complications due to the simplicity of the test case.

Nonetheless, the example helps to illustrate that part of the

methodology. The interaction models have been simplified to

the transmission of the support and the external force as

boundary conditions for the beam models. However, the

beam case illustrates very well the modelling of a component

model: from the model reduction to the flexible model

assembly. The results from the simulation reflect the

advantage of using such a scheme and also its capability to

accurately simulate the non-linear beam behaviour in real-

time.The specification of the multi-agent system is very small

due to the limited number of components in the example.

Finally, the conceptual diagram and the implementation

diagram provide the collection of components and interac-

tions, and the clustering of virtual or real elements.

The features of the granular modelling methodology can

be summarized as follows:

. Simplicity. The environment is considered as a collection

of components (virtual and real) and the interactions

that relate them. Modelling virtual prototypes with

components and interactions as building blocks has an

Figure 16. Implementation diagram for the cantilever beam.


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advantage: prototype variations are easily derived by

changing certain virtual components.

. Human integration. The human is modelled as a

component of the environment. Since the granular

description is employed, only the relevant human parts

are integrated (i.e. the extended virtual prototype). The

virtual prototype environment model comprises the

object-object interactions (virtual-to-virtual) as well as

the object-human interactions (virtual-to-real and real-

to-virtual).

Figure 17. Evolution of the granular model for the cantilever beam. (a) Conceptual diagram (exhaustive); (b) conceptual

diagram (non-exhaustive); (c) implementation diagram.


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It is important to notice the evolution of the granular model

for entities and relations to component models and inter-

action models, to finally arrive at the component agent and

interaction agent specifications. This evolution can be

observed in figure 17.

9. Conclusion

A granular modelling methodology for virtual prototyping

has been presented. The environment is abstracted as a set

of components and interactions. Two complementary views

of the granular model are included: the conceptual diagram

(mechanical-oriented) and the implementation diagram

(computational-oriented).

The conceptual diagram is constructed after the applica-

tion of several design tools to establish an organic decom-

position of the environment. It is expected that the

information from the design activities can be reused. Also,

a component-interaction graph is created as the basis of the

implementation diagram.

The implementation diagram is the representation of the

environment defined by the concept diagram, towards the

computational implementation. In the proposed methodol-

ogy, the implementation diagram reflects the VP environ-

ment as a multi-agent system where components and

interactions are modelled as component agents and inter-

action agents with one-to-one mapping of the component

models and interaction models. In the classification of

Wooldridge (2002), the interaction agents can be seen as

reactive agents (they correspond to the interaction of a

component agent with the environment), while the compo-

nent agents behave as pro-active agents that adapt their

behaviour correspondingly to the status of the environment,

while trying to maintain good performance (in terms of

accuracy and speed).

The methodology has been used for the simulation of a

design with a cantilever beam object. This ongoing work

aims at validating the methodology within the application

in an industrial case study.

Acknowledgements

The support from the grant provided by ESTIA is gratefully

acknowledged.

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Appendix

{ �} discrete set of elements or components

{ �}(1) discrete set of components at systemic level i

A area of the cross-section (m2)

/B beam definition

(B ,D ) behaviour and validity domain tuple

/C0 undeformed configuration

CAD computer-aided design

/CD deformed configuration

C-I graph component-interaction graph

ck environmental component in a MAS

d displacement (m)

DMU digital mock-up

/E environment

E Young’s modulus (MPa)

E set of edges, subset of V �V

ek environmental entity of a MAS

EVP extended virtual prototype

f solicitations (N)

G (V,E ) vertex-edge graph

/H human

ID interactive design

il (ej ,ek ) environmental interaction in a MAS

Izz moment of inertia of the cross-section (m4)

L length of the beam (m)

MAS multi-agent system

/O object in the environment

pg geometric properties

8 behavioural model

8I linear model

pm material properties

S-F graph substance-field graph

uz rotation at the free end of the beam (rad)

u displacements (m)

V set of vertices or nodes

VP virtual prototyping or virtual prototype

VR virtual reality


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Documents

Granular modelling for virtual prototyping in interactive design