applied sciences

Article A Time Correlation Based Clustering Method for a of a Transformable Product

Jinpu Zhang 1,2, Guozhong Cao 1,2,*, Qingjin Peng 3 , Runhua Tan 1,2, Huangao Zhang 1,2 and Wei Liu 1,2

1 School of Mechanical , Hebei University of Technology, Tianjin 300401, China; [email protected] (J.Z.); [email protected] (R.T.); [email protected] (H.Z.); [email protected] (W.L.) 2 National Engineering Research Center for Technological Innovation Method and Tool, Tianjin 300401, China 3 Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB R3T5V6, Canada; [email protected] * Correspondence: [email protected]; Tel.: +86-132-1206-2906

 Received: 6 December 2019; Accepted: 2 January 2020; Published: 5 January 2020 

Abstract: A single-function product cannot meet various needs of different users when the product user or use environment changes. A transformable product with multiple functions can meet different needs of users. It is critical to determine product functions that a transformable product should have in the . However, it is a challenge to decide required functional components of a transformable product in the design process. A clustering method is proposed in this paper using undirected graphs for segmentations of needs in the time dimension. A need-based function model is built to form product function chains based on cost of the function transition distance between different function chains. Undirected graphs of the function chains are constructed according to the similarity of product functions. The interrelated subgraphs are then used to form multiple functions of a transformable product based on segmentations. A wheelchair is developed as an example to verify the proposed method. The method improves the design process of transformable products accurately and effectively.

Keywords: product design; transformable product; function chain; transition distance; graph representation

1. Introduction A product has to meet diverse requirements of various users in order to be competitive in the market. Although different products have been developed to meet different user needs, many products provide only a single function, which cannot fully utilize capacity of product resources such as material and for a variety of user needs. There are products with multiple functions in the market. Some of these products perform different functions through the structural reconfiguration, and some provide multiple functions using a fixed structure. Because of the importance of multi-functional products, different methods have been proposed for design of multi-functional products, such as the reconfigurable design, adaptive design, , and product family design. There are two kinds of reconfigurable design applications: one is the reconfiguration of manufacturing system resources to meet different design requirements [1–4], and the other is the reconfiguration of product function modules to form different design solutions [5–7]. The adaptive design was proposed by Gu et al. [8] to design products that can meet different needs in product design and applications. Design adaptability refers to the ability of the existing design to create new or modified design to meet changeable requirements. Product adaptability refers to the ability of the product to meet

Appl. Sci. 2020, 10, 406; doi:10.3390/app10010406 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 406 2 of 21 changing needs in applications [9]. The modular design is widely used to form a product by using independent function modules [10,11]. The module refers to a unit composed of a component or a group of components to perform a function of the product. Each module can be easily attached, detached, modified, relocated, and replaced for upgrading, modifying, recycling and reusing of the product [12,13]. Common modules of the product can be used as platforms [14,15]. The concept of the product platform can be used to design flexible products with similar common function modules to meet different customer needs [16,17]. These existing methods can effectively guide the design of multi-functional products. However, when there is a need for a product to change functions only through structural transformation without replacing components, the modular product will not be able to meet the requirement. A transformable product is necessary to meet the need. A product is called the transformable product that can change its physical structure to perform different functions or enhance existing functions. For example, the Osprey plane can be transformed between helicopter and aircraft, and Aquada can be formed as either a car or ship [18,19]. There are also many transformable products applied in the and furniture industry [20–22]. Transformable products can often be smaller and lighter than equivalent single-state products or a set of single-function products [23]. Transformation is an action of changing the physical structure of a product in order to perform different functions or enhance an existing function. In order to effectively design transformable products, transformation are required [24]. Comparing with a general product, the transformable product uses less material and space to meet different use requirements. It is critical to determine product functions that a transformable product should have in the product design. Although many approaches have been proposed for design of the transformable product, there is a lack of the effective way to identify all potential functions and select the appropriate set of functions for a transformable product. This paper reviews the related work of the design method of transformable products, and proposes a new method to decide required functional components of a transformable product in the design process. This paper focuses on the stage of transformable products as the early stage of design determines 80% of product lifespan cost [25]. This paper proposes an effective approach to improve the design for transformable products. The approach integrates methods of needs clustering based on the time correlation, decision-making of the function chain similarity based on transition distances, and segmentation of graph representation. We will first introduce the representation of users’ needs using a standard form. The needs are clustered according to the time dimension. Function chains of the needs are then established after clustering, and the transition distance between function chains is determined according to the cost measure. The similarity between function chains is obtained according to the transition distance, and final functions of the transformable product are determined based on the similarity. A wheelchair is developed to verify our proposed method. The proposed method improves the conceptual design process of transformable products. A mathematical model is developed to make the design process of transformable products accurately and effectively. The systematic design process enables the computer-aided design of transformable products.

2. Related Research Different methods have been proposed for design of transformable products. Singh et al. [24] developed transformation products through induction and deduction using three principles and twenty facilitators. A proposed transformation principle provides a general direction to form a certain type of mechanical transformation. The transformation facilitator is a design structure to help create mechanical transformation. Weaver et al. [23,26] analyzed the transformation process of a large number of transformable systems. The use frequency of transformation principles and facilitators in each system is counted. Correlations between transformation principles and facilitators are decided for their use priority in the design process. Transformation principles and facilitators can also be used together with modified mind-maps, and other methods such as T cards, word trees, case-based automated design, and example design [27–31]. Son et al. [32,33] studied the human behavior influenced by Appl. Sci. 2020, 10, 406 3 of 21

Appl. Sci. 2020, 10, 406 3 of 21 transformable products to develop new tools for in conceptual design of transformable products. Difficulties that designers may encounter in designing transformable products were found, products were found, causes of the difficulties were analyzed, and the effective design process of causes of the difficulties were analyzed, and the effective design process of transformable product was transformable product was inferred [34]. A transformable product is normally designed based on inferred [34]. A transformable product is normally designed based on following three considerations: following three considerations: (1) the product needs packaging for portability and deployment; (2) (1) the product needs packaging for portability and deployment; (2) multiple functions are required in multiple functions are required in one system for the use convenience; (3) multiple-functions one system for the use convenience; (3) multiple-functions products with dissimilar configurations products with dissimilar configurations share common material and/or energy flow [27–29]. Four share common material and/or energy flow [27–29]. Four transformation indicators were proposed transformation indicators were proposed including sharing functions; adhering to a variable; including sharing functions; adhering to a variable; accommodating a process; and storing [30]. The accommodating a process; and storing [30]. The design solution can be improved to enhance quality, design solution can be improved to enhance quality, novelty, and feasibility by categorizing the novelty, and feasibility by categorizing the problem context to decide whether a product is suitable problem context to decide whether a product is suitable for a transformable product or a single function for a transformable product or a single function product [31]. The above existing research involves product [31]. The above existing research involves many aspects of transformable products, but how many aspects of transformable products, but how to determine the final function of transformable to determine the final function of transformable products has not been solved. products has not been solved. As the transformable product is closely related to the need of users and use environments, As the transformable product is closely related to the need of users and use environments, a a human–machine–environment system should be considered in the design of transformable human–machine–environment system should be considered in the design of transformable products products [35], as shown in Figure1. [35], as shown in Figure 1.

Figure 1. A human–machine–environment system [36]. [36].

