Engineering Design Functional Interdependence and Product ... · Functional Interdependence and Product Similarity Based on Customer ... ing functional interdependence provides a

Functional Interdependence and Product Similarity Based on Customer Needs

Daniel A. McAdams1, Robert B. Stone2 and Kristin L. Wood1

1Department of Mechanical Engineering, The University of Texas, Austin, TX;2Department of Basic Engineering, University of Missouri-Rolla, MI, USA

Abstract. In this paper, related product functions aredetermined for a group of approximately 70 consumerproducts. Using customer need data, a new matrix approachis introduced to identify these relationships. Techniques arethen created for determining product similarity. Thesetechniques are clarified and validated through three casestudies, including beverage brewers and material-removalproducts. The results of these case studies are argued to havesignificant impact on design-by-analogy procedures, bench-marking methods, mass customization strategies and modulardesign. The paper concludes with a discussion of applicationsand related procedures for product development.

Keywords: Design-by-analogy; Functional analysis;Mass customization; Modular design

1. Introduction

It is demonstrated in the literature (Hubker and ErnstEder 1988; Ulrich 1995; Pahl and Beitz 1996; Ullman1997) that customer-need-based, functionally-descrip-tive design methodologies are valid and effective. Inthis paper, we build on this philosophical background.We develop a method to determine the occurrence andimportance of interdependent design functions1 ingroups of products. Interdependent functions are thosethat, throughout a set of products, occur in groups andhave a significant impact on customer needs.

1.1. Motivation: The Niche of the Research

To understand the motivation for this research,consider the following questions: Why analyzeproducts at a functional level? Such an approachallows fundamental explorations in design to be

performed independent of and prior to the existenceof form or structure. It also allows us to make a clearconnection between customer needs, function, andform. Such connections are often implicit duringproduct development; we wish to make them explicitand measurable. Why investigate interdependentfunctions; what impact can such methods have onpractical design and design research? The identifica-tion of important interdependent functions in a groupof products impacts product architecture, design byanalogy, benchmarking, modularity, mass customiza-tion and product planning.

With the tools developed in this paper, specificarchitectural and form solutions for interdependentfunctions can be reviewed in a large class of products.Thus, design-by-analogy approaches may extendbeyond singular functional comparisons, yet remainat a fundamental functional level. A designer’scurrent design-by-analogy vocabulary can be ex-tended beyond their immediate experience, providingaccess and contributions to new domains by discover-ing different products with common significantinterdependent functions.

For redesign and product benchmarking efforts, themethod developed here presents a quantitativemeasure of product similarity. This measure allowsa designer to locate products for benchmarking whosesimilarity, or comparability, is not initially clear.

Identifying important interdependent functions in agroup of products locates avenues for modularity thathave an impact beyond a single product. Recognitionof such information enables development andmanufacturing on larger, more efficient, economiesof scale. In addition, modules incorporating over-lapping interdependent functions may be used todevelop product architectures that enable, or simplify,mass customization and bus modularity (Rosenau etal. 1996).

Developing and evaluating modularity at a func-tional level has key advantages over structurally-based modularity. Modules developed post structure

Research in Engineering Design (1999)11:1–19ß 1999 Springer-Verlag London Limited

Research in

EngineeringDesign

Correspondenceand offprint requests to: Dr K. L. Wood,Department of Mechanical Engineering, The University ofTexas,Austin, TX, USA1From here forward, the word ‘function’ will be used inter-changeablyto meanoverall productfunction andsub-function.

are fully dependenton the form of the product,andthusonly the solutionparameterscanbe changed.Ifmodularity is approachedat a functional level, themoduleitself becomesa designparameter.Differentmodulesandmoduleembodimentscan be combinedwith distinct product architecturesand evaluatedduring conceptualdesign.

Also presentedin this paperaretools that assistinproductplanningand resourceallocation.Determin-ing functional interdependenceprovides a solidfoundationfor companiesto explorethedevelopmentof new productsusing their existing, thoughperhapsnot readily evident,expertisein functionally similarproducts.By measuringtheimpactof customerneeds,companiesmay understandtheir competitiveadvan-tage and allocateresourcesfor improvementsalongcritical paths.

1.2. Related Work

Although functional analysisis a commontopic ofresearch,functional interrelationshipshavea limitedtreatmentin the literature.Suh (1990) promotesthedecouplingof function requirementsin design.Theindependenceof functional requirements allowsdesignparametersto havea controllableeffect on aspecificfunctionalrequirementandminimal negativeimpact on other functional requirements.Suh doesnot, however,explore the relationshipbetweensub-functions that are used to achieve an overallfunctional requirement.Johannesson(1996) extendsSuh’s axiomatic approachto functional coupling inmachine design. Johannessondefines functionalcoupling to be the negativeinteractionbetweentwosub-system solutions in achieving a functionalrequirement.His work is largely concernedwith theimpact of a given function solution on otherfunctional requirements,or solutions, and not thespecificfunction interdependency.

1.3. Overview

Thesub-functionrelationshipsexistingin 68 productsareexploredin this paper.The productsinvestigatedcover a wide range of consumer applications,customerneeds,and overall product function. Theproductsaremainlyconsumeroriented,mechanicalorelectro-mechanicaldevices including toys, smallkitchen appliances,small construction tools, andothersmallhouseholdappliances.Thissetof productsrepresentsover onehundredpersonyearsof work inreverseengineeringand redesign.The redesignsand

casestudiesaretakenfrom coursework andresearchat The University of Texas at Austin, as well asproductdevelopmentin industry.

The following section presentsa procedureforfunctional analysis.Using this functional analysis,atechniqueis presentedto groupproductsinto logicalsubsets.Usingthis groupingmethod,theanalysisanddiscussion of two product subsets follows. Thespecificsof function interdependencyandmodularityare explored in detail through casestudies in thissection.Thesecasestudiesalsoprovidevalidationofthe functional interdependencemethod. The paperconcludeswith a generaldiscussionof theresultsandpotentialapplicationsof the procedure.

2. Procedure of Investigation

The goal of this section is to develop a numericalmeasureof the importanceof interdependentfunc-tions for a domainof products.Sucha goal presentstwo problems.First,a domaincomparablemeasureofsingle function importance is needed. Secondly,interdependentfunctionsneedto be identified. Withthese two problems solved, the single functionimportancemeasuremay then be usedto assignedameaningful importancemeasureon the interdepen-dent functions.

To determinethe importanceof a single function,we use the methodologydevelopedby Little et al.(1997).We then extendthe methodologyto identifywhich functionsoccurtogetherandassigna customerneedrelatedimportanceindex.Also presentedin thissectionare methodsto select a set of productsforanalysisandthedeterminationof theresolutionof theinterdependentfunction importance.We presenttheentireprocedurein sufficientdetail so that it may berepeated.Figure1 showstheprocedurein termsof theinputs,steps,andoutputof the overall process.

