Supporting Creative Mechanical DesignKun Sun and Boi Faltings

Artificial IntelligenceLaboratory (LIA)Swiss FederalInstitute of Technology(EPFL)

IN - Ecublens, 1015 Lausanne,Switzerland

Fax: +41-21-693-5225e-mail: sun©lia.di.epfi.ch

Abstract

Knowledge-basedCAD systemslimit designers’creativity by constrainingthem to work with theprototypesprovided by the systems’ knowledgebases. We investigateknowledge-basedCAD sys-temscapableof supportingcreativedesignsin theexampledomainof elementarymechanisms.

We presenta techniquebasedon qualitativeex-planations which allows a designer to extendthe knowledge baseby demonstratinga struc-ture which implements a function in a creativeway. Structureis defined as the geometryof theparts, and function using a generallogical lan-guagebasedon qualitativephysics.We arguethatthe techniquecan accommodateany creative de-sign in the exampledomain, andwe demonstratethe techniqueusing an exampleof a creativede-sign.

The useof qualitativephysicsasa tool for extensi-bleknowledge-basedsystemspoints out anew andpromising applicationareafor qualitativephysics.

IntroductionWe consider those knowledge-basedCAD systemswhere designerscancomposedesignsfrom alibrary ofprototypes([Gero,90])which the CAD system“knows”how to instantiateand adapt during the design pro-cess. Such systemslimit designers’creativity by con-strainingthem to designswhichcanbe constructedascombinationsof prototypes provided by the systemsknowledgebase. Creativeideasoften fall outsidethisscopeandthuscannotbe accommodatedin suchasys-tem.

We would like to proposethat a design is creativeif cannotbe composedexactlyfrom the prototypesinthe system’sknowledgebase. The CAD systemsup-portscreativedesign if it allows the designerto definenovel prototypesto cover his ideas. It is creativeifit discoversnew prototypesby itself. New prototypesare createdby envisioningthe prototypesof knowledgebasein adifferent environment.

The techniqueswe describein this paperallow de-signersto extenda prototypebaseby providing:

• amodel of thefunction that their creativeideasad-dress, expressedin agenerallogical languagebasedon qualitativephysics.

• a geometricmodel of adevice that implementsthisfunction.

The system envisions the qualitativebehavior of thedevice and identifies the behavior which implementsthe functionthat the designerintends. Thisallows thesystemto explain and generalizethe idea, and definea new prototype for it. The new prototypecan thenbe instantiatedin anynovel devicethe designermightwant to constructwith it. Note that the examplede-vice given by the designercanbe very different fromthe devicewherethe creativeideawill be used.Forex-ample,abehaviorobservedin rockscould be reusedinthe design of a mechanism.If the representationlan-guagesusedfor structureand function are sufficientlygeneral,our techniqueis guaranteedto cover any cre-ative designwhich designersmight propose.

Creativity is generally associatedwith extendinga spaceof design alternativesor variables([Gero,92,Sargent,92]).Suchextensionsare alwayspossibleonlyif the spaceof possibleprototypesis unbounded.Thisis the caseonly if

(i) the set of possiblefunctionsis infinite,

(ii) the set of structureswhich can implementthem isinfinite, and

(iii) thereis no context-freemappingbetweenprimitivesof structureandfunction which would allow compo-sition of anyprototypefrom a small set of primitiveones.

One such domain is designing geometricshapeswhich implementkinematic functions. For kinematicfunction,we defineagenerativequalitativerepresenta-tion languagewhich allows an infinite set of differentexpressions.We representshapesby polygons,whichallow aninfinite set of shapes.Kinematicfunctionsaregeneratedby contactsbetweenshapes,and therethusexistsa direct mappingbetweenelementaryfunctions

Y

Figure 1: Composingprototypesinto a novel device.

and structures. To satisfy requirement(iii), we mustshow that this mappingis not context-free,i.e. thatthe function of a particular structureis not indepen-dent of the context it is used in. Becauseof interac-tions through the geometryof the shapes,this is thecase. As an example,considerthe design of a devicewhich preventsa block from dropping in the negativeY-direction,a function which could be representedas:

behavior:Y(A) � 0

This function can be composedfrom two prototypesimplementedby singlecontacts,shown in Figure 1 (a)andspecified as follows:

• Device-i (A, B1)

behavior: Y(A) = E) —~ X(B1) = o• Device-2 (A, B

2)

behavior: Y(A) = —* X(B2) = ED

The classicalabductivereasoningsays that if weknow ~3andc~—÷ j3, then the bestexplanationfor /3 isthat & is true. It meansthat creativedesign canalsobe consideredas finding the best explanationfor thedesign goal.