For design of a product that can be changed to m meeteet needs needs of of environments environments or or function function changes, changes, Desouza etet al.al. [[37]37] proposed proposed a a method method to to let let users users participate participate in thein the design design process. process. Hazelrigg Hazelrigg et al. et [38 al.] [38]simplified simplified the designthe design into twointo steps:two steps: generating generating all possible all possible design design concepts concepts and selectingand selecting the best the bestsolution. solution. In order In order to fully to obtainfully obtain possible possible solutions, solutions, all the all user the needs user haveneeds to have be considered. to be considered. Needs Needscan be can acquired be acquired through through user interviews, user interviews, group discussions,group discussions, and Big and Data Big analysis Data analysis [39,40]. [39,40]. Needs Needsare then are processed then processed by designers by designers in product in product design design to meet to meet the needs.the needs. A normalized A normalized expression expression of ofneeds needs was was used used to translateto translate users’ users’ descriptions descriptions into in designto design specifications specifications [41]. [41]. An An extension extension theory theory has hasbeen been applied applied in product in product design design to study to study possibility possibility of function of function expanding expanding using using engineering engineering laws laws and andmethods methods for innovation for innovation [42]. The[42]. extension The extension theory cantheory describe can describe and analyze and designanalyze using design an extensionusing an extensionmatrix. Quality matrix. Function Quality Deployment(QFD)Function Deployment(QFD) is a multi- is a multi-level deductive deductive analysis method analysis to method transform to transformcustomer requirementscustomer requirements into design specifications,into design sp componentecifications, characteristics, component characteristics, process requirements, process requirements,and production and requirements production [requir43,44].ements Axiomatic [43,44]. design Axiomatic divides design design divides problems design into problems four domains: into fouruser domain,domains: function user domain, domain, structurefunction domain,domain, andstructure process domain, domain. and User process requirements, domain. function User requirements, designfunction parameters, requiremen andts, variables parameters, are applied and process in the designvariables process. are applied The mapping in the processdesign process. from the The user mapping domain to process function from domain the canuser guide domain the creativityto function of designers,domain can the guide mapping the processcreativity from of designers, a functional the domainmapping to process physical from domain a functional can assist domain designers to physical in conceptual domain designcan assist of designerstransformable in conceptual products [45design–47]. Scenariosof transformable can be proposedproducts for[45–47]. dynamic Scenarios descriptions can be of proposed user–system for dynamicinteractions descriptions [48]. Scenarios of user–system are usually interactions narrated [4 in8]. the Scenarios form of are stories, usually including narrated settings, in the form actors, of stories,agent’s including goals, scenario’s settings, goals, actors, plot, agent’s and goals, timeframe scenario’s [49]. goals, Building plot, scenarios and timeframe based [49]. on needs Building can scenariosevolve functions based on of transformableneeds can evolve products. functions Functional of transformable decomposition products. can recognizeFunctional design decomposition problems. Throughcan recognize decomposition, design problems. designers Through can get decomposit a clear understandingion, designers of design can get problems a clear understanding and requirements. of designMany scholars problems have and studied requirements. the process ofMany functional schola decompositionrs have studied from dithefferent process perspectives of functional [50–52]. Adecomposition functional decomposition from different process perspectives is shown [50–52]. in Figure A functional2. decomposition process is shown in Figure 2. Appl. Sci. 2020, 10, 406 4 of 21 Appl.Appl. Sci.Sci. 20202020,, 1010,, 406406 44 ofof 2121

FigureFigure 2.2. FunctionalFunctional decomposition decomposition [52]. [[52].52].

TheThe lowestlowestlowest sub-functions sub-functionssub-functions can cancan be bebe arranged arrangedarranged in ainin logical aa logicallogical relationship relationshiprelationship to form toto form aform function aa functionfunction chain, chain, whichchain, whichreflectswhich reflectsreflects the process thethe processprocess of realizing ofof realizingrealizing the functions thethe functionfunction [53]. Analyzingss [53].[53]. AnalyzingAnalyzing the similarity thethe similaritysimilarity between betweenbetween function functionfunction chains chainsofchains single ofof single functionsingle functionfunction products productsproducts can determine cancan determinedetermine whether whwhetherether they theythey should shouldshould be merged bebe mergedmerged into intointo function functionfunction chains chainschains of oftransformableof transformabletransformable products. products.products. There ThereThere are twoareare two formstwo formsforms of the ofof function ththee functionfunction chain: chain:chain: serial serial andserial parallel andand parallelparallel chains, chains,chains, as shown asas showninshown Figure inin3 Figure.Figure 3.3.

((aa)) ((bb)) Figure 3. Two forms of the function chain [53]. (a) serial function chain; (b) parallel function chain. FigureFigure 3.3. Two formsforms ofof thethe functionfunction chainchain [[53].53]. (a)) serialserial functionfunction chain;chain; ((bb)) parallelparallel functionfunction chain.chain.

AlthoughAlthough thesethesethese methods methodsmethods are areare not notnot specially speciallyspecially used usedused to design toto designdesign transformable transformabletransformable products, products,products, they can theythey greatly cancan greatlyassistgreatly the assistassist design thethe fordesigndesign needs forfor acquisition needsneeds acquisitionacquisition and function andand functionfunction design of designdesign transformable ofof transformabletransformable products. products.products.

3.3. Proposed Proposed Method Method ForFor aaa largelargelarge number numbernumber of ofof user useruser needs, needs,needs, the thethe need needneed correlation cocorrelationrrelation can becancan analyzed bebe analyzedanalyzed using using theusing extension thethe extensionextension theory theoryas follows: as follows: theory as follows:   N User u1   NuNuUserUser 1   Scene u21    SceneScene uu2  Time u32  N = .  ActivityTime uu3  = Time u43 . NN =. CurrentActivityActivity situation uu45   4   ExpectedCurrentCurrent situationsituation situation uu56 5 Expected situation u6 User means people have the need. SceneExpected is the scenario situation whereu6 the need exists. Time is when the need is required. Activity means actions to respond to the need. The current situation is the state of UserUser meansmeans peoplepeople havehave thethe need.need. SceneScene isis thethe scenarioscenario wherewhere thethe needneed exists.exists. TimeTime isis whenwhen thethe current activities at the time of the application. Expected situation means the expected activities at the needneed isis required.required. ActivityActivity meansmeans actionsactions toto respondrespond toto thethe need.need. TheThe currentcurrent situationsituation isis thethe statestate ofof time of the product application. Potential need sets of a basic product are represented by N = [N1, N2, currentcurrent activitiesactivities atat thethe timetime ofof thethe application.application. ExpectedExpected situationsituation meansmeans thethe expectedexpected activitiesactivities atat ... , Ni, ... , Nm]. u1–u6 are specific descriptions of user, scene, time, activity, current situation, and thethe timetime ofof thethe productproduct application.application. PotentialPotential nneedeed setssets ofof aa basicbasic productproduct areare representedrepresented byby NN == [[NN11,, expected situation. The importance of each need is determined by a comparing table [54] as shown in NN22,, …,…, NNi,i, …,…, NNmm].]. uu11–u–u66 areare specificspecific descriptionsdescriptions ofof user,user, scenscene,e, time,time, activity,activity, currentcurrent situation,situation, andand Table1. expectedexpected situation.situation. TheThe importanceimportance ofof eacheach needneed isis determineddetermined byby aa comparingcomparing tabletable [54] [54] asas shownshown inin TableTable 1.1. Table 1. Comparison of the importance of each need.

NeedsTableTable 1.1. ComparisonComparison N1 ofof thetheN2 importanceimportance... ofof eacheach need.need.N m

N1 N1 N2 ... N1 NeedsNeeds NN11 NN22 …… NNmm N2 N2 ... N2 ...... NN11 NN11 NN22 …… NN11 Nm NN22 NN22 …… NN22 Nm …… …… …… NNmm NNmm Appl. Sci. 2020, 10, 406 5 of 21