2.1. Organizing the Functional Product Data

In this subsection,we detail the steps required toorganize the product-function data. To begin,customerneed data and functional descriptions,orfunction structures2, are neededfor eachproduct inthegroup(HubkerandErnstEder1988;Ulrich 1995;PahlandBeitz 1996;Ullman 1997).The first stepinthe procedureis to transform the product functionstructures into a common terminology of basicfunctions and flows. This transformation enables

2A function structure is an abstractgraphicalmappingof inputmaterial,energy,or signalflows to desiredproductoutputflows.

2 D. A. McAdamset al.

comparisonandidentificationof thesamefunction indifferent products.Thesebasic functions and flowsarea basisset:a functionstructurefor a largeclassorproducts can be generatedfrom this finite set offunctionsandflows. AppendixA containsdefinitionsfor the class functions as well as tables of basicfunctions,basic flows, and the correspondingsyno-nyms. The complete formal definitions for thesefunctions and flows, and a detailed example of afunction structure transformation,are presentedinLittle et al. (1997).

With product functionality described using aconsistentterminology, the function structuresarenow reviewed and revised in the next step. Thefunction structuresare updatedto expressan equallevelof complexityanddetail in thefunctionalmodel.For thedatasetof 68 productsanalyzedin this paper,the product complexity required approximately20functions for a completefunctional description.Theproductscannow beaccuratelycomparedat a purelyfunctionallevel astheyareexpressedwith a commonterminologyandanequallevel of functionaldetail inrepresentation.

Customerneedweightsare usedto determinethefunctionalimportance.Beforerelatingcustomerneedsto functions,customer-needratingsfor eachproductare translatedto a scaleof 1 (‘optional’) to 5 (‘musthave’), using an appropriatemethod (Otto 1996).Recappingthe procedurethus far, all the functionstructuresare representedusinga commonterminol-ogyandall thecustomerneedweightsarerankedonacommonscale.Next,functionsarerelatedto customerneedsandassigneda numericalimportance.

To determinethe importanceof a function, theimpactof a functionon a customerneedis evaluated.If a functionaffectsa specificcustomerneed,thentheweight of that customer need is assignedto theimportancevalueof thatfunction.Proceedingthrougheach customer need, the assignedcustomer needweights are summed to determine the functionimportance.

It is importantthat thedesigneraccuratelyassessestherelationshipbetweencustomerneedsandfunctionssothatfunctionsareappropriatelyweighted.To assurethat the function importancevalue is accurateandrepeatable,a two stage processis used. First, thematerial,energy,and signal flows from the functionstructure are assignedto the appropriatecustomerneeds.For example,a customerneedfor ‘quiet opera-tion’ is relatedto theflow of acousticenergy.After thecustomerneedflow assignment,flows are relatedtofunctionsby following thepathof theflow throughthefunctionstructure.In thismanner,functionsarerelatedto flows,andin turn to customerneeds.

A summaryof the processso far is most easilyexpressedby recognizingthesimilarity of thecurrentproduct-functionrepresentationwith a vector space.At thispoint,eachproductis representablein asimplemanneras a vector. Each elementof this functionvector is the importancemeasureof that function.Similarly, thefunctionvectorsnaturallyassembleintoa product-functionmatrix. This matrix representationprovidesa clear and compactway of reviewing thedata. Also, this approach to data organizationfacilitatescomputationson the importancemeasures.

Before assemblingthe vectors into a product-functionmatrix,weaddthevalueof one(1) to eachofthe function importance values. This shift isperformed so that the product vectors may beassembledinto a matrix. In the product-functionmatrix, the functionsthata productdoesnot havearerepresentedby a zero.The function importancescaleis now a 1 to 6 point scale. Functions with animportanceof 1 – those not directly related to acustomerneed– aresupportingfunctions.A functionimportancevalueof 6 or higherindicatesanessential,or highly important, function. Valuesgreaterthan 6can occur when one function relates to severalcustomerneeds.

The product-functionmatrix, �, is a mxn (m totaldifferent functions,n products)matrix. Eachelement�i j is thecumulativecustomer-needimportanceof the

Fig. 1. The stepsfor determiningthe productinterdependentfunctions.

Inputproduct functional descriptions

customer needs

Outputcustomer weighted function

chain importance

Organize ProductFunctional Data

Select ProductSubsets

Find ImportantInterdependent Functions

transform to basic functionsreview and equalize function structure

complexityrank customer needs on a 1-5 scalecorrelate customer needs to functionsassemble product function matrixnormalize the product function vectors

determine functional similarityform product similarity matrixcalculate function vector inner products

follow energy conversionor

form the function-function matrixrescale matrix elements

FunctionalInterdependenceandProductSimilarity Basedon CustomerNeeds 3

ith function for the jth product.� matricesfor twosubsetsof products are shown in Appendix B asexamplesof the resultof the procedurethusfar3.

Different product complexity and customer en-thusiasm (during the customer need acquisitionprocess)will affect the magnitudeof the �i j ’s foreachproduct.To compensatefor thesedifferences,�is normalized to validate comparisons betweenproducts. The philosophy used to normalize thefunction-productmatrix consistsof two complimen-tary aspects:

1. all productsare of equal importance(to compareproducts),and

2. productswith more functionsare more complex;thus the customer-needrankingsmust be normal-ized to compensatefor varying complexity.

First, to equalizeproducts,thecustomer-needvalueofeach function is scaledso that the sum of a givenproduct’s importancelevel is equal to the averagesumof thecustomerneedimportancefor all products.Secondly, to representvarying levels of productcomplexity, each product function is scaledby theratio of thenumberof functionsin thatproductto theaveragenumberof functionsper product.

Implementingthesestepsprecisely,theelementsofN, the normalizedversionof �, are

�ij � �ij

��

�j

��j

�

��1�

The averagecustomerneedis

� � 1n

Xm

i�1

Xn

j�1

�ij �2�

The total customerneedfor the jth productis

�j �Xm

i�1

�ij �3�

The numberof functionsin the jth productis

�j �Xm

i�1

H��ij � �4�

andthe averagenumberof functionsis

� � 1n

Xm

i�1

Xn

j�1

H��ij � �5�

H is a Heaviside function, n is the number ofproducts, and m is the total number of differentfunctionsfor all products.

2.2. SelectingData Setsfor Investigation

Before determining function relationshipsand im-portanceacrossa groupof products,we presenttwotechniquesfor reducing the product domain to asubsetof products.By so doing, we will be able toidentify potentialproductfamilies.First,we presentaproduct hierarchy based on the primary flow ofenergy,andenergyconversions,throughthe productsystem. The second technique uses customerweighted product sub-function similarity to createproductsubsets.