We canexpect the knowledge-basedCAD systemtobe capableof proposing a compositionwhere B1B2 B, basedon the following abductivereasoning:

• Y(A) ~ 0 if Y(A) 0 implies a contradiction.

• X(B) = 0 andX(B) Gi is a contradiction.

However, not all waysof composingthe two devicesactually lead to the composedfunction. For exam-ple, the compositionof Figure 1 (b) is legal, but inFigure 1 (c) both contactscan not occur simultane-ously andthusthe device doesnot implementthe de-sired function. This problem occurswhenevera con-tact can be subsumedby another.To satisfy the com-posed function, the device has to satisfy a composi-tional constraint(Figure1(d))which becomeapparentonly whenthe contextof the deviceis known. But thisalso meansthat the compositionof severalprototypesdefinesa new and different prototype which was notknown before. Thus, in designswhich involve geome-try thereis no direct mappingbetweenfunctions andstructures,and such situationsallow creativedesignsevenwithin fizedrepresentationlanguagesfor structureand function.

Now assumethat a designerhasdecided to imple-ment thesupportfunctionby combiningthe two proto-types, a designwhich the CAD systemdoesnot knowabout. As the system’s knowledgeis insufficient toguaranteethat the prototypecompositionwill work asexpected- the systemdoes not know the differencebetweencases (b) and (c) in Figure 1 - the designerhimself must draw a correctsolution. By qualitativeanalysisof the device, our systemthen computesacausalezplanationof theway it implementsthe givenfunction. In particular, this explanationwill show theadditional constraint which has to be satisfied in or-der to avoid the subsumptionin Figure 1 (c). Thisexplanationis now usedto automaticallydefinea newprototype which is addedto the systemsknowledgebase.

The systemcould be made creative by itself if itwere providedwith a mechanismfor exploring possi-ble functionsandgeometricstructures.However,sucha processmustbe guided by an evaluationof the in-terestingnessof functions, known to be a very hardproblemin the learningcommunity. When a desiredfunction is given, it is sometimespossible to use thisto guide the processof exploration( [Faltings,92b]).

A more complex example of a kinematic pair isa clock escapement,shown in Figure 2. Usingthe theory of qualitative kinematics ( [Faltings,90,Forbus et al.,9i]), the qualitative behaviorand func-tion of any kinematicpair can be computed.Further-more, it is possibleto invert the computationto deter-minethe limits up to which it is valid ( [Faltings,92a})andthus the explanationneededto define anew pro-totype. Our techniquesconcentrateon the conceptualdesignstagewhere creativity takesplace. Subsequentdetail design can further optimize the dimensionstoaccommodatenon-qualitativespecifications.

Ourwork builds on theideaof prototypes([Gero,90]),but isalso influencedby work on designsystemsusingmodel-basedabductivereasoning(for example:[Williams,90],[Neville and Weld, 92], [Sycaraand Navinchandra,90]).

C d

• Device (A, B)

Pawl

Scape wheel

Figure 2: Am escapementdesign producedusing oursysterrr. The wheel is driven clockwise, and the pawlis attachedto a pendulumwhich createsan oscillationwith constantperiod.

However, existing work on model-baseddesign hasbeen basedon the use of context-independentpro-totypes which do not consider the geometry oftheir composition. Design of kinematic chainsby composing kinematic pairs has been studiedin [Subramanian,93].For certain classesof kinematicpairs, Subramaniangives an algorithm to determinetheir dimensionsand arrangementsin a chain un-der the assumptionof uniform motion. Synthesisof kinematic pairs with considerationsof geometricshapeshas been studiedby Joskowiczand Addanki

[JoskowiczandAddanki,88]), but they only treatedthe trivial casesof convexobjectswhere no subsump-tions andthusno compositionalconstraintscan occur.

We first discussthe representationformalisms un-derlying our technique: a languagefor representingkinematicfunction basedon qualitative physics, anda formalismfor representingshapefeatures. We thenshow how the analysis of a particular device can begeneralizedto definethe shapefeatureswhich are re-sponsiblefor the its function and thusdefine a newprototype,andhow this prototypecanbe used in de-sign. Finally, we give an exampleof a a creativede-sign in which creativeideasdevelopedby observingaratchet mechanismare used to design a novel kind offorward-reversemechanism.