According to the frequency of needs appearing in the matrix, the importance of needs can be decided and recorded as wi. For two needs with the high importance, the relationship between them will also be very important in the needs set. The sum of the two needs importance is used to express the weight of the two needs relationship. Dividing the sum by m 1 is for the weight normalization, − where m is the number of needs. The weight of the relationship between two needs is decided using Equation (1): wNi + wNj w = . (1) NiNj m 1 − Different functions of a transformable product are applied in different time periods [1], such as 0, 1, 3, 6, and 10, can be used to indicate the degree of time dependency [55]. Transformable products meet different needs at different times, so needs should be clustered in the time dimension to facilitate the design of transformable products. The time correlation between potential needs can be expressed in levels of 0, 0.3, 0.6, and 1. As shown in Equation (2),  ( ) ( ) =  0 CNi u3 CNj u3 0  ∩  0.3 (C u ) (C u ) 0 and  Ni 3 Nj 3 ,  ∩ h i ∂(CN u3)  (CN u ) (CN u ) , (CN u ) or (CN u ) i, j [1, m]; i = i 3 ∪ j 3 i 3 j 3 ∈ , (2) (C u )  (C u ) (C u ) = (C u ) and i j ∂ Nj 3  0.6 Ni 3 Nj 3 Nj 3 , .  ∩  (C u ) (C u ) = (C u )  Ni 3 Nj 3 Ni 3  ∪  1 (CN u ) (CN u ) = (CN u ) (CN u ) i 3 ∩ j 3 i 3 ∪ j 3 where (CN u3) (CN u3) = 0 represents that there is no intersection of two needs in the same i ∩ j h i time, (CN u ) (CN u ) , 0 and (CN u ) (CN u ) , (CN u ) or (CN u ) mean that there is a partial i 3 ∩ j 3 i 3 ∪ j 3 i 3 j 3 intersection of two needs in the use time. (CN u ) (CN u ) = (CN u ) and (CN u ) (CN u ) = (CN u ) represent that the usage time of i 3 ∩ j 3 j 3 i 3 ∪ j 3 i 3 Nj is a true subset of the usage time Ni. (CN u ) (CN u ) = (CN u ) (CN u ) represents that N and N work at the same time. i 3 ∩ j 3 i 3 ∪ j 3 i j The time related degree of all needs can be obtained by calculating the time correlation of each pair of two needs. According to Equations (1) and (2), the time independence between needs can be obtained using Equation (3): w NiNj ∂(CNi u3) rij = n o , (3) × ∂(CN u3) Max ωNiNj j where Max{wNiNj } is the correction coefficient for values in the matrix easily distinguishable. According to Equation (3), the relationship matrix of needs can be established using Equation (4):   N1  r11 r12    N  r  2  22  R = .   .  ..  . (4) .  .    Nm rmm N N Nm 1 2 ··· The graph theory uses a graph as its object of study to transform the relationship matrix into a graph [56]. According to the relationship matrix, we can draw a need-related undirected graph, in which nodes are needs and edges are the relationship between the needs. Segmentations of the undirected graph are decided by setting an appropriate threshold. Each interconnected subgraph forms a kind of need with the time dependence. Each kind of need corresponds to a potential state of the product. Function design is conducted for each product form to obtain a function chain of the product in each use state. Appl. Sci. 2020,, 1010,, 406406 6 of 21

Appl. Sci. 2020, 10, 406 6 of 21 the product. Function design is conducted for each productproduct formform toto obtainobtain aa functionfunction chainchain ofof thethe product in each use state. FunctionFunction chainschains expressexpress sub-functionssub-functions andand theirtheir relationships.relationships. A directed graphgraph cancan representrepresent thethe logicallogical relationshiprelationship betweenbetween nodesnodes [[56].56]. Function chainschains cancan bebe expressed byby directeddirected graphs,graphs, forfor example,example, G == (((FF,, , LL),), where where FF === {{F{1F,, 1F,2F,, 2…,…,, ... Fn,},F Ln },== L{{L=1,, L{L2,,1 …,,…,L2 L, n...}. G, Lisisn }.aa functionfunctionG is a function chain,chain, F chain, isis aa setsetF isofof asub-sub- set offunctions sub-functions of function of function chain G, chain and L G, is and a set L of is arelationships set of relationships among sub-functions. among sub-functions. Figure 4a Figure shows4a a showsdirected a directedgraph of grapha function of a functionchain in chainwhich in a whichproduct a productperforms performs one function one function... InIn practice,practice, In practice, aa productproduct a productfunctionfunction can be used can bemany used times. many Atimes. chain of A chainmultiplemultiple ofmultiple functionsfunctions functions isis shownshown is inin shown FigureFigure in 4b.4b. Figure 4b.

(a) (b)

FigureFigure 4.4.Function Function chains chains (a )( functiona) function chain chain that performsthat performs one function; one function; (b) function (b) function chain that chain performs that multipleperforms functions. multiple functions.

WhenWhen aa productproduct needsneeds toto performperform multiplemultiple functions,functions, itit needsneeds toto bebe transitedtransited fromfrom oneone functionfunction chainchain toto another.another. Much research has been done on the transition from one graph to another [57–60]. [57–60]. TheThe costcost of of a a transition transition is is directly directly related related to its to suitability.its suitability. The lowerThe lower the cost the of cost the of transition, the transition, the higher the thehigher possibility the possibility that the that two the function two function chains can chains be converted cancan bebe convertedconverted to each other. toto eacheach The other.other. higher TheThe the higherhigher similarity thethe betweensimilarity the between two function the two chains, function the easierchains, conversion the easier ofconversion the chains. of The the transitionchains. The from transition one function from chainone function to another chain requires to another a series requires of operations, a series of including operations, the including node converting, the node deleting, converting, adding, deleting, and edgeadding, deletion and edge and deletion addition. and Two addition. function Two chains function G1 and chains G2 are G shown1 andand GG in2 areare Figure shownshown5. inin FigureFigure 5.5.

(a) (b)

FigureFigure 5.5. TwoTwo functionfunction chainschains ((aa)) functionfunction chainchain G G11;(;; ((bb)) functionfunction chainchain GG2.2.

TheThe sum of costs of of all all operations operations from from GG1 1tototo GG2 isis2 iscalledcalled called thethe the distancedistance distance ofof oftransitiontransition transition fromfrom from G1 Gtoto1 Gto2,, Gexpressed2, expressed by byTransTrans{G1{,,G G1,2}.G 2The}. The similarity similarity between between G1G and1andand GG2 2isisis expressedexpressed expressed asas as Sim{{G1,,, GG22}} usingusing EquationEquation (5):(5): Trans G1, G2 Sim G1, G2 = 1 Trans{,{ G G }}, (5) =−TransP{, G12 G } Sim{ {, G12 G} }1=−− Gi ,, 12 |G | (5)  Gii where |Gi| is the total number of nodes and edges in G1 and G2. The distance of transition from G1 to Gwhere2 is calculated |Gii| is the by total Equation number (6): of nodes and edges in G1 andand G2.. TheThe distancedistance ofof transitiontransition fromfrom G1 toto G2 isis calculatedcalculated byby EquationEquation (6):(6): Trans G , G = con(F , F ) + add(F ) + add(L ) + add(L ) + add(L ), (6) { 1 2} 1 4 5 6 +7 3 Trans{, G12 G }=(, con F 14 F )+()+()+() add F 5 add L 6 add L 7 add () L 3,, (6) where con(Fi, Fj) converts node Fi to node Fj, del(Fi) deletes node Fi, add(Fi) adds node Fi, del(Li) deletes where con(Fii,, Fjj) converts node Fii toto nodenode Fjj,, del(Fii) deletes node Fii,, add(Fii) adds node Fii,, del(Lii) deletes edge Li, and add(Li) adds edge Li. edge Li, and add(Li) adds edge Li. edgeThe Li, and cost add( of deletingLi) adds and edge adding Li. one node or edge can be assigned as one unit currency. Because The cost of deleting and adding one node or edge can be assigned as one unit currency. Because there may be some similarity between two nodes, the cost of converting nodes is designed as 1-Sim{Fi, there may be some similarity between two nodes, the cost of converting nodes is designed as 1-Sim{Fii,, Fj}. Sim{Fi, Fj} is the similarity between nodes Fi and Fj. The higher the similarity, the lower the Fj}. Sim{Fi, Fj} is the similarity between nodes Fi and Fj. The higher the similarity, the lower the cost of costFj}. Sim of conversion.{Fi, Fj} is the Semanticsimilarity similaritybetween nodes computation Fi and Fj has. The many higher applications the similarity, in information the lower the retrieval, cost of conversion. Semantic similarity computation has many applications in information retrieval, informationconversion. extraction,Semantic wordsimilarity sense computation disambiguation, has and many machine applications translation in [ 61information,62]. In this paper,retrieval, we information extraction, word sense disambiguation, and machine translation [61,62]. In this paper, useinformation it to calculate extraction, similarity word between sense disambiguation, two nodes based and on the machine semantic translation similarity. [61,62]. All words In this are paper, stored we use it to calculate similarity between two nodes based on the semantic similarity. All words are onwe ause word it to tree calculate according similarity to the semantic between relationship. two nodes based The similarity on the semantic of words similarity. can be calculated All words based are stored on a word tree according to the semantic relationship. The similarity of words can be onstored their on distance a word in thetree word according tree. The to similaritythe semantic of nodes relationship. is calculated The bysimilarity numbering of words them for can their be distance on the word tree using Equations (7)–(10) [63]. Appl. Sci. 2020, 10, 406 7 of 21