Figure 2 showsa producthierarchybasedon theenergy conversion technique.The primary energyinput is followedthroughtheproductuntil it leaves.Ahierarchical distinction is made at each energyconversion.A bottomlevel in thehierarchyrepresentsproducts with common energy conversions. Forexample,in Fig. 2, the primary energyinput chosenis electricity. In Section4, function relationshipsareinvestigated for the electricity?heat?materialgroup.

An alternative approachfor identifying productdomainsis to determinesub-functionsimilarity acrossa set of products.We use the function vector-spacerepresentation,N, to calculate this similarity. Theproductvectorsfrom Eq. (1) arerenormalizedso thattheir normis 1. We thencalculatetheinnerproductofthe normalizedproductvectorsfor eachcombinationof products.Forming the inner product betweenaproducta anda productb, a � b, givestheprojectionof producta on productb. Formingthe inner productof a product with itself (the completely similarproduct)givesa valueof 1; forming theinnerproductof a product with one that shares no commonfunctionsyields a resultof zero.

A matrix of theseprojectionsis

� � N TN �6�N is the matrix of unity normalizedproductvectors,similar to N. Eachelement,�ij , is theprojectionof theith product on the jth product. � is the productsimilarity matrix.Usingmatrix multiplication to formtheproductsimilarity matrix �, andcoupledfunctionimportancematrixSS (presentedbelow),is similar to atechniqueTaylor (1996)usedto determinetopicsandfrequencies of discussion on internet newsgroupcommunicationin studentdesignteams.

Table1 is a subsetof productsgeneratedusingthefunctional similarity method.The subset-generatingproduct is a Dewalt hand held palm sander.Theproductsin Table 1 are those,of all 68 reviewedinthis study, with the 12 largestprojectionsonto thehandsander.

3The techniquesused to select these subsetsfrom the entireproductsetarepresentedlater in this paper.


For any set of products,a conglomerateproductcan be constructed.The conglomerateproduct isdefinedas a vector in the sub-functionspace,whereeachscalarcomponentof the vector is

p0i �Xn

j�1

�ij �7�

The vector p' is then unity normalizedgiving theconglomerateproduct vector p. The conglomerateproduct represents the customer need weightedfunctionality of the entire product domain. Anapplicationfor the conglomerateproductis discussedin Section4.

2.3.Creating the Function-Function Matrix andSolving for Function Chains

In this subsection,we presentthe final portion of theprocess:the computationsfor finding the importantfunctiongroupsareintroduced.To determineproductfunction relationshipsthroughouta domain, repeat-edly occurringfunction groupswith a high customerneed are found. These function chains are thencategorizedbasedon commonflows in the group offunctions.

Thefirst stepin determiningfunctiondependenciesis to form the function-function matrix, SS. Theconstruction begins with the formation of theunscaledfunction importancematrix SS0. Let

SS0 = NNT (8)

Electricity

Bubble Toy

Liquid

Vacuum

Fan

Hair Dryer

Power Blower

Gas

Massage Device

Solid

Bumble Ball Paint Roller

Liquid Solid

MaterialMaterial

Pneumatic

Material MaterialSignal

Vibration Hydraulic Translation

Toy Car

Convert

Weed Trimmer

Lawn Mower

Sander

Elec. Toothbrush

Can Opener

Pencil Sharpener

Real Power Tool Shop

Non-Food

Mixer

Blender

Food Processor

Cheese Grater

Veg. Stripper

Pasta Machine

Food

Solid

Material

Rotation

Signal

Metronome

Status

Elec. Screwdriver

Solid

Material

ConvertMaterial

Solid

Stun Gun

Thermal E. Force

Solid

Material

Putting Cup

Elec. Stapler

Material

Solid

Iron

Solder Iron

Sandwich Maker

Elec. Wok

Popcorn Poper

Crock Pot

Liquid

Coffee Maker

Iced Tea Maker

Humidifier

Deep Fryer

Thermal E.

Function Flow Product

key

Status

Video Tape Rewinder

Hot Glue Gun

Air Compressor

Hand Vacuum

Power Calk Toy Truck

Investigatedsubset

Fig. 2. Producthierarchy for productswith electricity asa primary input flow. Underlinedproductsare investigatedin this study.

Table 1. Product subset based on customer weightedfunctionalsimilarity to the palm sander

Product Projection

palm sander 1.000000fruit & veggiepeeler 0.808powerscrewdriver 0.797oscillatingsander 0.791electricknife 0.753handvacuum 0.752mini pro hair dryer 0.730electriccanopener 0.718electricpolisher 0.708handblender 0.688toy fishing reel 0.673electricpencil sharpener 0.668


Eachelementof SS0 is

s0ij �Xn

p�1

�ip�jp �9�

where n is the number of products.Note that theindicesof thesecondtermarejp (asopposedto pj) asa result of multiplication by the transposeof N.Therefore,each term in the sum of Eq. (9) is themultiplicative productof the ith function and the jthfunction for the pth product. The function chaincustomer importance, sij clearly relies on theexistence of both functions in a product. For aproduct to makea non-zerocontribution to sij , bothfunctionsmustappearin that product.

To maintainthe customerneedscalemagnitudeof6, the squareroot of the multiplicative product�ip�jp

is taken. The sum is divided by the number ofproducts,n. Equation(9) now becomes

sij � 1n

Xn

p�1

��ip�jpp �10�

Let SS be a mxm matrix with elementssij . SS is thecoupledfunction, or two function chain, importancematrix. Each sij is the customerimportanceof thecombinationof the ith functionandthe jth functioninadomainof products.Themeasureof s is ona6 pointscale,where 6 is must have,and 1 is a supportingfunctioncombination.For example,if s37 hasa valueof 6, the combinationof the functions3 and 7 is onaveragea ‘must’ for all productsanalyzed.

Equation (10) extendseasily to more than twofunctions.To determinethethreefunctionchains,Eq.(10) becomes

sijk � 1n

Xn

p�1

��ip�jp�kp

3p �11�

The interpretationof this relationshipis similar tothe two function case.Here, each element of thetensor,sijk , is the productof the i,j andkth functionscustomerneedrank, summedover all products.If aproduct does not contain all three functions, thecontributionto sijk is zero.

2.3.1.TheResolutionof sijThe initial customer importance ranking has aresolution of 1, on an integer 6 point scale. Thearithmeticmanipulationin Eqs(1) through(10) leadsto s valuesthatarenot integers.Initially, a discerniblecustomerneedshavea resolutionof 1. The questionarises:how doeschanginga customerneedrank in �by onepoint of resolution(1) affect a value in SS? In

this section, the resolution of s is determined.Theresultsof this analysisareusedin both the numericalpresentation and the customer need rank datapresentedin the following sections.

Defining the resolutionas

"ijpq � @sij

@�pq�12�

where sij and �pq are arbitrary, the derivation isstraightforward.

