Product Modeling: From Geometrical Modeling to Logical Modeling

Copyright © IFAC Infonnation Control Problems in Manufacturing Technology, Toronto, Canada, 1992

PRODUCT MODELING: FROM GEOMETRICAL MODELING TO LOGICAL MODELING Z, Tong, R. Tang and Y. Sun Department of Mechanical Engineering, Zhejiang Universiry, Hangzhou 3 J0027, PRC

Abstract scheme language types

product

theory.

of

logical

paper

The for

investigates modeling

The

product

rationality

modeling:

modeling,

are

the

and

linguistic

formalizes and

and

scheme

effectiveness

geometrical

analyzed

characteristics

the

modeling,

compared

of

the

feature

from

with

the

of

formal

three

major

modeling

and

integration

of

CAD/CAM. Kevwords

CAD, CAM, formal languages, modeling, product modeling, logical

modeling

INTRODUCTION

and

logical

modeling

which

describes

machine parts with logical entities (Tang, The sufficient and

proper

of machine product

is

representation factor

to

realize the integration of CAD/CAM and

to

offer

a

convenient

a

key

design

manufacturing

This paper focuses

environment .

Ideally, all the product information in

1990) .

processes

used

should

computer.

conventional

In

use for

thinking,

product

information

tools

description,

transfer.

Now,

• to establish

manual

practice, designers and manufacturers as

of

and

product

framework

for

product

• to describe the schemes in terms of

the

framework;

and

role

a

modeling schemes from linguistics;

• to discuss the representation capability

computerized

product models can play the same

analysis

be

engineering

drawings

the

modeling. The goals of the paper are

organized and represented as models within a

on

comparison of the three types

of the schemes from CAD/CAM.

as

engineering. LINGUISTIC CHARACTERIZATION OF Product modeling is about how to represent all information of products that are in

design

within

and

a

manufacturing

computer.

Many

PRODUCT MODELING SCHEMES

used

activities

efforts

have

Linguistic Characteristics

already been made in research into product modeling

and

many

developed since

schemes

been to

Language

these

exchange

information.

schemes can be classified into three major

essential

factors :

types :

which

the symbols to be used,

shape

described and syntax giving the rules

their

mid-1960'.

have

of Modeling Schemes

geometrical

describes information geometrical

the of

According

components,

fundamental

modeling geometrical parts

with

entities (Requicha,

machine

1980),

feature modeling which

describes

parts with feature entities (Shah,

to

is

describe

a

tool

the

to

represent It

vocabulary

three

providing

objective

objective

and

has

to

with

be how the

vocabularies. In addition, there are three

machine

common features of all languages:

1988) ,

language

335

must

be

described

with

1)

any some

language, 2)

finite patterns can

be

objectives, and 3)

syntactically

of

the language

is

defined;

correct

guarantee

representation cannot

vocabulary over which

used

to describe a potentially infinite set

P

is a finite

set

of

productions;

productions are of form a

semantic

~

the

6, where a

is in (VNU V T ) * VN(V,J-'V ) * and /3 is T (V,J.JV ) * ; that is, a is any string

validity.

in of

T

Engineering

drawing

is

engineers to represent

tool

a

and

transfer

information about machine parts in and manufacturing activities. found that factors

it

and

has

the

three

It

three

common

for

nonterminals

all

least one

design can

terminals, and

with

at

is

any

B

string of nonterminals and terminals ; S

be

essential

features

and

nonterminal

is a special nonterminal

called

start

symbol.

of Suppose each production in P is of form

language.

~ 6,

where A is in V

N

and 6 in

A

(V,J-'VT)

*'

then G is a context-free grammar(Aho,1968)

The three factors: • Vocabulary element geometrical

entities

point, line and arc,

such

Suppose, in a context-free grammar G, each

as

compound geometric

terminal

and

nonterminal

is

associated

entities such as projective, cutaway and

with a finite set of attributes

sectional view

production is associated with a finite set

and

each

• Objective part drawings

of semantic rules defined over the domains

• Syntax geometric projection and drafting rules

grammar( Knuth, 1968).