Prototypes for kinematic pair designPrototypesfor kinematicpair designconsistof a qual-itative function anda shapefeaturewhich implementsit. Both must be expressedin a well-defined repre-sentationlanguageso that they can be composedbythe CAD system.For creative design,theselanguagesmustbe generativeandcapableto expressanypossiblefunction or structure. In our system,we usea hierar-chy of representationlanguages,as shownin Figure 3.In this section, we presentthe languageswe use for

model example language~

tativ~~vecto~environmentof use

F = (+1 —1)

functionalfeature VX place(x) 1y...

quantifiedlogicalexpressions

vocabularyplace ~ç’~i~11..behaviorpredicates

configurationspace

contacts

metricdiagram

verticesedgesdimensionsconstraints

Figure 3: Representationsused in our CAD system.Polygonal shapesare representedby a metric diagramconsistingof vertices,edgesand their dimensions.Thisstructure defines a configurationspace of the device,which shows the possible contacts betweenparts. Be-havior predicatesmodelqualitativefeaturesof the con-figuration space, and make up a place vocabularymodel of the space. Finally, functions are defined aslogical ezpressionsinvolving the environmentof u~and theplace vocabulary.

Pendulum

modelingqualitative function andshapefeatures.

Metric diagram representation of shapeShapesare representedusing a metric diagram. Themetricdiagramconsistsof a symbolicstructurewhichdefinesvertices, edgesand metric parametersfor thepositionsof the vertices. In our current implementa-tion, the metric diagramis restrictedto polygons,butcanbe extendedto include circular arcs.A metric di-agramrepresentsseveralobjects,eachof which has awell-defineddegreeof freedom.

Using the metric diagram, a shape feature (whichmayinvolve severalobjects) is definedby:

• a set of vertices andedges,

• the metric parametersassociatedwith them,

• a set of constraintswhich musthold simultaneouslyfor the shapefeatureto be present.

For example,the shapefeature which correspondsto the possibility of the top of theratchetsleverbeingableto touchthe wheel (Figure 3) canbe expressedasfollows:

• must exist: vertices Vi, v2

• constraints: d— ru < r2

A language for modeling qualitativekinematic functionForsupportingcreativedesign,it is crucial to be ableto model any function that adesignermight consider.In thissection,we presenta generativelanguagecapa-ble of representingany kinematic function. Functionis a propertyof behaviorcausedby certainexternalin-fluenceson the device. Forexample,the function of aratchetis to block the motionof wheel in onedirectionwhenthe pawl is forced downwardsand to not blockit in the other direction. We define a set of behaviorpredicatesanda formalism for expressingexternal in-fluenceson mechanisms.Functionsare then definedby logical expressionsconnectingexternal influencesand behaviorpredicates. The languageis similar tolanguageslike CFRL ([Iwasaki et al., 93]), but allowsgenerallogical expressionswhich are requiredto rep-resentmany mechanicalfunctions.

tepresenting qualitative kinematic behaviorfextbooks on the subject explain kinematic behaviorqualitativelyby sequencesof kinematic states.Exam-ples of kinematic statesof a ratchet deviceare shownin Figure 4.

In qualitativephysics terminology, a graph of kine-maticstatesand transitionsis called an envisionment.It can be computed basedon a place vocabulary, agraph where each node representsa different combi-nation of contact relationships, and each arc repre-sentsa potential transition betweenthem. The en-visionment is obtainedby combiningeachnode of theplace vocabulary with assumedmotionsand keeping

A

E

Figure 4: Ezamplesof kinematicstatesand transitionsin a ratchet.

only the statesand transitions consistentwith exter-nal forcesandmotions. We havedevelopedandimple-mentedcompletealgorithms to computeplacevocab-ulariesfor arbitrary two-dimensionalhigherkinematicpairs in fixed-axismechanisms.Thesehavebeenusedto computeenvisionmentsfor anumberof mechanisms,such asamechanicalclock ([Forbus et al.,91]).

Behavior predicates We representplace vocabu-laries usinga set of behaviorpredicateswhich charac-terizeplaces,theirfeaturesandtheir connectivity. Fora kinematicpair, the placevocabularydefinesagraphcontainingthreetypes of kinematicstates,correspond-ing to two, oneandno contacts,andidentified by thefollowing behaviorpredicates:

• point-place(x): the contactsin x hold only in asingleconfiguration.

• edge-place(x): the contacts in x hold in a one-dimensionalset of configurations.

• face-place(x):x is a placewithoutany contactsandtwo-degreesof freedom.