For brevity, the complete derivation is notpresentedhere.Two functionsaredefinedto expressthe resolutioncompactly.The first is definedas

f �a; b; c; d� � 1; when a = b andc = d0; otherwise

��13�

The secondis

g�a; b� � 1; when a = b0; otherwise

��14�

Using these two functions, the resolution isexpressedas

"ijpq � 1n

Xn

k�1

12

1��ik�jkp

��k�

��k

��15�

��f �i; p; k; q� � �ik

�1�ÿ 1�k

g�k; q��

�jk� �16�

�ik

�f �j; p; k; q� � �jk

�1�ÿ 1�k

g�k; q��

�17�

Equation (17) is the changein sij with a 1 pointchangein �pq.

For eachof theÿ

m2

�combinationsof ", therewill

bemndifferentvalues.To simplify interpretationandcommunicationof the resolution, an average"ij isused.Table 2 lists the top 10 function pairs, the svalue,andthe associatedaveragesensitivity.The "’sindicatethat a variation in customerneedof 1, for asinglefunction on a singleproduct,will changesij inthe seconddecimalplace.In all the following tables,thes valuesarelistedto two decimalplaces.Also, thespecific resolution values are used to distinguishbetweendifferentgroupsof functionchains.Functionchainvaluesindistinguishablewithin their repsectiveresolutionsare consideredequivalentwith respecttocustomerimportance.


3. Analysis and Example CaseStudies

In this section,thelinked functionrelationshipsfor anenergy conversion hierarchy group and a devicesimilarity groupareanalyzedanddiscussed.To verifythe functional interdependenceprocedure,specificcasestudiesareexaminedfor thetwo productsubsets.Thefirst caseinvolvesanapplesto applescomparison(sameproduct, different manufacturer),the secondcaseis moreof an applesto crabapplescomparison(similar product,slightly different materialflow), thelast is akin to an apples to orangescomparison(different products, same family). The three casestudiesidentify actual modulesthat agreewith theresults of the functional interdependencemethod,providing validation of the method as a tool formodule identification. Furthermore,it demonstratesthatwhile modulecreationin productdesignmaynothavea formal framework,it is usedat variousstagesin industry.

The casestudyprocedurelooks at actualproductsfrom the68 productfunctiondatabase.Thefour stepsof the procedureare:

1. generatethe function dependencychains for aproductfamily,

2. disassemblethe product(from the productfamilyin step1) anddocumentits components,

3. actualmodulesin the product,and4. comparewith the predictedmodulesfrom step1.

Before discussingthe specific groups and casestudies,someterminology is introducedto simplifythe discussionandcategorizationof the results.

Commonflow function chains are thosein whicheachfunction operateson a commonbasicflow. Forexample, in a small electrical palm sander, thefunctions convert electricity to rotation and actuateelectricity operateon the commonflow of electricity,

thus these two functions form a common flowfunction chain.Distinctionsbetweenthe sequenceofthe functions in the chainsare not made.Commonflow functionchainswith a high customerimportanceare those most suitable for function sharing,mod-ularity, function solution optimization, and functioninteractionanalysis.

Flow independent,causallylinked function chainsarethosewith an obviousflow link, thoughnot all ofthe functions operateon the same flows. In somecases,the existenceof one function necessitatestheother. The function import human hand may be acausal function for a dissipatevibrations function.The customerneedsin this caseare comfort issues.The presenceof the hand in the systemcausestheneed to prevent vibrations from causing handdiscomfort. In other causally linked cases, thefunctions may be linked by control or preventionrelationships.In thehot gluegun(from thefunctionalsimilarity productsubset),transmitheatandregulateelectricity areconsideredcausallylinked becausetheregulate electricity function controls the amountofheat transmitted. In general, determining whichfunction chains are causally linked requires someknowledge of the product group. Finding flowindependent, causal function chains has a keyapplication in redesign.Changing (improving) thecausalfunction to eliminate the needfor the causedfunction simplifiesandimprovesan entiredomainofproducts.

Independentflow,non-causalfunctionchainsshareno commonflow, operateseparatelyfrom eachother,and often result from distinct customerneeds. Inpractice, these function chains are identified byremoving one of the functions from the proposedchain.If eliminatinga functionallowstheremovalofanother function in the chain (from the functionstructure) while still meeting all customer needs,thesefunctions are not independent– some causal

Table 2. Sensitivityof s to customerneedrankingfor function coupling

Functioncombination s "

import humanforce+convertelectricity to rotation 2.464211 0.038523dissipatesound+convertelectricity to rotation 1.949093 0.030458dissipatetranslation+convertelectricity to rotation 1.892236 0.029581convertelectricity to rotation+actuateelectricity 1.800231 0.028466import solid+importhumanforce 1.797064 0.028230import humanhand+importhumanforce 1.789280 0.027945import humanforce+dissipatetranslation 1.769951 0.027721convertelectricity to rotation+changerotations 1.763166 0.027557import humanforce+changerotation 1.731498 0.027121securesolid+importhumanforce 1.665674 0.026137


relationship exists. Independent flow, non-causalfunction chainsare not interdependentchainsin thesenseof theprevioustwo functiongroupings.In fact,combinationsin this chain indicate functions thatshouldnot be groupedtogetherinto modules.Thesechains, however, do have an important impact onmodulardesign.

Identification of important independentflow non-causalchainshasimplicationsfor masscustomizationand productarchitecture.The function combinationsmay indicate module boundarieswhere interfaceissues become important. For example, modularcasingscan be constructedwhere function solutionscanbe ‘pluggedin’ usingbusmodularity techniques,similar to the fashion in which automobile manu-

factures handle option cutouts on a dashboard(Rosenauet al. 1996). Here, a single housingcouldprovidethe interfacefor differentmodules.Likewise,independentflow, non-causalfunction chains withhigh occurrencepresenta startingpoint for designforrecycle-ability analysisincluding materialsselectionandpotentialclumpingoptions(Marks et al 1993).

The resultsof theanalysispresentedin this sectionare shown in Tables3 through 7, eachof which isorganizedin the following manner.Columnoneliststhe function chain. Column two lists the function-chain customerneed importance index s. Columnthree is the occurrenceof the function chain as apercentageof the total possible(the total numberofproductsanalyzedin thegroupor subset).Within thetable,the function chainsarebrokendown into threesub-groups:the first is commonflow functions; thesecondflow independent,causally linked functions;andthelastis flow independent,non-causalfunctions.Within the sub-groups,the function chainsare listedin descendingorder of customerimportance,s. The25 function chainslisted are thosewith the highestrankingcustomer-needvalues.

3.1. The Energy Conversion Hierarchy Subset

The first set of productsanalyzedis the electricity!heat!material subset of the total 68 products.Table3 presentsthe two function chains,Table4 thethreefunctionchains.Theproductsin this group(Fig.2) area sandwichmaker,a popcornpopper,a coffeemaker, an iced tea maker, a hot glue gun and ahumidifier.