The three features:

Product Modeling with Formal Language

of attributes, then

•

it is described with natural language

•

it can represent an

infinite

machine part

finite

entities

using

and

finite

kinds

Since

of

geometrical

projection

model

computers,

and

product

manufacturable

and

meets

a

The

the

use

of

attributed

language

products

modeling

implemented with formal

• it cannot guarantee that the represented

an

is

represent information of

drafting rules part is

product

is

G

grammars

product modeling can be

can

language and

to

within be

theory.

languages

broken

in

into

two

needs of functions even if it is correct

areas: the generation and the

in projection and drafting rules

language strings with the grammar defining

parsing

of

the language. Here, the generation problem That is, engineering drawing is a language engineering.

in

Similarly,

as

"engineering drawing" used

by

product model

the

would

have

an

computers, form

can be used to imitate the

design

part

the

representation,

problem

and

can

analysis

be

and

and

used

to

imitate

utilization

characteristics of language.

representation.

Formal Language Theory

used in program design,

Formal language theory

of

have

a

method to describe language

A

grammar. system

grammar

defining

is

a

a

mathematical exactly it

the

been

widely design,

If

product

modeling is carried out in terms of formal

with

language

theory,

then

a

lot

ripe

of

theory, method and experience can be

mathematical

language,

a

part

a

compiler

pattern recognition and etc .. Formal Language theory is

of

parsing

used

for reference.

has

following general form Consequently, it is

dominant

to

realize

product modeling with formal language.

G

where V N

is

a

finite

set

of

SCHEMES FOR PRODUCT MODELING

non terminals

disjoint from V ;

---- GEOMETRICAL MODELING

T

V

T

is a finite set

of

terminals

in

the

336

::=1

Schemes Geometrical

modeling

is

the

earliest

The B-rep

scheme for product modeling, it represents

scheme

can

be

also

formally

defined with the similar way.

the shape information of machine part with geometrical

entities.

There

have

been

numbers of geometrical modeling methods. Among

them,

the

Constructive

Components of Information

solid

geometry(CSG) and Boundary representations (B-rep) methods are to be most

currently

In

considered

geometrical

components

important and useful.

machine

modeling

of

part

the can

scheme,

information be

the of

illustrated

a

as

follows: In CSG, the geometrical shape of a machine part

is

represented

as

the

Boolean

constructions or combinations of geometric

Manufacturing

cube, torus and

etc ..

The

primary

+

lGeOmetric shapel

primitives such as cylinder, cone, sphere,

Requirements

data

structure of CSG can be illustrated with a

...

(ordered) binary tree(or CSG tree). In the tree,

nonterminal

nodes

represent

operators,

which

may

motions

or

regularized

intersection,

or

nodes are either

be

represent subsets of E which

,

rigid union t

difference; 3

leaves

either

primitive

terminal

leaves

which

contain

the a

from the application of the the node to the left and The root of the tree is

operation

right the

in

manufacturing

"labeled

on"

the geometrical shape. From the integration of part

shape

is

are

represented

CAD/CAM, this representation of a

formed

tree

then

interior

local

the

is the

and

defining

representation of the machine part

of

the geometrical shape advance,

requirements

or transformation

arguments of rigid motions. Each node

Machine part information

is

provided

with

machine following

the

problems:

of

1) the geometrical shape and manufacturing

subtrees.

requirement are two

kinds

of

coordinate

of

a

total

shape

and inseparable attributes

representation of the machine part,

while

part, but they are artificially

the leaves of the tree are the primitives.

and moreover the later is

machine separated

represented

as

an attachment of the former; The CSG scheme can be formally defined recursive

the

BNF

notation

of

by 2)

a

context-free grammar as follows

only

the

low

geometrical

level

information such as geometry and for B-rep and

primitives

and

for CSG, or the geometrical

topology operations

relationships

where

between the local components of a

V = { , , , N , }

part,

= {, , , , T , , , , , , }

local

V

S

represented,

are

technological

relationships

components

are

not

which results in that is

unable

to

be

the

the

between

the

represented, representation directly

used

downstream applications

= {}

machine

while

such

as

in

process

planning, manufacturing;

P: ::= ::=1 1 ::=l1 1 I 1 .• , ::=l1

3) only the design results of the designer

are represented, while the thinking of the designer

is

not

fully

represented,

and

the

relationships

in

and

definitely

inherent

function,

design

logic and

manufacturing between the local components of a machine part, which are given by designer, are not represented.