(1) If two words are not in the same tree. n o Sim Fi, Fj = 0.1. (7)

(2) If two words are in the same tree.   0.65 In the second branch;    !  π n k + 1  0.80 In the third branch; Sim Fi, Fj = cos n −  (8) { } × 180 n ×  0.90 In the f ourth branch;   0.96 In the f i f th branch; where n is the total number of nodes in the branch layer, and k is the distance between two branches. (3) When numbers are same and the end number is ‘=’. n o Sim Fi, Fj = 1, (9)

(4) When numbers are same and the end number is ‘#’. n o Sim Fi, Fj = 0.5. (10)

Using the semantic similarity calculation software of the synonym forest, we can calculate the similarity of two words according to the above definitions [64]. After calculating transition distances of function chains, the transition distances are weighted according to Equation (11): P P wNi + wNj w = N Sp N Sq, (11) SpSq z 1 i ∈ j ∈ − where z is the number of function chains, divided by z 1 to make the sum of the weights be 1. The − weighted transition distance of two function chains is calculated by Equation (12): n o wSpSq Sim Gp, Gq WSim Gp, Gq = n o , (12) { } Max wSpSq

where Max{ωSpSq } is the correction coefficient to make values in the matrix easily distinguishable. For an undirected graph A = (G, W), where G = {G1, G2, ..., Gn}, W = {W1, W2, ... , Wm}. G is a set of function chains, and W is a set of similarity between function chains. Using threshold value W0 removes edges less than W0 in the undirected graph and deletes independent nodes. A new subgraph A0 is generated. Interconnected nodes in subgraph A0 are the function chains of the transformable product. The connection between nodes indicates that the function chains represented by these nodes can be transformed each other. Each interconnected node represents a state of a transformable product, and these nodes form the concept of a transformable product. As it is difficult to map the functional domain to physical domain directly, physical components can be designed by refining functions in the mapping process, as shown in Figure6. For a certain function, the solution to realize the function can be selected by designers firstly. Components for implementing the function are then determined. The number of identical components in each state represents the space and material savings of the transformable product. The effectiveness of the method can be evaluated according to the proportion of shared components, as shown in Equation (13): NCT P = P , (13) NCSi where P is the proportion of shared components, NCT is the number of components in the transformable product, and NCSi is the number of components in the i-th state. The trend of technological evolutions Appl. Sci. 2020, 10, 406 7 of 21

calculated based on their distance in the word tree. The similarity of nodes is calculated by numbering them for their distance on the word tree using Equations (7)–(10) [63]. (1) If two words are not in the same tree.

Sim{, Fij F }=0.1. (7)

(2) If two words are in the same tree.  0.65 In the second branch ; π −+ 0.80 In the third branch ; =×nk1 × Sim{ Fij , F } cos n  (8) 180 n 0.90 In the fourth branch ;  0.96 In the fifth branch ;

where n is the total number of nodes in the branch layer, and k is the distance between two branches. (3) When numbers are same and the end number is ‘=’.

Sim{, Fij F }=1, (9)

(4) When numbers are same and the end number is ‘#’.

Sim{, Fij F }=0.5. (10)

Using the semantic similarity calculation software of the synonym forest, we can calculate the similarity of two words according to the above definitions [64]. After calculating transition distances of function chains, the transition distances are weighted according to Equation (11): ww+ NNij wNSNS=∈∈ , (11) SSpq z -1 i p j q where z is the number of function chains, divided by z − 1 to make the sum of the weights be 1. The weighted transition distance of two function chains is calculated by Equation (12): Appl. Sci. 2020, 10, 406 wSimGG{,} 8 of 21 = SSpq p q WSim{,} Gpq G , (12) Max{} w SSpq is used towhere improve Max{ the𝜔 level} is the of correction idealization coefficient [65 to]. make The calculationvalues in the matrix equation easily ofdistinguishable. idealization levels is as follows: For an undirected graph A = (G, W), where GP = {G1, G2, ..., Gn}, W = {W1, W2, …, Wm}. G is a set of function chains, and W is a set of similarity betweenUF function chains. Using threshold value W0 I = P P , (14) removes edges less than W0 in the undirected graphHF +and deletesEX independent nodes. A new subgraph A0 is generated. InterconnectedP nodes in subgraph A0 are the functionP chains of the transformable where I is the idealized level, UF is the sum of useful functions, HF is the sum of harmful functions, P product. The connection between nodes indicates that the function chains represented by these nodesP and EXcanis expensesbe transformed including each other. cost, Each space, interconnect consumeded node energy, represents noise, a state etc. of In a this transformable paper, UF is the P number ofproduct, useful functions,and these nodesHF formis assumedthe concept as of 0a becausetransformable the harmfulproduct. As function it is difficult should to map not the be proposed P in design,functional and EX domainis the to number physical ofdomain components directly, physical in the product.components can be designed by refining functions in the mapping process, as shown in Figure 6.

FigureFigure 6. Mapping 6. Mapping of of functions–solutions–components. functions–solutions–components.

Comparing the idealization level of a transformable product to multiple products with the same functions can effectively determine whether the function implementation has been improved. The idealization level of a transformable product divided by the idealization level of existing products is the change degree of the idealization level, as shown in Equation (15):

I C = t , (15) Ie where C is the change degree of the idealization level, It is the idealization level of a transformable product, and Ie is the idealization level of existing products.

4. Case Study A wheelchair is developed in a case study to verify our proposed method. The wheelchair is required to meet needs of people with walking difficulty due to illness, injury, or disability [66]. Different user groups or different usage environments may have different needs for the wheelchair. The collected user needs are listed in Table2.

Table 2. User needs for a wheelchair.

No. Needs 1 Climbing stairs without the other help 2 Backrest can be adjusted 3 Avoiding sun and rain in wheelchair 4 Sleep in wheelchair 5 Working in wheelchair 6 Moving for navigation 7 Using in the bathroom 8 Taking a bath in a wheelchair

These needs are formalized for details as shown in Table3. Appl. Sci. 2020, 10, 406 9 of 21

Table 3. User needs.

Current Expected No. User Time Scene Activity Situation Situation With other’s N All the user Travel time Stair case Climb the stairs Without help 1 help Seat angle not Seat angle N Paralyzed user Changing posture Indoor Sitting 2 adjustable adjustable Where there is Driving wheelchair N All the user Outdoor No shelter Have shelter 3 sunshine or rain forward

N4 All the user Afternoon Indoor Sleep Sit down Lie down Work in N Business people Work time Office Work Work at desk 5 wheelchair Driving wheelchair Have N Outgoing user When going out Outdoor No navigation 6 forward navigation When going to the N Paralyzed user Bathroom Use the toilet With help Without help 7 toilet When taking a N Paralyzed user Bathroom Take a bath With help Without help 8 bath

Needs in Table2 are compared for the importance as shown in Table4.

Table 4. Comparisons for the importance of needs for a wheelchair.

Needs N1 N2 N3 N4 N5 N6 N7 N8

N1 N1 N2 N1 N1 N1 N1 N7 N8 N2 N2 N2 N2 N2 N2 N2 N2 N3 N3 N4 N3 N3 N7 N8 N4 N4 N4 N4 N7 N8 N5 N5 N5 N7 N8 N6 N6 N7 N8 N7 N7 N7 N8 N8

The needs are weighted based on results of Table4, as shown in Table5.

Table 5. Weight of needs.