For each place, the place vocabulary defines the al-lowedqualitativedirectionsof motion:

• qualitative-motion(d): d is a qualitative vector(d

0, d

1) whosecomponentsindicatethe direction of

motion of eachobject: d~E {—, 0, +}.

• allowed-motion(x,d): motion d is possibleevery-where in placex.

For eachlink betweenstates,the place vocabularyde-fines the directionswhich can causea transition:

• transition(x,y,d): motion d can causea transitionfrom placex to y.

D

Qualitative motions The kinematic states of amechanismare obtainedby combining each place nwith its maximalset of possiblequalitativemotions:

Maii(n) = {m I allowed-motion(n,m)}.

In an actualbehavior,only thosemotionsM(z) whichin fact causedby an externalinfluence actually occur.The set of transitionsbetweenstatesis the set:

Tm = { (n,y) (3d E M(n)) transition(n,y,d)

More details on envisioning mechanismsusing placevocabulariescan be found in [Nielsen,88].

Representing external influence In kinematicpairs, external influencescan be either forces, repre-sentedby a set~ of qualitativevectors,or motions,representedby a setMa

35alsoconsistingof qualitative

vectors. Sincea qualitative force vector causesaqual-itative motion in the directionof the samevector,theset of possiblemotions M

1causedby external forces

is then given as:

= {v I V E ~Fass }The actual set of motions M(n) to be consideredinstaten is then:

M(n) = Mass(n) fl Mj fl Mal~(2~)

Formulating functions Functionsarepropertiesofbehaviorunder certain environment. In our system,they are the assumedforces and motions. Therefore,qualitative functions can be defined as logical condi-tions on placevocabularieswithout first constructingthequalitativebehavior. Using logical expressionsonthe behaviorpredicateswhich representthe placevo-cabulary,aset of functions can be definedas requiredfor theapplication,andextendedwheneverrequiredtoexpressa new specification. For example,somefunc-tions our currentprototype systemusesare:

• transmitting-place(z, dir1

, dir2

):(Vd = (d

1,d

2)){d

1= dir

1~ d

2= dir

2}A{d

2=

—dir2

=~d~.= —diri}

• blocking-place(z):-i(3d E M (z))allowed-motion(z, d)(a place blocks motionsif it doesnot allow any ofthe assumedmotions).

• partial-blocking-place(n, dirs):-i(3d ~ dirs)allowed-motion(x, d)(a partial blocking place blocks the specified mo-tions)

• possible-path(no, na):(xo=n~)V3S~(no,nu,n

2,...,z~)(Vi< n)(3d~

M(z~))transition(n~,n~+i,d)(There is a path from placeno to placen~wheneverthereis asequenceof placeswith transitionsbetweenthem under at least oneassumedmotion)

• cycle(zo,C):C = (zo,xi,n2,. . .,zn,no) (Vn~ E C)(3d fiM(xt))transition(n~, nmod(i+1,n÷1),d)(there is acycle of statesC suchthat transitionsbe-tweensubsequentstatesareconsistentwith assumedandallowed directionsof motion.)

A place vocabularycan only fulfill the requiredfunc-tions if the numberof statesandtheir connectednessissufficient. Reasoningaboutsuch topological featuresisdifficult in the placevocabularyitself, since it is basedonly on individual boundariesof shapeswhich cannotbe modified individually. We usean explicit represen-tation of the kinematictopology([Faltings et al.,89]) ofthe mechanismto detect caseswhere the topology ofparticular object shapeswould not permit the speci-fied function. An exampleof afunction definedon thebasisof kinematic topology is:

• cycle-topology(c,di,d2): if the first or secondob-ject haverotational freedom, the cycle involves d

1rotations of the first or d

2rotations of the second

object. This predicateis defineddirectly on thekine-matictopology of the mechanism.

which can be defined formally using similar behaviorpredicatesas thosewhich define placevocabularies.

The function of aratchet can now be definedquali-tatively as follows:For all starting statesa in which the orientationof thelever is in the interval [0. .ir] (pointing to the left suchthat the momentgravity exerts on it is positive):

• for Mass={(+, *)} A .‘Fass {(*, +)} (the “i” standsfor either +, 0 or -):- cycle(a,C) A cycle..topology(c,1, 0)- —i(3z)blocking-place(n)A possible-path(a,n)(assumingthat the wheelturnscounterclockwiseandthe lever is forced onto it, there is a cycle of stateswherethe wheel can rotate, andno reachableblock-ing statefrom any starting state a.)