The commonflow functions for the two functionchainsare, predictably,thosewhich manipulatetheelectricity, the heat (thermal energy),and the solid.Theflow independent,causallylinked functionchainsare those that manipulate electricity and thermalenergy.In the function chain transmitheat+regulateelectricity, the electricity is regulatedto determinehowmuchthermalenergyis transmitted.Thetransmitheat+regulateelectricity function chainmay be usedto connectmodulesfrom thecommonflow functions,creating a larger module. Similarly, transmit heat+import electricity may be usedto join the commonthermal energy and common electricity functionchainsto createlargermodules.

Table 4 containsonly one commonflow functionchain,convertelectricity to heat+stopheat+transmitheat for the set of products.This result is clearlyconsistentwith the techniqueused to generatetheproductsubset.Thehighestrankingflow independent,non-causalthreefunction chain is convertelectricity

Table 3. Customerneedindex and% occurrencefor threefunction chainsin theelectricity!heat!materialproducts

Functioncombination s %

CommonFlow

transmitheat+convertelectricity to heat 6.61 100securesolid+importsolid 3.29 67import electricity+convertelectricity to heat 2.98 100transmitheat+stopheat 2.58 67

Flow independent,causallylinked

import solid+importhumanforce 3.82 67transmitheat+importelectricity 3.34 100storesolid+importhumanforce 3.13 83storeliquid+import humanforce 2.90 50transmitheat+regulateelectricity 2.48 50

Flow independent,non-causal

transmitheat+importhumanforce 6.34 83transmitheat+importsolid 5.23 83import humanforce+convertelectricity to heat 5.14 83import solid+convertelectricity to heat 4.40 83transmitheat+storeliquid 4.21 67storeliquid+convertelectricity to heat 4.18 67transmitheat+storesolid 3.78 83storesolid+convertelectricity to heat 3.40 83transmitheat+securesolid 3.27 67import solid+importelectricity 3.00 83storeliquid+import solid 2.98 50transmitheat+cleanproduct 2.90 50securesolid+convertelectricity to heat 2.74 67convertelectricity to heat+cleanproduct 2.56 50regulateelectricity+importhumanforce 2.51 50import humanforce+cleanproduct 2.50 50import solid+guideliquid 2.41 50


Table 4. Customerneedindex and% occurrencefor threefunction chainsin the electricity!heat!material products


CommonFlow

convertelectricity to heat+stopheat+transmitheat 2.86 67

Flow independent,causal

convertelectricity to heat+importelectricity+transmitheat 3.88 100


convertelectricity to heat+importhumanforce+tramsitheat 5.73 83convertelectricity to heat+importsolid+transmitheat 4.67 83convertelectricity to heat+storeliquid+transmitheat 4.34 67import humanforce+importsolid+transmitheat 4.25 67convertelectricity to heat+storesolid+transmitheat 4.22 83import humanforce+storesolid+transmitheat 4.10 83convertelectricity to heat+importhumanforce+storesolid 3.70 83convertelectricity to heat+importhumanforce+importsolid 3.59 67import electricity+importsolid+transmitheat 3.43 83import electricity+importhumanforce+tramsitheat 3.29 83import humanforce+storeliquid+transmitheat 3.28 50import solid+securesolid+transmitheat 3.25 67convertelectricity to heat+importhumanforce+importliquid 3.23 50cleanproduct+convertelectricity to heat+transmitheat 3.19 50cleanproduct+importhumanforce+transmitheat 3.13 50convertelectricity to heat+importelectricity+importsolid 3.12 83convertelectricity to heat+securesolid+transmitheat 3.03 67import humanforce+requlateelectricity+transmitheat 3.01 50convertelectricity to heat+importsolid+securesolid 3.00 67import solid+storeliquid+transmitheat 2.97 50import solid+storesolid+transmitheat 2.90 67convertelectricity to heat+importelectricity+importhumanforce 2.89 83cleanproduct+convertelectricity to heat+importhumanforce 2.88 50import humanforce+stopheat+transmitheat 2.85 67

Table 5. Identifiedmodulesin BrandA andBrandB iced teabrewers

IdentifiedmoduleDescription BrandA BrandB Assoc.Fig.

electricity to heat,importselectricity,actuateselectricity, regulateselectricity,convertselectricity to heat,transmitsheat,measuresheat,stopsheat,transportsliquid

exists exists 3

ice containmentimportshumanforce,importssolid, storessolid, securesolid

exists exists 4

filter, teacontainmentimportshumanforce,importssolid, storessolid, securesolid

exists doesnot exist asa module 5

liquid containmentimportshumanforce,imports liquid, storesliquid

exists exists 4


to thermal energy+import human force+transmitthermal energy. This function chain is representedin 5 of the 6 functional descriptionsfor this productsubset and is a customer ‘must.’ Any domainredesign,reorganization,or modularity efforts needto consider the function chain interaction, orinterference,constraintsof thesefunctions.

3.1.1.Case1: Applesvs.Apples- Iced TeaMakersIn theapplesvs. applescomparisonof theelectricity-heat-materialfamily, we look at two iced teabrewersfrom different makers,Brand A and Brand B. Theconjecture is that for two functionally similarproducts, the better product should make use ofmoremodules.

The function chains for this product family arelisted in Tables 3 and 4. Modules found upondisassemblyof the two iced teabrewersare listed inTable 5. Both products sharedmany of the samemodules,with theBrandA icedteabrewerexhibitinga greaternumberof modules.

The commonflow function combinationslisted inTable3 all appearin theicedteabrewersasall or partof a module.Theelectricity to thermalenergymodulein Fig. 3 contains three of the four common flowfunctionchainsassubmodules:transmitheat+convertelectricityto heat, transmitheat+stopheat, andimportelectricity+convert electricity to heat. The fourthfunction chain, securesolid+import solid, manifestsitself as the pitcher and lid (for holding the ice) for

Table 6. Coupledfunctionsrankedby s and% occurrencefor productssimilar to thepalmsander.Thoseproductsarea fruitandvegetablestripper,a powerscrewdriver,an oscillatingsander,an electricknife, anda handvacuum


CommonFlow

securesolid+removesolid 5.09 67convertelectricity to rotation+actuateelectricity 3.79 100import electricity+convertelectricity to rotation 3.27 100convertelectricity to pneumatics+convertelectricity to rotation 3.08 50securesolid+positionsolid 2.87 50


import humanhand+actuateelectricity 4.24 100removesolid+dissipatevibrations 3.12 50positionsolid+importhumanhand 2.83 50


import humanhand+convertelectricity to rotation 6.57 100import humanhand+importhumanforce 6.46 100import humanforce+convertelectricity to rotation 5.73 100securesolid+importhumanhand 5.68 83securesolid+convertelectricity to rotation 4.87 83removesolid+importhumanhand 4.87 67securesolid+importhumanforce 4.86 83removesolid+importhumanforce 4.50 67removesolid+convertelectricity to rotation 4.34 67import humanforce+actuateelectricity 3.63 100import humanhand+importelectricity 3.60 100import humanforce+importelectricity 3.29 100securesolid+actuateelectricity 3.21 83separatesolid+importhumanhand 3.18 67import humanhand+dissipatevibrations 3.12 50removesolid+importelectricity 3.09 67import humanhand+convertelectricity to pneumatics 3.08 50securesolid+importelectricity 3.07 83