Needs N Weight W

N1 0.14 N2 0.22 N3 0.08 N4 0.11 N5 0.06 N6 0.03 N7 0.19 N8 0.17

Weights of needs in Table5 were decided by using the method proposed in Table1. All needs are compared by a pairwise method. For two needs, the more important one is listed in Table4 after the comparison. The final weight of a need is decided by its appearance times in Table4. Weights in Appl. Sci. 2020, 10, 406 10 of 21

Appl. Sci. 2020, 10, 406 10 of 21 Table5 are normalized values; therefore, the total weights are 1. According to Equation (1), wNiNj is calculated as shown in Equation (16): N 0 0.051 0.031 0.036 0.028 0.024 0.047 0.044 1   N1 0 0.051 0.031 0.036 0.028 0.024 0.047 0.044 N2  0 0.043 0.047 0.04 0.036 0.059 0.055    NN2  0 0.0430 0.047 0.027 0.04 0.02 0.036 0.016 0.059 0.039 0.055 0.038  3   N  0 0.027 0.02 0.016 0.039 0.038  N3  0 0.024 0.02 0.043 0.04  = 4   wNN N4  0 0.024 0.02 0.043 0.04  w =ij N  0 0.013 0.036 0.033  NiNj 5  . (16) N5  0 0.013 0.036 0.033  . (16) N  0 0.031 0.028  N 6  0 0.031 0.028  6   N7  0 0.051  N7  0 0.051    NN8 8 00

N NN1 12345678 N2 N N3 N N4 N N5 N N6 N 7 N 8

UsingUsing EquationEquation (3),(3), thethe relationshiprelationship matrixmatrix ofof needsneeds isis establishedestablished asas shownshown inin EquationEquation (17):(17):

N1  00.260.1600000 N1  0 0.26 0.16 0 0 0 0 0  N  0 0.22 0.48 0.41 0.18 0.3 0.28  N 2  0 0.22 0.48 0.41 0.18 0.3 0.28  2   N  00.14 00.08 0 0 N33  0 0.14 0 0.08 0 0    NN44  000000 0 0 0 0  R =R =     NN55  00000 0 0 0 . .(17) (17)   NN6  0000 0 0  6     NN7  000 0  7   N8 0 N8 0 N1 N2 N3 N4 N5 N6 N7 N8 NNNNNNNN12345678 According to the relationship matrix, we can draw the needs-related undirected graph as shown According to the relationship matrix, we can draw the needs-related undirected graph as shown in Figure7. in Figure 7.

FigureFigure 7.7. Needs-related undirectedundirected graph.graph.

DesignersDesigners cancan choose didifferentfferent thresholds in didifffferenterent scenesscenes based on the design requirements. ForFor aa givengiven thresholdthreshold valuevalue RR == 0.4, the resulting segmentations ofof thethe graphgraph areare shownshown inin FigureFigure8 8.. Appl. Sci. 2020, 10, 406 11 of 21

Appl. Sci. 2020, 10, 406 11 of 21

Appl. Sci. 2020, 10, 406 11 of 21

FigureFigure 8. Segmentations 8. Segmentations of of needs-relatedneeds-related undirected undirected graph. graph. As shown in Figure 8, the needs are divided into six categories corresponding to six potential As shown in Figure8, the needs are divided into six categories corresponding to six potential states, as shown in Table 6. states, as shown in Table6. Figure 8. SegmentationsTable 6. Scenario of descriptionneeds-related of six undirected states. graph.

States Needs Table 6. Scenario description Scenario ofDescription six states. As shown in Figure 8, the needs are divided into six categories corresponding to six potential Go downstairs in a wheelchair, climb stairs to a smooth road and continue to S1 N1 states,States as shown Needs in Table 6.drive the wheelchair forward. Scenario Description AdjustGo angle downstairs of the seatback in a wheelchair,to change sitting climb posture, stairs adjust to a smooth table board road for and S S2 N2, NN4, N5 Table 6. Scenario description of six states. 1 1 office use,continue and adjust to drive seat theto sleep wheelchair flat during forward. break. S3 N3 Drive the wheelchair in rainy days, adjust the shelter to block wind and rain. States Needs Adjust angle of the seatbackScenario toDescription change sitting posture, adjust table S S4 N ,NN6 ,N Guide road when driving a wheelchair 2 2 4 Go5 downstairsboard forin a o wheelchair,ffice use, and climb adjust stairs seat to to a sleep smooth flat road during and break. continue to S1 S5 N1 N7 Go to toilet and clean in wheelchair drive the wheelchair forward. S6 N8 Take aDrive bath in the wheelchair wheelchair in rainy days, adjust the shelter to block wind S3 N3 Adjust angle of the seatback to change sitting posture, adjust table board for S2 N2, N4, N5 and rain. The product functionsoffice use, in andthe scenarioadjust seat are toobta sleepined flat through during the break. description of the scenario. S4 N6 Guide road when driving a wheelchair S3 FunctionN chains3 of Drivethe six thestates wheelchair are obtained in afte rainyr the days, function adjust decomposition the shelter asto shown block inwind Figure and 9. rain. SS54 N6 N7 Guide roadGo when to toilet driving and clean a wheelchair in wheelchair

SS65 N7 N8 Go to toiletTake and abath clean in in wheelchair wheelchair S6 N8 Take a bath in wheelchair

(a) TheThe product product functions functions in in the the scenario scenario areare obtainedobtained through through the the description description of the of scenario. the scenario. FunctionFunction chains chains of the of the six six states states are are obtained obtained after after thethe function decomposition decomposition as asshown shown in Figure in Figure 9. 9.

(a)

(b)

(c)

(b)

(c)

Figure 9. Cont. Appl. Sci. 2020, 10, 406 12 of 21 Appl. Sci. 2020, 10, 406 12 of 21

(d)

(e)

(f)

Figure 9. Function chains of the six states. (a) function chain G1, (b) function chain G2, (c) function Figure 9. Function chains of the six states. (a) function chain G1,(b) function chain G2,(c) function chain G3, (d) function chain G4, (e) function chain G5, (f) function chain G6. chain G3,(d) function chain G4,(e) function chain G5,(f) function chain G6. According to Equations (7)–(10), transition distances between any two function chains can be According to Equations (7)–(10), transition distances between any two function chains can be obtained as shown in Equation (18): obtained as shown in Equation (18):

S1 0 12.48 5.67 5.8 19.49 21.49   SS 0 12.480 20.8 5.67 20.35 5.8 28 19.49 30 21.49 2 1     S3S2  0 20.80 20.35 0.9 17 28 19 30  Trans{,} G G =   pq S  01719.  4S3  0 0.9 17 19  (18) Trans Gp, Gq =   { } S5S  004.9 17 19  . (18) 4   S  0  6S5  0 4.9    S 6 SSSSSS123456 0 S S S S S S Using Equation (5), the similarity of two1 functional2 3chains is4 obtained5 as shown6 in Equation (19):

Using Equation (5), the similarityS of1  two0 functional 0.52 0.62 chains 0.61 is 0.19 obtained 0.17 as shown in Equation (19): S 0 0.17 0.19 0.18 0.17 2   SS10 0.520 0.62 0.94 0.61 0.26 0.19 0.24 0.17 = 3   Sim{,} Gpq G   SS2  0 0.170 0.19 0.26 0.18 0.24 0.17.  4   (19) S  0 0.94 0.26 0.24  S53  00.86  Sim Gp, Gq =   { } SS4  0 0.260 0.24  . (19) 6     S 5 SSSSSS 0 0.86   123456  S6 0 Based on Equation (11), weights of the distance between any two function chains are obtained S1 S2 S3 S4 S5 S6 as shown in Equation (20): Based on Equation (11), weights of the distance between any two function chains are obtained as shown in Equation (20): Appl. Sci. 2020, 10, 406 13 of 21 Appl.Appl. Sci. Sci. 20202020, 10, 10, 406, 406 1313 of of21 21