• for M(z)={(—, *)} A Fass—~{(*, +)}:- (Vy)possible-path(a, y) =~{-icycle(y) A(3z)(blocking-state(z) A possible~path(y,z))}(assuming that the wheel turns clockwise, no reach-ablestateleadsto a cycle andall statescaneventu-ally leadto a blocking state).

Notethat due to the ambiguitiesinherentin qualita-tive envisionments,theformalismalwaysovergeneratcbehaviors. It is thereforeonly possible to define necessary, but neversufficient specificationsof behaviorand, consequently,function. For example,we canex-pressthe specificationthat clockwise motion leads toa blocking stateonly in an indirect manner: if there isno possibility to cycle, andthereis at leastonereach-able blocking state, the device must eventually reachthis state.

Creating and using new prototypesExplaining functions New prototypesare definedby generalizinga particular device which implements

Shape: Metric Diagram

Figure 5: Analysis of a device defines a place vocab-ulary as a set of features, for examplethe possibilityof touch betweenthe tip of the lever and thebottom ofthewheelsteeth. Suchfeaturesdefinemetricpredicatessuch as the oneshown.

a novel function. The generalizationis basedon anexplanationof the function in termsof the structureofthe device.

A function is aquantifiedlogical expressionof behav-ior predicatesdefined on the placevocabulary. Whenthe function is implementedin a device,the envision-ment defines a set of behavior predicates. Amongthesepredicates,there is at least one logical conjunc-tion which satisfies the quantified condition definingthefunction:

functional feature~

behavior-pred1A behavior-pred2A

The essenceof acreativeidea is now formally definedby the choice of a particular conjunction of behaviorpredicateswhich satisfy the quantified logical expres-sion definingthefunction. Note that in general,findingall conjunctivepropositionswhich satisfy a quantifiedlogical expressionis a non-computableproblem, thusputting creativity is beyondthe scopeof algorithms.

Defining shape features Analyzing the behaviorof a deviceusinga place vocabularyproducesaset ofbehaviorpredicates. Eachof these predicatesis com-putedbasedon certain propertiesof the geometryofthe device being analyzed(Figure 5). The analysiswhich producedthe behaviorpredicatescan begener-alized to constraintswhich the shapemust satisfy inorder for the behavior predicatesto remain present.

Theseconstraints,takentogether,define a qualitativeshapefeaturewhich is associatedto the functional fea-ture. That is:

behavior-predi A behavior-pred2A ...

constraintson shapes~ shapefeature

Reversing the causal chain of the analysis thus es-tablishesamappingfrom functional featuresto shapefeatures,and we call such a process causal inversion.More detailson the mappingbetweenshapeandqual-itative behaviorcanbefound in [Faltings,92a].

For any functional feature identified in the placevo-cabularyof a device, we can thus construct a corre-sponding shapefeature which implements it. Theseshapefeatures, indexed by the functions, form newprototypeswhich areaddedto the system’sknowledgebase.

Kinematic pair design with prototypesA kinematic pair is specifiedby aconjunctionof qual-itative functions. Structureswhich satisfy thesefunc-tions are obtainedby combiningprototypesfrom thesystemsknowledge basesuch that all required func-tions are covered. Combining prototypesmeanscom-bining shapefeaturesusingthe following steps:

1. choose a unification of vertices and edgesof theshapefeaturesdefinedin the prototypes.

2. instantiatethecOnstraintsassociatedwith the shapefeatures and find a solution to the resulting con-straint network.

3. envision the solution to determine compositionalconstraintswhich must alsobe considered,addthemto the constraintnetwork and iteratefrom step(2).

This processposestwo major difficulties: satisfyingthe dynamic constraint network, and discoveringandaddingcompositionalconstraints.

Constraint satisfaction The constraint networkfor combiningshapefeaturesis dynamicand involvesmany nonlinear constraints. No reliable and efficientmethodexistsfor solvingsuchconstraintnetworks. Inour current prototype, we use a processof iterativerefinementwhere an initial partial solution, given forexampleby the deviceusedto define the prototype,isincrementally modified until all constraintsare satis-fied. The refinementprocessusestwo typesof modifi-cationoperators:

• dimensionalmodifications,where the dimensionsofpartsareadjustedto fit thefunctional requirements,and

• topological modifications, where vertices are addedto part shapes.A topological modificationis alwayscoupled with a dimensionalmodification to fix thedimensionsof thenew features.

v4

dvi

dv2v3

hape FeaturesMetric Predicates:e.g.,dv3+dv5>d

Functional Features:e.g., v3 can touch v5

Function:

Figure 6: Inferring a compositionalconstraintfrom ob-servingthebehaviorof a combinationof shapefeatures.