Table 7. Threefunctiondependencyfor productssimilar to thehandsander.Theproductsarea fruit andvegetablestripper,apowerscrewdriver,an oscillatingsander,an electricknife, anda handvacuum



import humanforce+importhumanhand+securesolid 5.22 83import humanhand+removesolid+securesolid 4.82 67actuateelectricity+convertelectricity to rotation+importhumanhand 4.65 100actuateelectricity+importhumanforce+importhumanhand 4.57 100import humanforce+removesolid+securesolid 4.52 67import humanforce+importhumanhand+removesolid 4.47 67


convertelectricity to rotation+importhumanforce+importhumanhand 6.19 100convertelectricity to rotation+importhumanhand+securesolid 5.20 83convertelectricity to rotation+importhumanforce+securesolid 4.67 83convertelectricity to rotation+removesolid+securesolid 4.44 67convertelectricity to rotation+importhumanhand+removesolid 4.33 67actuateelectricity+convertelectricity to rotation+importhumanforce 4.22 100import electricity+importhumanforce+importhumanhand 4.17 100convertelectricity to rotation+importelectricity+importhumanhand 4.15 100convertelectricity to rotation+importhumanforce+removesolid 4.07 67actuateelectricity+importhumanhand+securesolid 3.99 83convertelectricity to rotation+importelectricity+importhumanforce 3.87 100import electricity+importhumanhand+securesolid 3.69 83actuateelectricity+convertelectricity to rotation+securesolid 3.63 83actuateelectricity+importhumanforce+securesolid 3.58 83import electricity+removesolid+securesolid 3.47 67import electricity+importhumanforce+securesolid 3.42 83convertelectricity to rotation+importelectricity+securesolid 3.37 83import electricity+importhumanhand+removesolid 3.35 67convertelectricity to rotation+importhumanhand+separatesolid 3.35 67import humanforce+importhumanhand+separatesolid 3.26 67

Fig. 3. The convertelectricity to thermalenergymodulefor bothteabrewers.

Fig. 4. The secure solid+import solid and import force+storeliquid for both teabrewers.


bothproductsin Fig. 4. Additionally, in Fig. 5, BrandA hasamodulefor importingthefilter andteawhichisanothermanifestationof securesolid+import solidwhich theBrandB coffeebrewerlacks.

The flow independent,causally linked functionchains also representmodules found within bothproducts.They are again subsetsof the identifiedmodulesdiscussedabove,with the addition of theliquid containmentmodule identified by the storeliquid+import humanforcecombination.Thismoduleis shownin Fig. 4.

In both the commonflow and flow independent,causallylinked chains,the combinationsof functionsform all, or part, of assemblymodules.Assemblymodulesare components,or groupsof components,that solve related functions and are assembledinclearly distinct stagesto increaseassemblyease.

The three function dependencyshownin Table 4revealsonly two possiblemodulesin the commonflow and flow independent,causally linked chains.This fact comparesfavorablywith theresultsin Table3. The two, three function combinationsare bothsubsetsof the assemblymoduleelectricity to thermalenergyshownin Fig. 3, which is describedby threeout of four of the two function dependencycombinations.

As expected,no modulesarefoundwhich embodythecombinationsof theflow independent,non-causalcategory. In fact, this category is interpreted asfunctionsthat shouldnot be combinedasmodules.

3.1.2.Case2: Applesvs.Crab Apples– CoffeeMakervs. Iced TeaMakerContinuing analysis of the electricity-heat-materialproduct family, we look at two different products(coffee maker vs. iced tea maker) by the samecompany,Brand A. The functional interdependence

proceduresuggeststhat thesedifferent, but related,products share the same modules in embodiedsolutionprinciple, if not in actualparts.

The function dependencycombinationsfor thisproduct family are listed in Tables3 and 4. Threesharedmoduleswere found in the coffee makerandiced tea maker: the electricity to thermal energymodule(that wascommonto both teamakersin case1); a liquid containmentmodule; and a transportliquid+stop liquid flow module.

The electricity to thermalenergyassemblymoduleappearsasa sizable,or scalable,moduleandis shownin Fig. 6. Here, we define a sizablemodule as onewhich is physically identical to another moduleexcept for the its scale. In both products, theelectricity to thermal energy module is made fromthe sameextrudedtubing asevidencedin Fig. 6. Theactuateenergyfunction solution is slightly different,dueto theautomaticshut-offfeatureof theteamaker.Recall that both the two and three functiondependencychainspredictsubsetsof this module.

The secondmodule,predictedby the two functiondependencycombinationstore liquid+import humanforce, is a conceptualmodule.A module similar inconcept,or a conceptualmodule, is one in whichdifferent products exhibit a module for the samefunctionchainsandthephysicalprincipleof solutionsis thesame.Detailsof embodiment,suchaschoiceofmaterials, specific geometries,scales,and etc. aredifferent. Here, a conceptualmodule usesthe samesolution principle in both products,but the physicalincarnationis different.Comparedto the teabrewer’splastic, essentially cylindrical liquid containmentmodule, the coffee maker’s is glass, and moresphericalin shape.

Fig. 5. The import human force+import solid and storesolid+securesolid solution for the BrandA teabrewer.

Fig. 6. The convertelectricity to thermal energymodulefor theBrandA teabrewer(left) andthe BrandA coffeemaker(right).


The third moduleidentified, transport liquid+stopliquid flow, is shown in Fig. 7. This module is anexactmodule.Exact modulesare thosein which thesamepart is usedin bothproducts.This moduleis notidentifiedin eitherTable3 or 4. However,this is notashortcoming of the functional interdependencemethod.Both transport liquid and stop liquid floware supporting functions and, thus, only have arelativecustomerneedrankof one.Thenormalizationprocedureof the function-functionmatrix will neverrank this combination above that of a supportingfunction (i.e. a valueof 1). The combinationsshownin thetablesareonly thosewith a customerneedrankgreaterthanone.

To sum up Case2, three moduleswere found toexist betweenthe BrandA coffeemakerandiced teamaker:onesizable,oneconceptual,andthe lastexactin both products. Opportunities exist for furthermodularity. For example,the iced tea maker has a

teaandfilter containmentmodule.The coffeemakercould incorporate a sizable or exact containmentmodule for coffee and filter. This caseshowsthat,within product families, the functional interdepen-dence method provides a framework for modulesharingbetweendifferent products.