S1 0 0.106 0.044 0.034 0.066 0.062 S1 0 0.106 0.044 0.034 0.066 0.062 S2  0 0.094 0.084 0.116 0.112  S1 0 0.106 0.044 0.034 0.066 0.062 S2  0 0.094 0.084 0.116 0.112  S3 0 0.022 0.054 0.050  ω = S2  0 0.094 0.084 0.116 0.112  SS S  0 0.022 0.054 0.050  ω iq= S3  0 0.044 0.040 . SS 4S  0 0.022 0.054 0.050  (20) iq =S 3  0 0.044 0.040  ωSiSq 4  .  (20) S5 S  0 0.04400.072 0.040  . (20) 4   S5  00.072 S6S5  0 0.0720    S6  0  S 6 SSS123 SSS 456 0 SSS123 S 1 S 2 S 3 SSSS 456 4 S 5 S 6 According to Equation (12), the weighted similarity is obtained as shown in Equation (21): AccordingAccording to to Equation Equation (12), (12), the the weighted weighted simila similarityrity is is obtained obtained as as shown shown in in Equation Equation (21): (21): S1 0 0.48 0.24 0.47 0.11 0.09 S1 0 0.48 0.24 0.47 0.11 0.09  S2 S1  00 0.48 0.14 0.24 0.14 0.47 0.18 0.11 0.16 0.09    S2 S  00 0.14 0.14 0.14 0.14 0.18 0.18 0.16 0.16  S32  0 0.18 0.12 0.10  WSim{,} G G =   pqS3 S3  00 0.18 0.18 0.12 0.12 0.10 0.10  WSimWSim{,} G GG == S4  0 0.10 0.08 . (21) pqp, q   { } S4 S4  00 0.10 0.10 0.08 0.08 .  .(21) (21) S5  00.53 S  0 0.53  S5 5  00.53  S6 0  S6 0 S6 0 SSS123 SSS 456 S1 S2 S3 S4 S5 S6 SSS123 SSS 456 An undirected graph of the matrix in Equation (21) is then established as shown in Figure 10. AnAn undirected undirected graph graph of of the the matrix matrix in in Equation Equation (21) (21) is is then then established established as as shown shown in in Figure Figure 10. 10 .

Figure 10. The undirected graph of the weighted similarity. FigureFigure 10. 10. TheThe undirected undirected graph graph of of the the weighted weighted similarity. similarity. For a given threshold value R = 0.4, the resulting segmentation of the graph is formed in Figure 11. ForFor a agiven given threshold threshold value value R = 0.4,0.4, the resulting segmentationsegmentation ofof the the graph graph is is formed formed in in Figure Figure 11 . 11.

FigureFigure 11. 11. SegmentationsSegmentations of of the the undirected undirected graph graph based based on on the the weighted weighted similarity. similarity. Figure 11. Segmentations of the undirected graph based on the weighted similarity. Therefore, two final concepts can be formed for the wheelchair based on two segments formed in Figure 11, and the first concept has three states S1,S2, and S4. Its function chain is shown in Figure 12. Appl. Sci. 2020, 10, 406 14 of 21

Therefore, two final concepts can be formed for the wheelchair based on two segments formed Appl. Sci.in Figure2020, 10 11,, 406 and the first concept has three states S1, S2, and S4. Its function chain is shown in Figure14 of 21 12.

FigureFigure 12. 12.Function Function chain of of the the first first concept. concept.

FollowingFollowing the the mapping mapping process process in in Figure Figure6 6,, thethe relationship between between functions functions and and components components of theof first the first concept concept can can be be formed formed as as shown shown inin TableTable 77.. Based on on corresponding corresponding components components to meet to meet the requiredthe required functions, functions, a conceptual a conceptual model model ofof thethe wheelchair can can be be proposed. proposed. The The computer-aided computer-aided design(CAD)design(CAD) model model of theof the first first concept concept is is shown shown in Figure 13. 13 . Appl. Sci. 2020, 10, 406 15 of 21

Table 7. RelationshipTable between 7. Relationship functions between and functions components and components of the of the first first concept. concept.

StatesStates FunctionsFunctions Components Components

Drive the wheelchair forward Wheels

Fix the passenger Wheel rack Climbing state Climbing state Lift wheelchair height Frame

Unfix the passenger Seat plate (a) (b) Brake wheelchair Backrest

Adjust pedal angle Handrail

Adjust seat angle Track Working and sleeping state Rotate table board Working and Track frame sleeping state Put the seat down Track wheel Fold table board (c) (d) Pedal hinge Figure 13. The first conceptual design of the wheelchair.Put the seat up (a ) in climbing state, (b) in working state, (c) in sleeping state, (d) in navigation state. Pedal Drive the wheelchair forward

Backrest hinge Navigation state Drive the wheelchair forward

Navigation Board Expose the navigation state

Fold the navigation Navigation rack

Appl. Sci. 2020, 10, 406 14 of 21

Therefore, two final concepts can be formed for the wheelchair based on two segments formed in Figure 11, and the first concept has three states S1, S2, and S4. Its function chain is shown in Figure 12.

Figure 12. Function chain of the first concept.

Following the mapping process in Figure 6, the relationship between functions and components of the first concept can be formed as shown in Table 7. Based on corresponding components to meet theAppl. required Sci. 2020, 10 functions,, 406 a conceptual model of the wheelchair can be proposed. The computer-aided15 of 21 design(CAD) model of the first concept is shown in Figure 13.

(a) (b)

(c) (d)

Figure 13. TheThe first first conceptual conceptual design design of of the the wheelchair. wheelchair. ( (aa)) in in climbing climbing state, state, ( (bb)) in in working working state, state, ( (cc)) in sleeping state, (d) in navigation state. Appl. Sci.insleeping 2020, 10, 406 state, (d) in navigation state. 16 of 21

The second concept consists of S5 and S6, its function chain is shown in Figure 14. The second concept consists of S5 and S6, its function chain is shown in Figure 14.

Figure 14. Function chain of the second design concept.

According to to the the mapping mapping relationship relationship of offunc functions–solutions–componentstions–solutions–components in Figure in Figure 6, the6, relationshipthe relationship between between functions functions and components and components of the ofsecond the second concept concept is mapped is mapped as shown as in shown Table 8.in Table8.

The CAD model of the second conceptual design is shown in Figure 15.

(a) (b)

Figure 15. The second design of the wheelchair. (a) in toilet state, (b) in bathing state.

According to Equation (13), the proportion of shared components in the first concept can be calculated as 70%. The proportion of shared components in the second concept can be calculated as 75%. More than half of the parts are reused, which saves a lot of material and space resources compared to the single-function wheelchairs. The number of useful functions and number of components are shown in Table 9.

Appl. Sci. 2020, 10, 406 16 of 21

Appl. Sci. 2020, 10, 406 17 of 21 Table 8. Relationship between functions and components of the second concept. Table 8. Relationship between functions and components of the second concept.

StatesStates Functions Functions ComponentsComponents Brake wheelchair

Support passenger

Take off clothes

Collect dirt Toilet Toilet state state Clean body

Wheels Support passenger

Wheel rack Wear clothes

Handrail Drive the wheelchair forward

Frame Brake wheelchair Carer Support passenger

Backrest hinge Take off clothes

Pedal Clean body

Seat plate Bathing Change posture Bathing state state Backrest Clean body

Support passenger

Wear clothes

Drive the wheelchair forward

The CAD model of the second conceptual design is shown in Figure 15.

According to Equation (13), the proportion of shared components in the first concept can be calculated as 70%. The proportion of shared components in the second concept can be calculated as 75%. More than half of the parts are reused, which saves a lot of material and space resources compared to the single-function wheelchairs. The number of useful functions and number of components are shown in Table9. Appl. Sci. 2020, 10, 406 16 of 21

The second concept consists of S5 and S6, its function chain is shown in Figure 14.

Figure 14. Function chain of the second design concept.

According to the mapping relationship of functions–solutions–components in Figure 6, the relationship between functions and components of the second concept is mapped as shown in Table Appl.8. Sci. 2020, 10, 406 17 of 21

(a) (b)

Figure 15. The second design of the wheelchair. ( a) in toilet state, ( b) in bathing state.