337

the

Therefore, geometrical modeling scheme not

a

suitable

representation

is

for

the

integration of CAD/CAM. where V is a finite set of N

are

SCHEMES FOR PRODUCT MODELING

used

nonterminals

to

which

primary

represent

features.

FEATURE MODELING V

T

is a finite set of terminals which

are

used to represent subfeatures.

S

Schemes

is the initial graph.

P Feature modeling is developed in mid-1980' to overcome the deficiency of

of

graph

feature

as

entities.

feature is generally defined to be

a

A set

B

where a and

are

of information related to a machine part's

embedding of B which

for

of

design

manufacturing

and

specify how to replace the

inspection purposes, etc •• There are

four

types

of

or

features

to

used

be

a set of

E

graphs,

description. The description could be purposes,

productions

geometrical

modeling. It represents a machine part the combinations of

is a finite set

with following form:

usually

logical

is

an

consists

functions

which

subgraph

a

of a graph by another subgraph B.

in

representing a machine part as follows: Components of Information

•

form features (nominal geometry)

•

precision features (allowable deviations from nominal geometry)

• material features (material and condition) •

In feature model i ng scheme, the components of the information of a

machine

part

is

illustrated as follows

composition

technology features (information related to part performance and operation)

IGeometric Structure I

+

All types of features are considered to be frames

whose

defined

in

features

properties

generic advance.

are

used

Among as

the

primary

fundamental

features

can

be

thought

of

the

major

shape.

that is, the information of a machine part

primary as

shapes, while subfeatures are to

divided

subfeatures:

and

.\.

Machine part information

form

representation. Form features are into

are

them,

is

major

alterations

The

decomposed

geometric

structural

graph,

and

component

of a machine part

precision,

form

with a

feature

which records

both

child-parent

links

fe~tures

the

represented

relationship adjacency

graph

links

between

and

part.

features

is

manufacturing which

requirement

described

is

material

with

technology

and

features. In the representation scheme,

of

level geometric structure

precision,

Then,

technology

which

and

primary

and subfeatures which consist

machine

matarial

first

components:

component

represented with form feature relationship

relationships between the local components are

two

into

structure

represented with form

are

the

higher

information

features,

and

is the

thinking of the designer is represented to

defined independently and networked to the

some

form features of the feature

applications such as process planning. But

relationship

graph.

extent,

there are still

which

are

following

favourable

to

problems

from

CAD/CAM:

Form

feature

relationship

fundamental representation

graph,


a

part in feature modeling, can~'be defined by a

web

grammar

or

the

machine

1)

formally

the

geometric

manufacturing

undirected

information

information

are

separated artificially, and the

graph grammar(Fu, 1982) as follows

still attached to the former;

338

and still

later

is

2) the information of a

machine

part

organized completely on the basis

is

of

is the part to be represented.

the

form feature relationship graph, thus only the

geometric

between the local components of a part

fully

are

can

machine

represented,

technology

manufacturing

The formal description of logical modeling

relationships

structure

be

where D

represented,

to

which

is

such

as

applications

V

is a finite set of the domains is a finite set including

modeling

is

a

scheme, the fundamental

following

newer

modeling

modeling

theory,

the formal description of modeling

the

of

the

nonterminal

vocabularies, vocabulary

V

N

and terminal vocabulary V . V, v and T N VT are used to represent PC, CPC and EPC, respectively. Associated with each

scheme

and the practical applications in

of

attributes of V;

process planning. Feature

the

the

between the local components are not fully unfavourable

with

relationships

and

definitely

implemented

grammar :

CAD/CAM

vocabulary in V are a symbol S

and

attribute frame A. The frame A is

are to be investigated.

an used

to describe the attributes of PC .

P SCHEMES FOR PRODUCT MODELING

is a finite

productions. P contains two parts: symbol producing rule (syntactic rule) SR and attribute computing rule (semantic rule) AR, as follows: Each

LOGICAL MODELING

set

of

production

in

the

Schemes (SR)

V

m

Logical

modeling

is

developed

authors(Tang, 1990) from

the

by

the

integration

of CAD/CAM. In the scheme, a machine is represented as the logical of Part

Components

(AR)

part where V 0- VN and Vk- V (k=l,

combination

Part

hierarchically .