Dimensionalmodification varies the valuesof dimen-sionalparameters,thuschangingthe appearanceof oneplaceandits properties (for example,inference rule).Topologicalmodificationareproposedwhenthereis nodimensionalmodificationwhich can satisfy additionalconstraints.More detailsaboutthe computationof di-mensionaland topological modificationscan be foundin [Faltings and Sun,93].

Discovering compositional constraints As dis-cussedin the introduction, combinationof shapefea-tures often implies novel interactionswhich result inadditional compositional constraints. In kinematics,the only interactionswe haveto consideraresubsump-tions, where one shapefeaturesmakesthe contact ofanother impossibleor alters the way it occurs. Com-positionalconstraintswhich ensurethe absenceof sub-sumptionscan be formulated most easilyonce asub-sumptionhasbeenobserved. For example,if we ob-servethe subsumptionshownin the introduction (Fig-ure 1), we can infer anovel compositionalconstraintasshownin Figure 6 by expressingthe condition that thesubsumingcontactmaynot occursimultaneouslywiththesubsumedcontact asanalgebraicinequality. Sub-sumptionconstraintsare relatively simple expressionsin the case of translational motion, but can be con-siderablymore complexin the caseof kinematic pairs

Creative design of a forward-reversemechanism by composition

As anexampleof usingcompositionfor creativedesign,we showhow a novel forward-reversemechanismcanbe conceivedby composingtwo ratchets.

A forward-reversemechanismis used to transforman oscillating motion into a rotation which advancesin one direction and, after a period of rest, reversesthemotion to alesserdegree.A solution for this prob-lem in the literature ([Newell and Horton,67]) is shownin Figure 7. It uses4 partsandafriction-basedmech-anismwhich is problematicfor maintenance.

Using the functional features defined earlier, thefunction of a mechanismwith forward-reversemove-ments can be specified as follows:

1. (~arrayX= {xo, x~,x~,. . ., x~~i}) of states such

that:(Vx~ E X)transmitting-p1ace(z~,(+, —))Aarray-topology(X, 1,0)(Thereis aarray of stateswhich transmitscounter-clockwisemotionof input driver to clockwisemotionof wheel.)

2. (~arrayY = {Yo,Y1,y2,...,Yn—1}) of states suchthat:(Vy~ E Y)transmitting-place(y~,(—, +))Aarray-topology(y, 1,0)(Thereis aarray of stateswhich transmitsclockwisemotionof input driver to counterclockwisemotion ofwheel.)

3. for .Ta88(0,+), Mas.~{(, +), (0, +), (-i-, +)}:(Vx~E X)possible-path(x~,y~),yj e Y(When the input driver changesthe motion fromcounterclockwiseto clockwise, there exists a pathfrom placex~to y~)

4. for F.~3=(0,_), Ma38

{(, _), (0, _), (+, —)}:

Figure 7: A forward-reversemechanismas found in apopularmechanismbook.

involving rotations.

(a)

one contact no contact

I(e)

Figure 8: Creative design of forward-reversemecha-nism by composingtwo ratchets, a), known deviceofstart design. a), b) and c), interesting aspectsof func-tiomalfeaturesdiscoveredby envisionment.d), compo-sition of shapefeatureswith subsumptions.e), iterativesatisfactionof subsumptionconstraints.

(Vy~ Ey)possible-path(y~,Xmod(j+1,n)), xmoa(i+1,n) E ~(When the input driver changesthe motion fromclockwise to counterclockwise, there exists a pathfrom place Yi to the place xmod(i+1,n) in the arrayX.)

5. (Vx~E X)(Vy~E 3)) { disti(y~,Ymod(i+1,n), (+, *)) <

disti(z~,xmod(i41,n), (—, *)) }

(Thecounterclockwisemotion angleof wheel in eachperiod is smaller than its clockwisemotion angle.)

Discovering functional features in theenvisionment

Assumethat thedesignerhasnoticedthataratchetde-vice, when usedin the environmentof forward-reversemechanism,canachievesomeof the requiredfunctions.In an envisionmentof the ratchetsbehaviorin the en-vironmentof the forward-reversemechanism,the de-signer specifies the following correspondencesto thefunctional specifications:

1. there is one array of states,Figure 8 (a), in whichthe lever can drive the wheel. The counterclockwisemotionof the leverturns the wheel clockwise. There-fore, it canbe usedto satisfyfunctional specification(1).

2. there is another array of states, Figure 8 (b), inwhich the levercan also drive the wheel. The clock-wise motion of the lever pushesthe wheel counter-clockwise,which meetsthe requirementof specifica-tion (2).