3.2. The Functional Similarity Subset

A secondsubsetof six products,selectedbasedonsub-functionalsimilarity, is analyzedin this section.The productsare the first six appearingin Table 1Table6 containsthetwo functionchains,andTable7contains the three function chains for these sixproducts.For this productsubset,the commonflowtwo functionchainsarethosewhichmanipulatesolidsandelectricity.

Within this subset,there are three flow indepen-dent, causallylinked function chainsof importance.The first is that all productsrequire import humanhand to actuateelectricity. The second,existing inhalf of theseproducts,is the removesolid functioncausinga needto dissipatevibrations. Also, half theproductsrequire import humanhandwhich is causalto position a solid creating the third importantfunction chain.

3.2.1.Case3: Applesvs.Oranges- PalmGrip Sandervs. Fruit PeelerConsideringa wider productfamily thantheprevioustwo cases,two different products from the palmsander similarity subset are examined, the palmsanderitself and a fruit and vegetablepeeler.As inCase 2, the functional interdependencemethodpredicts modulesacrossthe product family. Tables6 and 7 list the two and three function dependencycombinations for the family. The two functioncommon flow chain deals with manipulating thesolid and electricity. In the two function flowindependent, causally linked combinations, twotypes of chains exist. The first type shows thatremove solid necessitatesa need to dissipatevibrations. The second type of chain deals withimporting human force to manipulate solids andenergies. The three function flow independent,causallylinked combinationsmimic the two functioncombinations,with the exception of the dissipatevibrationschain.

Upondisassemblyof the two products,no exactorsizable modules are found. However, conceptualmodules are located. In particular, the manipulatesolid modulespredictedby thetwo andthreefunctioncommonflow and flow independent,causallylinked

Fig. 7. The transport liquid+stop liquid flow solution for thecoffee maker and the tea brewer. (a) Coffee maker, (b) teabrewer.

a

b


combinationsexist and are shownin Fig. 8. On firstreview, their embodimentappearsdifferent, thoughthey eachsolve the samefunctions of securesolid,removesolid, andpositionsolid. However,the peelerandthesanderusesimilarmeansof securingthesolid.Note in Fig. 8(b) that the peelerhasa spring loadedarmto hold thebladenextto thesolid for peeling.The

sander,in Fig. 8(c) usesspring arms to securethesandpaperon its block. As an additional meansofsecuringthe sandpaper,the sandercould incorporatepiercingprongsasthe peelerdoesin Fig. 8(a).

Anotherconceptualmoduleof import electricity+-convert electricity to rotation is found in both thesanderandpeeler.Thesemodulesareshownin Fig. 9.An opportunity for part sharing of motors existsbetweenthe two if theoutputcanbegeareddownforthe peeleror, conversely,if a smallermotor can begeared up and maintain adequatetorque for thesander.

This casestudy purposelysoughta device familywith a wider scope(devicesthat are not obviouslysimilar) anddevicesmadeby differentmanufacturers.Sincemodulesare found underthesecircumstances,

Fig. 8. Manipulatesolidsolutionsfor thefruit andvegetablepeeler(a andb) andthe handsander(c).

a

b

c

a

Fig. 9. The convert electricity to rotation solution for the handsanderand the fruit andvegetablepeeler.(a) Fruit andvegetablepeeler,(b) handsander

b


the functional interdependencemethodhaspassedarigorous test. Although no exactor sizablemodulesare located in thesedevices,opportunitiesfor suchmodulesexist. Specific examplesare the use of apiercing methodto hold sandpaperand the useof acommon motor. This module information couldprovide a companywith a meansof identifying anew device to manufacturethat can draw on itscurrentline of componentsandexpertise.This is thepower of identifying conceptual modules – theyprovide a first step toward greateruse of exact orsizablemodulesandthe associatedcostsavings.

4. A Project Planning Appli cation

Three case studies have shown the utility of thefunctional interdependencemethod for identifyingmodulesand opportunitiesfor modular architecture.The procedure,used to determineand rank relatedfunctions,hasapplicationsotherthanmodulardesign.It is clearly usefulaspart of a designer’stoolkit. Thefunctioncouplinganalysistechniquecanbeappliedtoproduct planning. A sampleapplication is outlinedhere.

Organizationsinvolved with product design andmanufacture can use function dependency andproduct functional similarity knowledge to selectnew productsfor development.This methoddependson an existingknowledgeof productneed.Also, thismethodallows a companyto predict their successindelivering a quality, and thus successful,productbased on their existing design and manufacturingknowledge.

To begin, it is necessaryto collect and organizeinformation about the company’s existing productline. To do this, all the existingproductsare reverseengineered.Then, a product-functionmatrix for thecompany’sproductline, or specificsubsetis created.With theexistingproductinformationwell organized,design begins on the proposednew products.Theconceptual design, through the generation of afunction structure, is completed for each of theseproducts. The proposed products can now becompared to the company’s existing, customerweighted (satisfied),design and manufacturingex-pertise. This is done by inserting the potentialproduct’ssub-functionvector into � andcreatingN.Then,the new productis comparedto the companiesexisting design and manufacturing expertise bycalculating the inner product of the proposednewproduct’s sub-functionvector and the conglomerateproduct,p, yielding a measureof productsimilarity.This procedureis repeatedfor eachof the potential

products.The productwhich scoresthe highest,i.e.has the most sub-functionsimilarity, is the productwhich will draw largely on the company’sexistingknowledge, and requires a minimum of new pre-prototypetestingandanalysis.

Once a product is chosenfor development,thedesignandimplementationteamcanbechosenusingtheproductsimilarity technique.Productdevelopmentteams that have worked on a functionally similarproduct have the most knowledge of the atomicfunctionaloperationof the new productandthusaremostsuitedfor asuccessfulcontinuationof theprojectthroughdetail design,manufacturing,andtesting.

5. Conclusion

In this paper, a novel procedurefor determiningfunctional interdependencebasedon customer-needdatais presented.Theprocedureis usedto investigatethe importanceof function chains in specific andgeneralsetsof products.A resultof this analysisis aquantitativeframework for identifying sub-functionsthat can be grouped into assemblymodules.Casestudiesperformedon specific product subsetsshowthat modulesare presentin current devices,specifi-cally within device families and competing manu-facturersof the samedevice.Among manufacturersthat haveseveraldevicesin onedevicefamily, exactandsizablemodulesexist,with opportunitiesfor moreexact module incorporation.An application of thefunctional interdependenceprocedure for productdevelopmentis briefly presented.

Acknowledgements

Theresearchreportedin this documentwasmadepossible,in part, by a Young InvestigatorAward from the NationalScienceFoundation.Theauthorsalsowish to acknowledgethe supportof Ford Motor Company,TexasInstruments,DesktopManufacturingCorporation,andthe UT JuneandGene Gillis Endowed Faculty Fellow. Any opinions,findings, conclusions,or recommendationsare those ofthe authorsanddo not necessarilyreflect the views of thesponsors.