According to EquationTable 9. Useful (13), the functions proportion and related of shared components components in two concepts. in the first concept can be calculated as 70%. The proportion of shared componentsNumber in the of second Useful concept canNumber be calculated of as Product 75%. More than half of the parts are reused, which savesFunctions a lot of material andComponents space resources comparedTransformable to the single-function product in first wheelchairs. concept The number 13of useful functions and 14 number of componentsMultiple single-function are shown in products Table 9. in first concept 13 20 Transformable product in second concept 8 9 Multiple single-function products in second concept 8 12

According to Equations (14) and (15), the change degree of the idealization level can be calculated as 1.43 in the first concept, and 1.33 in the second concept. The results show that our proposed method increases the level of the product idealization and conforms to the trend of technological system evolutions in the design for transformable products.

5. Discussion A transformable product uses the less resource and space than single-function products. Methods were proposed in this paper to decide required functional components and conceptual design of transformable products. Although there are many methods proposed to decide the need and design of transformable products [27–31], the method proposed in this research improves the existing methods by providing an effective tool to assist designers in the design of transformable products. A mathematical model was established for the design process of transformable products accurately and effectively. It proposed the time correlation to cluster the needs, which is a quantitative clustering method that can better assist designers to cluster needs. Segmentations of needs were used to form scenarios of function chains. The transition distance was determined by the cost of transition between different function chains. By calculating the distance between function chains, the similarity between them are more objectively. A weighted undirected graph was built according to the transition distance. After the undirected graph segmentation, the connected subgraphs were used to form final design concepts of transformable products. The segmentation of graph makes the final concept more systematic. The case study verified our proposed method in the design of a transformable wheelchair. Compared to the existing wheelchairs on the market that can only drive passengers on the smooth road, two concepts of the proposed transformable wheelchair can meet various needs of operation functions. Although the number of the possible detailed constructions of wheelchairs is huge or infinite, the conceptual design of wheelchairs to meet transformable requirements is limited considering the available functional components and configurations. We used benchmarking and expert evaluations to generate concepts and select the feasible solution. The design results were evaluated by comparing the idealization level Appl. Sci. 2020, 10, 406 18 of 21 of transformable products with the existing products. The two concepts generated in the case study demonstrated effectiveness of the proposed method. The results show that our proposed method increases the level of the wheelchair idealization and conforms to the trend of technological system evolutions in the design for transformable products. In this paper, we evaluate results by comparing the idealization level of transformable products with the existing products. If the idealization level is improved by the proposed method, it shows that the method is effective. We are working on considering more factors to evaluate transformable products. The optional solution will be searched in the further work. It will consider not only the technical implementation but also expectations of the industry and users to evaluate transformable products. The method improves the conceptual design process of transformable products. However, the process is mainly a manual process which needs the of designers. The current method is for the redesign of an existing product, not for development of new products. The design process is mainly a manual process that needs the design knowledge of designers. The further work will extend the method to the new product design. More factors will be considered to search an optional solution and evaluate design solutions. The method will include not only the technical implementation but also expectations of the industry and users. A software tool will be developed for the automatic design of transformable products. Further work will also apply the proposed method to different transformable products for the method improvement. Interfaces of transformable products will be considered. A machine learning method will be used to decide the change need of transformable products from one state to another.

Author Contributions: Conceptualization, J.Z., G.C., and H.Z.; methodology, J.Z., G.C., Q.P., and R.T.; writing—original draft preparation, J.Z.; writing—review and editing, Q.P., W.L., and J.Z.; supervision, G.C.; project administration, R.T.; funding acquisition, G.C. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National innovation method work special project, Grant No. 2019IM020200, the Innovation Ability Promotion Project of Hebei Province, Grant No. 18961823H, the Support Scheme for 100 Outstanding Innovative Talents in Colleges and Universities in Hebei Province, Grant No. SLRC2017030, the Natural Science Foundation of China, Grant No. 51675159, the Central Government Guides Local Science and Technology Development Project, Grant No. 18241837G, and the Project Supported by Hebei Provincial Department of Education for Innovation Ability Training of Graduate Students, Grant No. cxzzbs2019033. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Koren, Y.; Heisel, U.; Jovane, F.; Moriwaki, T.; Pritschow, G.; Ulsoy, G.; Van Brussel, H. Reconfigurable manufacturing systems. CIRP Ann. 1999, 48, 527–540. [CrossRef] 2. ElMaraghy, H.A. Changeable and Reconfigurable Manufacturing Systems; Springer: London, UK, 2008. 3. Musharavati, F. A method for optimizing the reconfiguration design task in manufacturing systems. In Proceedings of the 2011 International Conference on Industrial Engineering and Operations Management, Kuala Lumpur, Malaysia, 22–24 January 2011; pp. 603–609. 4. Aguilar, A.; Roman-Flores, A.; Huegel, J.C. Design, refinement, implementation and prototype testing of a reconfigurable lathe-mill. J. Manuf. Syst. 2013, 32, 364–371. [CrossRef] 5. Carbonari, L.; Callegari, M.; Palmieri, G.; Palpacelli, M.-C. A new class of reconfigurable parallel kinematic machines. Mech. Mach. Theory 2014, 79, 173–183. [CrossRef] 6. Katz, R. Design principles of reconfigurable machines. Int. J. Adv. Manuf. Technol. 2007, 34, 430–439. [CrossRef] 7. Bi, Z.M.; Lang, S.Y.T.; Verner, M.; Orban, P. Development of reconfigurable machines. Int. J. Adv. Manuf. Technol. 2008, 39, 1227–1251. [CrossRef] 8. Gu, P.; Hashemian, M.; Nee, A.Y.C. Adaptable design. CIRP Ann. Manuf. Technol. 2004, 53, 539–557. [CrossRef] 9. Gu, P.; Xue, D.; Nee, A.Y.C. Adaptable design: Concepts, methods, and applications. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 2009, 223, 1367–1387. [CrossRef] 10. Gershenson, J.K.; Prasad, G.J.; Zhang, Y. Product modularity: Definitions and benefits. J. Eng. Des. 2003, 14, 295–313. [CrossRef] Appl. Sci. 2020, 10, 406 19 of 21