3. when the lever changesthe motion from counter-clockwiseto clockwise, thereis a possiblepath fromonestate of array X to one state of array 3) in thesameperiod, which fulfills specification(3).

4. when the lever changesthe motion from clockwiseto counterclockwise,thereareno pathsfor satisfyingspecification (4), sincefrom one stateof array 3), itreturns to onestateof array X in the sameperiod.

5. when the wheel is driven by the lever, clockwise andcounterclockwisemotion anglesof the wheel areal-ways equal,which meansthat specification(5) can-not be satisfied.

Thedesignernow searchesfunctional featuresto sat-isfy specifications(4) and (5). For solving thediscrep-ancy with specification (5), the designerhas to adda set of stateswhere motion of the lever results in aclockwise motionof the wheel:

(~arrayZ= {zo,Zi, Z2

, . . . ,Vz~{transmitting-p1ace(z~,(+, *))}Aarray-topology(Z, 1,0)(Statesz transmitssomemotion of the leverto aclockwisemotion of the wheel.)

The envisionmentof the ratchet in fact containssuchan array of statesz, shownin Figure 8 (c). We assumethat the designerdecidesto use this set of statestomakeit possibleto satisfy specification(5). However,(5) refersto thetransitionsdefinedin specification(4),which arenot yet satisfiedin thesimpleratchetdevice.Assumethat the designerdecidesto satisfy specifica-tions (4) and (5) by creating pathspassingthroughintermediatestateschosenfrom thearray Z. He com-municatesthis to the system by identifying in theen-visionmentof a ratchetthe statesz E Z and thetran-sitions which should be connectedto statesin X and3), thus defining the shapefeaturesand their relativepositionsused in the design.

Defining a new prototype

The new prototype consistsof the functional feature,definedby the logical expressiongiven earlier, andthecorrespondingshapefeaturewhich implementsit. Theshapefeatureis definedby the explanationunderlyingthe envisionment.For example,the existenceof statez in Figure 8 (c) can be translatedto the existenceof verticesv

3,V4, v

5, the centerdistanced, andthe fol-

lowing constraints:

Cl: \/~+y~—\/a3~+y~>0

C2’ 2 —d~2

---(dx(4

)+s4

x(va)+y4x(c4

—~s))2

>

0

C3: (xz — x4) x (y~— y4) — (y3 — y4

) x (z5

— 24) > 0

two contacts

(b) (c)

(d)

C4: Z3 x (x~— xs) + (ya — d) x (y~. ys) > 0

Composing prototypesThe functional features havebeen mappedinto twoshapefeatures,eachdefined asa set of constraintsonthe metric diagram of a single ratchet device. Fur-thermore,the identified transitionsimposeconstraintson the relative positions of the shapefeaturesin thecombineddevice. For the output member,thesecanbe satisfied by one and the sameobject, but the in-put driver hasto be a compositionof two levers imple-mentingspecifications(1)-(3)andspecification(4)_(5),respectively. The resulting composeddevice is shownin Figure 8 (d).

Satisfying compositional constraints

Not all compositionalconstraintscan be specifiedbe-fore composition,but manyare only discoveredwhenthe composeddevice is envisioned. For example,thecomposeddevice has subsumptionsas illustrated inFigure 8 (d), wheretips of the levers touchtwo teethof the wheel simultaneously. In this case, the com-posedleversareblocked from further clockwise move-ment. Therefore, the pathsfrom state y to z in thereplacedspecification(4) arebroken. A new subsump-tion constraint is addedto avoid this behavior,start-ing a searchfor a better solution which satisfiesallconstraints.

We have seenthat the constraintsdescribing thestate z and subsumptionsinvolve v

3,v

4, v

5and d,

which are highly nonlinear. Their satisfactionis verydifficult. We attack this problem by an incrementalrefinement. In this example,assumethat the designerchoosesto changevertex v

3to searchfor a solution.

By carryingout a regionsearch,thesystemchangesitsposition to v

3= (7.58,24.00). This resultsin anewde-

vice asshownin Figure 8 (e). Renewedenvisionmentshows that it is in fact a functional forward-reversemechanism,andthe designis finished.