References

Hubka V, Ernst Eder W (1998)Theory of technicalsystems.Springer-Verlag,Berlin

JohannessonHL (1996) On the natureand consequencesoffunctionalcouplingsin axiomaticmachinedesign.Proceed-ings of the 1996DETC, 96-DETC/DTM-1528,Irvine, CA,August18–22


Little AD, Wood KL, McAdams DA (1997) Functionalanalysis: A fundamental empirical study for reverseengineering,benchmarkingand redesign.Proceedingsofthe1997ASME DETC,97-DETC/DTM-3879,Sacramento,CA, September14-17

Marks MD, EubanksCF, Ishii K (1993)Life-cycle clumpingof product designsfor ownershipand retirement.DesignTheoryandMethodologyProceedings,Volume 53, ASME,September1993,pp 83–90

NamP Suh(1990)Theprinciplesof design.Oxford UniversityPress,New York

Otto, K (1996) Forming product design specifications.Proceedingsof the 1996 ASME Design Theory andMethodology Conference, 96-DETC/DTM-1517, Irvine,CA

Pahl G, Beitz W (1996) Engineeringdesign: a systematicapproach.Springer,New York

RosenauMD Jr et al. (editors)(1996) The PDMA handbookof new productdevelopment,Chapter16, Wiley, pp 216–235

Taylor D (1996)Processmetricsfor asynchronousconcurrentengineering.Proceedingsof the 1996 DETC, 96-DECT/DTM-1500, Irvine, CA, August18–22

Ullman D (1997) The mechanicaldesignprocess.McGraw-Hill, New York

Ulrich KT, EppingerS (1995) Productdesignand develop-ment.McGraw-Hill, NY

Appendix A: Functions and Flows

In this section,flows from TableA1 areclarified andclassfunctionsfrom Table A2 are defined.We have

attemptedto make the definitions consistentwithengineeringterminologyandstandardEnglishdefini-tions. However, some definitions used are not thecommonprimary definition. Also, the meaningof aword is often restricted. Our object here is notcompletelinguistic accuracy,but operationalclassi-fication. The goal is to presenta terminology forresearchanddiscussion.

Flows. Flows are first distinguished by classmaterials, energy, and signals (Pahl and Beitz1996), then by basic flows and, if desired, intocomplimentflows, asshownin TableA1.

Humanenergyandhumanmaterialare both basicflows. This inclusion is a resultof the importanceofhuman-productinteraction and generally improvesfunctional descriptionsand design solutions. It isoften known early in a product design that certainenergyandmaterialinputsaregoing to bea person’sinteractionwith the product.

The complimentsubdivisionof flows allows for amoreconcretedescriptionof theflow to beused.Thecompliment flow terminology should only be usedwhen it is requiredby the operationalconstraints,orcustomerneeds,of the product.Using the basicflow,or classflow, terminologyallows a broaderand lesssolution-associatedfunctionaldescription.

Signals are a separateflow class, even thoughsignals are either material or energy. The relevant

Table A1. Basicflows

Class Basic

SolidMaterial Liquid

HumanGas

Human Motion, ForceBiological

Translation,Force,Rotation,Torque,Mechanical Randommotion, Vibration

Rotationalenergy,TranslationalenergyElectrical Voltage,CurrentHydraulic Pressure,Volumetric FlowThermal Conduction,Convection

Energy Pneumatic Pressure,Volumetric FlowChemicalRadioactiveAcousticOpticalSolarMagnetic MagnetomotiveForce,Flux Rate

Status Pressure,Temperature,Signal Position,Displacement

Control


featureof a signal flow is the information it carries.The specifics of how that information is carried,including embodimentas energy or materials, is asolutionfor that signalmanipulation.

Specificdefinitionsfor theflows listed in TableA1are not given here.The definitions we usedfor theflows are consistent with those commonly used.Discerningbetweenbasic flows may not always beclear. For example, is asphaltbest characterizedaliquid or a solid?Is dusta gasor a solid?Theanswerto thesequestionsis a technicalone,and not one ofcategoricalphilosophy.

Functions.The samephilosophyusedto categorizeflows is usedto categorizethe functions.Definitionsaregiven for eachfunction class.

. Channel: To control the motion, or path, of amaterialor energyflow.

. Support: To firmly fix a material into a definedlocation,or secureanenergyinto a specificcourse.

. Connect: To bring two or more energies ormaterialstogether.

. Branch:To causea materialor energyto no longerbe joined or mixed.

Table A2. Functionclasses,basicfunctionsandsynonyms.Italics indicatea repeatedsynonym

Functionclass Basic function Flow restricted Synonyms

Channel Import Input, Receive,Allow, Form Entrance,CaptureExport Discharge,Eject, Dispose,RemoveTransfer

Transport Lift, MoveTransmit Conduct,Transfer,Convey

Guide Direct, Straighten,SteerTranslateRotate Turn, SpinAllow DOF Constrain,Unlock

Support Stop Insulate,Protect,Prevent, Shield,InhibitStabilize SteadySecure Attach, Mount, Lock, Fasten,HoldPosition Orient, Align, Locate

Connect Couple Join,Assemble,AttachMix Combine,Blend, Add, Pack,Coalesce

Branch Separate Switch, Divide, Release,Detach,Disconnect,Disassemble,Subtract,Value

Remove Cut, Polish,Sand,Drill, LatheRefine Purify, Strain,Filter, Percolate,ClearDistribute Diverge,Scatter,Disperse,Diffuse, ResistDissipate Absorb,Dampen,Dispel, Diffuse, Resist

Provision Store Contain,Collect, Reserve,CaptureSupply Fill, Provide,Replenish,ExposeExtract

Control Magnitude Actuate Start, InitiateRegulate Control, Allow, Prevent, Enable/Disable,Limit, Interrupt

Limit, InterruptChange Increase,Decrease,Amplify, Reduce,Magnify

Normalize,Multiply, Scale,Rectify, AdjustForm Compact,Crush,Shape,Compress,Pierce

Convert Convert Transform,Liquefy, SolidifyEvaporate,Condense,Integrate,Differentiate,Process

Signal Sense Perceive,Recognize,Discern,Check,Locate,VerifyIndicate MarkDisplayMeasure Calculate


Fig. B1. Phi matricesfor both subsetsof productsinvestigated.


. Provision: To accumulateor provide material orenergy.

. Control Magnitude:To alter or governthe sizeoramplitudeof materialor energy.

. Convert: To changefrom one form of energyormaterialto another.

. Signal: To provideinformation.

Appendix B: Function-Product MatricesFunctional analysis of a large set of products issimplified by representingproductsas a vector offunction importanceweights in a vector spaceofdesign functions. Function-productmatrices,� forthetwo productsubsetsusedasexamplesin thispaperareshownin Fig. B1.


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