••• t

m)

the vocabularies; w (q=l,

1)

q

Component (PC) is a logical component with

the

attribute

computing

rules.

are is The

attributes which are used to represent the

production is used to represent logical

form features, manufacturing

combinative relationships

and adjacent links of the it is

logically

requirements

component,

provided

with

and

where

relative

SR

relationships

is

between

for

and

structural for

AR

PCs

attribute

independence and consistence in

function,

relationships. The production

provides

Part

Component

the producing

rules

language

defined by G L is a finite

set

design and manufacturing. divided

Compound

Part Component (CPC) and Element Part Component

can

be

into

(EPC). Compound Part Component is Component which is logically other

Part

Components

and

subdivided, Element Part

F

functions

defined

composed

of

auxiliary

procedures

able

be

to

Component

represented

combination

is

as

supporting a , for

supporting

the



and

as the logical Hole_Set>

(CPC)

combination and

CPCs,

and

attached

the to

A

vocabulary

corresponding

number

of

productions and vocabularies which can

a

large

be

fixing,

knowledge

base.

represented of


In

Components of Information

of part

a

In

representation tree, the nonterminal nodes (interior nodes) are

D

stored in a part representation



(EPC) .

is the start

The grammar may have

for

represented as the logical combination

auxiliary

the

over

to the part to be represented.

(CPC)

etc .. can be again

the

which are used by the productions.

Vs

a

logical

(CPC)

of

of

Part

a

Part Component which is logically unable to be subdivided. For example, a box-type part can be

of

the

terminal

nodes (tree leaves) are EPCs and the

logical

information

modeling of

a

scheme, machine

all

the

part

are

represented at the same level. Because the information

root

339

of

the

machine

part

is

represented and organized Components on have

various

consistence

in

the

design

Part

ACKNOWLEDGEMENTS

which and

We would like to acknowledge

design

and

of

results

and

Zhejiang Province,

function,

manufacturing,

the

independence

relative

the

with

hierarchies

the

Natural

support

Foundation

China.

Any

findings,

represented and able to be

this publication are those of the authors.

directly

conclusions

of

opinions,

design thinking of the designer are ' fully used

and

Science

the

expressed

in

in manufacturing. modeling

Thus, logical the

problems

of

scheme

overcomes

preceding

modeling

REFERENCES Requicha,A.A.G.(1980). Representations for

schemes, and is a best tool representing a machine

part

CAD/CAM,

for

the

especially

integration

for

the

Rigid

of

knowledge

Solids:

Theory,

Methods,

Shah,J.J. and Rogers,M.T.(1988).Functional

based integration of CAD/CAM.

Requirements and Conceptual Design the ~

information computer,

of

a

product

product

modeling

is

the

from

schemes to

of

System, Journal,

1988, 9-15. Study

on

Product

Modeling and Expert System for Process Planning Theory,

The

Based

PhD

Formal

Language

Dissertation,

on

Zhejiang

for

University, Hangzhou, P . R. China.

and

Aho,A.V. and Ullman,J.D.(1968). The Theory

realize

of

language

formal

Modeling

Engineering

Tang Renzhong(1990). A

provided

linguistics,

dominant with

the

within

characteristics.

characterizes

modeling

transfer part

modeling

proposes that it is product

and

machine

with the linguistic paper

Feature-Based

Computer-Aided

CONCLUSIONS As a tool to represent

and

Systems, Computer Surveys,l£i 437-464.

Language,

Theory,

theory.

£L

Mathematical

System

97-125.

Knuth,D.E.(1968).Semantics of Context-Free Languages, Mathematical System Theory,

Logical modeling is a scheme

for

£L

product

modeling directly based on formal language theory,

it

can

represent

all

the

information of a machine

part

rationally

and effectively,

best

among

it

is

127-145.

Fu,K.S.(1982). Recognition

Syntactic and

Pattern application,

Englewood Cliffs, N.J. : Prentice-Hall.

the

three major types of product modeling from the integration of CAD/CAM.

340