ConclusionsA main shortcomingof knowledge-basedCAD systemsis the fact that precodeddesign knowledgedoes notallow designersto expresstheir creativeideas. In thispaper, we havepresentedan implementedtechniquewhichshowsthat knowledge-basedtechnologyandcre-ativity are not contradictory concepts. Qualitativephysicsprovidesthe extensiblerepresentationsneededto accommodatecreative ideas in a knowledge-basedsystem. Qualitative physics hasexactly the function-ality required for extendingdesign spaces,as postu-lated by many researchersin creative design. Usingmore completedomain modelssuch as developedforIIICAD ([Kiriyama et al.,92]), the techniqueis appli-cableto more generaldomainsthan elementarymech-anisms. This points to a new and asyet unexploitedapplicationof qualitativephysics asa tool to supportextensibleknowledge-basedsystems.

Our current approach is geared towards support-ing creative designs, not generating them automati-

cally. By automatically searchingthe spaceof possi-ble geometricstructures, it would be possibleto con-structafully automatic“creative” system.Such searchmight be made more efficient using a large mecha-nism library and suitableindexing techniquessuch as[Sycaraand Navinchandra,90].However, it is not clearhow sucha generationprocesscould be guidedto onlyfurnish functionalities which are in fact interesting.Oneway to do this might be to provide such a searchwith asetof specificationstakenfrom astandardmech-anismtextbook andaskit to find novelsolutions whichsatisfythem. However, the combinatorialproblemsas-sociatedwith such a searchare considerable,and weconsider that only supporting a designer’screativityhasa greaterpracticalimportance.

References

Boi Faltings,EmmanuelBaechler,Jeff Primus. Rea-soning about KinematicTopology. Proceedingsof the11th International Joint Conferenceon Artificial In-telligence,Detroit, 1989

Boi Faltings. QualitativeKinematicsin Mechanisms.Artificial Intelligence,44(1), 1990

Boi Faltings. A Symbolic Approach to QualitativeKinematics. Artificial Intelligence,56(2), 1992

Boi Faltings. Supporting Creativity in SymbolicComputation. Second International Round-TableConferenceon ComputationalModels of CreativeDe-sign, Heron Island, Queensland,Australia, 1992

Boi Faltings, Kun Sun. Computer-aided CreativeMechanismDesign. Proceedingsof the18th International Joint Conferenceon Artificial In-telligence, Chambery,France, 1993

Ken Forbus,Paul Nielsen,Boi Faltings. QualitativeSpatial Reasoning.theCLOCK Project. Artificial In-telligence, 51(3), 1991

John Gero. Design Prototypes: A Knowledge Rep-resentationSchemafor Design.Al Magazine, 11(4),1990

John Gero. Creativity, emergenceand evolution indesign.SecondInternational Round-TableConferenceon ComputationalModels of Creative Design, HeronIsland, Queensland,Australia, 1992

Y. Iwasaki, R. Fikes,M. Vescovi,B. Chandrasekaran.How things are Intended to Work: Capturing Func-tional Knowledgein DeviceDesign.Proceedingsof the13th International Joint Conferenceon Artificial In-telligence, Chambery,France,1993

Leo Joskowicz,S. Addanki. From Kinematics toShape: An Approach to Innovative Design. Proceed-ings of theAAAI, St.Paul,August 1988

TakashiKiriyama, Tetsuo Tomiyama,Hiroyuki Yoshikawa.Building a PhysicalFeatureDatabasefor Qualitative

Modeling andReasoning,AAAIFaI1 Symposium,De-sign from PhysicalPrinciples, Cambridge,MA, 1992

Dorothy Neville, Daniel S. Weld. Innovative DesignasSystematicSearch,AAAI Fall Symposium,Designfrom PhysicalPrinciples, Cambridge,MA, 1992

John Newell, Holbrook Horton. IngeniousMechanismfor DesignersandInventors, Volume IV.Industrial PressINC, New York, 1967

Paul Nielsen. A Qualitative Approach to Rigid BodyMechanics.Ph. D. Thesis,University of Illinois, 1988.

P.M. Sargent.A computationalview of creativesteps.Second International Round-Table Conference onComputationalModels of CreativeDesign, Heron Is-land, Queensland,Australia, 1992

Devika Subramanian.ConceptualDesign and Artifi-cial Intelligence.Proceedingsof the13th InternationalJoint Conference on Artificial Intelligence, Cham-bery, France, 1993, pp. 800-809

Katia Sycara,D. Navinchandra. Index Transforma-tion Techniquesfor Facilitating CreativeUse of Mul-tiple Cases.Proceedingsof the 12th IJCAI, Sydney,1991

Brian Williams. Interaction-basedInvention: Design-ing Novel Devicesfrom First Principles, Proceedingsof the National Conferenceon Artificial Intelligence,Boston, 1990