11. Gershenson, J.K.; Prasad, G.J.; Zhang, Y. Product modularity: Measures and design methods. J. Eng. Des. 2004, 15, 33–51. [CrossRef] 12. Jung, S.; Simpson, T.W. New modularity indices for modularity assessment and clustering of product architecture. J. Eng. Des. 2017, 28, 1–22. [CrossRef] 13. Kashkoush, M.; Elmaraghy, H. Designing modular product architecture for optimal overall product modularity. J. Eng. Des. 2017, 28, 293–316. [CrossRef] 14. Simpson, T.W.; Siddique, Z.; Jiao, J. Product Platform and Product Family Design, Methods and Applications; Springer: Berlin, Germany, 2006. 15. Jiao, J.; Simpson, T.W.; Siddique, Z. Product family design and platform-based product development: A state of-the-art review. J. Intell. Manuf. 2007, 18, 5–29. [CrossRef] 16. Saleh, J.H.; Mark, G.; Jordan, N.C. Flexibility: A multi-disciplinary literature review and a research agenda for designing flexible engineering systems. J. Eng. Des. 2009, 20, 307–323. [CrossRef] 17. Palani-Rajan, P.K.; Van-Wie, M.; Campbell, M.I.; Wood, K.L.; Otto, K.N. An empirical foundation for product flexibility. Des. Stud. 2005, 26, 405–438. [CrossRef] 18. BELL-BOEING V-22. Available online: https://www.skybrary.aero/index.php/V22 (accessed on 5 December 2019). 19. Aquada. Available online: https://www.gibbsamphibians.com/platform/aquada/ (accessed on 5 December 2019). 20. Liapi, K. Transformable structures: Design features and preliminary investigation. J. Archit. Eng. 2001, 7, 13–17. [CrossRef] 21. Andjelkovic, V. Transformation principles in the architectural design of a contemporary house. Arch. Doct 2016, 4, 87–107. 22. HOLMSUND. Available online: https://www.ikea.cn/cn/en/catalog/products/S09228206/ (accessed on 5 December 2019). 23. Weaver, J.; Wood, K.; Crawford, R.; Jensen, D. Transformation : A meta-analogical framework. J. Comput. Inf. Sci. Eng. 2010, 10, 031012. [CrossRef] 24. Singh, V.; Skiles, S.M.; Krager, J.E.; Wood, K.L.; Jensen, D.; Sierakowski, R. Innovations in design through transformation: A fundamental study of transformation principles. J. Mech. Des. 2009, 131, 081010. [CrossRef] 25. Dowlatshahi, S. Product design in a concurrent engineering environment: An optimization approach. Int. J. Prod. Res. 1992, 30, 1803–1818. [CrossRef] 26. Weaver, J. Transformer Design: Empirical Studies of Transformation Principles, Facilitators, and Functions. Master’s Thesis, University of Texas at Austin, Austin, TX, USA, 2008. 27. Singh, V.; Walther, B.; Krager, J.; Putnam, N.; Koraishy, B.; Wood, K.L.; Jensen, D. Design for Transformation: Theory, Method and Application. In Proceedings of the ASME International Design Engineering Technical Conference & Computers and Information in Engineering Conference, Las Vegas, NV, USA, 4–7 September 2007; pp. 447–459. 28. Weaver, J.; Wood, K.L.; Jensen, D. Transformation Facilitators: A Quantitative Analysis of Reconfigurable Products and Their Characteristics. In Proceedings of the International Design Engineering Technical Conferences, Brooklyn, NY, USA, 3–6 August 2008; pp. 351–366. 29. Singh, V. Design for Transformation: Design Principles and Approach with Concept Generation Tools and Techniques. Master’s Thesis, University of Texas at Austin, Austin, TX, USA, 2007. 30. Camburn, B.A.; Guillemette, J.; Crawford, R.H.; Jensen, D.J.; Wood, J.J.; Wood, K.L. When to transform? Development of indicators for design context evaluation. In Proceedings of the International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (ASME 2010), Montreal, QC, Canada, 15–18 August 2010; pp. 249–266. 31. Camburn, B.; Wood, K.; Crawford, R.; Robbens, J.; Jensen, D.; Patel, A. Advances in transformational design: Correlating context evaluation to quality feasibility and novelty. In Proceedings of the International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (ASME 2012), Chicago, IL, USA, 12–15 August 2012; pp. 447–460. 32. Son, J. Mechanical Transformation to Support Design for Environmentally Significant Behaviour. Master’s Thesis, University of Toronto, Toronto, ON, Canada, 2012. Appl. Sci. 2020, 10, 406 20 of 21

33. Son, J.; Shu, L.H. The mechanical transformation and environmentally conscious behavior. AI EDAM 2014, 28, 193–203. [CrossRef] 34. HaeBin, L. Difficulties in Transformable Design and Its Implications. Master’s Thesis, UNIST, Ulsan, Korea, 2016. 35. Li, S. Introduction to , 1st ed.; Tsinghua University Press: Beijing, China, 2009. 36. Liu, X. Research on Key Technologies of Situated Design for Innovative Process. Ph.D. Thesis, Hebei University of Technology, Tianjin, China, 2007. 37. DeSouza, K.C.; Awazu, Y.; Jha, S.; Dombrowski, C.; Papagari, S.; Baloh, P.; Kim, J.Y. Customer-driven innovation. Res. Technol. Manag. 2008, 51, 35–44. [CrossRef] 38. Hazelrigg, G.A. A framework for decision-based engineering design. J. Mech. Des. 1998, 120, 653–658. [CrossRef] 39. Song, W. Requirement management for product-service systems: Status review and future trends. Comput. Ind. 2017, 85, 11–22. [CrossRef] 40. Wang, Z.; Chen, C.-H.; Zheng, P.; Li, X.; Khoo, L.P. A novel data-driven graph-based requirement elicitation framework in the smart product-service system context. Adv. Eng. Inform. 2019, 42, 100983. [CrossRef] 41. Lowdermilk, T.; Rich, J. The Customer-Driven Playbook: Converting Customer Feedback into Successful Products; O’Reilly Media, Inc.: Sebastopol, CA, USA, 2017. 42. Cai, W. Extension theory and its application. Chin. Sci. Bull. 1999, 44, 1538–1548. [CrossRef] 43. Terninko, J. Step-by-Step QFD: Customer-Driven Product Design, 2nd ed.; Routledge: New York, NY, USA, 1997. 44. Zheng, P.; Xun, X.; Sheng, Q.X. A weighted interval rough number based method to determine relative importance ratings of customer requirements in QFD product planning. J. Intell. Manuf. 2019, 30, 3–16. 45. Suh, N.P. , Advances and Applications; Oxford university press: Oxford, UK, 2001. 46. Tang, D.; Zhang, G.; Dai, S. Design as integration of axiomatic design and design structure matrix. Robot. Comput. Integr. Manuf. 2009, 25, 610–619. [CrossRef] 47. Farid, A.M.; Luis, R. An axiomatic design of a multiagent reconfigurable mechatronic system architecture. IEEE Trans. Ind. Inform. 2015, 11, 1142–1155. [CrossRef] 48. Eilouti, B. Scenario-based design: New applications in metamorphic architecture. Front. Archit. Res. 2018, 7, 530–543. [CrossRef] 49. Carroll, J.M. Five reasons for scenario-based design. In Proceedings of the 32nd Hawaii International Conference on System Sciences, Maui, HI, USA, 5–8 January 1999. 50. Suh, N.P. The Principles of Design; Oxford University Press on Demand: Oxford, UK, 1990. 51. Otto, K.; Wood, K. Product Design: Techniques in Reverse Engineering and ; Prentice-Hall: Upper Saddle River, NJ, USA, 2001. 52. Pahl, G.; Beitz, W. Engineering Design: A Systematic Approach, 2nd ed.; Springer: Berlin, Germany, 2007. 53. Stone, R.B.; Wood, K.L.; Crawford, R.H. A heuristic method for identifying modules for product . Des. Stud. 2000, 21, 5–31. [CrossRef] 54. Ulrich, K.T. Product Design and Development, 2nd ed.; Tata McGraw-Hill Education: Boston, MA, USA, 2004. 55. Liu, W.; Tan, R.; Cao, G.; Zhang, Z.; Huang, S.; Liu, L. A proposed radicality evaluation method for design ideas at conceptual design stage. Comput. Ind. Eng. 2019, 132, 141–152. [CrossRef] 56. Bollobás, B. Modern Graph Theory; Springer: New York, NY, USA, 1998. 57. Gao, X.; Xiao, B.; Tao, D.; Li, X. A survey of graph edit distance. Pattern Anal. Appl. 2010, 13, 113–129. [CrossRef] 58. Neuhaus, M.; Horst, B. Automatic learning of cost functions for graph edit distance. Inf. Sci. 2007, 177, 239–247. [CrossRef] 59. Cech,ˇ P. Matching UML class models using graph edit distance. Expert Syst. Appl. 2019, 130, 206–224. [CrossRef] 60. Cortés, X.; Donatello, C.; Hubert, C. Learning edit cost estimation models for graph edit distance. Pattern Recognit. Lett. 2019, 125, 256–263. [CrossRef] 61. Montani, S.; Leonardi, G.; Quaglini, S.; Cavallini, A.; Micieli, G. A knowledge-intensive approach to process similarity calculation. Expert Syst. Appl. 2015, 42, 4207–4215. [CrossRef] 62. Zhang, S.; Zheng, X.; Hu, C. A survey of semantic similarity and its application to social network analysis. In Proceedings of the 2015 IEEE International Conference on Big Data, Santa Clara, CA, USA, 29 October–1 November 2015. Appl. Sci. 2020, 10, 406 21 of 21

63. Tian, J.; Zhao, W. Words Similarity Algorithm Based on Word Tree in Semantic Web Adaptive Learning System. J. Univ. Inf. Sci. Ed. 2010, 28, 602–608. 64. Semantic Similarity Computing and Programming Based on Synonym Forest. Available online: http: //download.csdn.net/download/huandaohack/4557989 (accessed on 5 December 2019). 65. Zhang, H. Innovative Design-Systematic Innovation Based on TRIZ; Machinery Industry Press: Beijing, China, 2017. 66. Wheelchair. Available online: http://wikipedia.moesalih.com/Wheelchair (accessed on 5 December 2019).

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).