Second Asan Symposum on Industral Automaton and Robotcs BITEC, Bangkok, Thaland May 7-8, 00 DEVELOPMENT OF DISASSEMBLY SUPPORT SYSTEM FOR MECHANICAL PARTS Ej ARAI, Hdefum WAKAMATSU, Akra TSUMAYA, Kech SHIRASE Dept. of Manufacturng Scence, School of Eng., Osaka Unversty - Yamadaoka, Suta, Osaka 6-087 JAPAN Hsash SASAJIMA Advanced Archtecture and Technologes Research and Development Headquarters Yamatake Corporaton --, Kawana, Fujsawa, Kanagawa -8 JAPAN Abstract: Assembly/dsassembly plannng of mechancal products s one of the mportant manufacturng actvtes that must be supported by computers. Furthermore, recently, the desgn for dsassemblablty/recyclablty becomes more mportant from the vewpont of Lfe Cycle Assessment or Emsson-Mnmum. Therefore, we develop a system whch can generate dsassembly sequences and whch can be appled to the desgn consderng the dsassemblablty. Frst, methods to calculate possble motons of parts and to detect confguratons where contact state transton occurs are ntroduced. Based on them, an algorthm for verfyng dsassemblablty of parts s explaned. Next, we propose a method for estmate the total number of feasble dsassembly sequences wthout actually generatng them. In order to reduce the number of dsassembly sequences, precedence constrants such as the assembly feature are ntroduced. Fnally, we mplement a dsassembly sequence generaton system based on our proposed methods and demonstrate ts effcency. Keywords: assembly, dsassembly, dsassemblablty, reuse, recycle.. INTRODUCTION Assembly/dsassembly plannng of mechancal products s one of the mportant manufacturng actvtes that must be supported by computers. Software systems that practcally generate mechancal assembly/dsassembly sequences must satsfy the followng requrements. They must guarantee the feasblty of the obtaned assembly/dsassembly sequences (Ara et al., 99). In order to satsfy ths requrement, they must deal wth varous evaluaton vewponts such as geometrcal nterference, the stablty of subassembles, and the functonalty of avalable assembly/dsassembly machnes (Uchyama et al., 99). They must reduce the number of obtaned sequences. Snce possble assembly/dsassembly sequences for practcal products often become surprsngly large, a great amount of computaton may be requred to generate the assembly/dsassembly sequences (Uchyama et al., 99). Furthermore, recently, not only the desgn for manufacturablty/assemblablty (Boothroyd et al., 99) but also the desgn for dsassemblablty/recyclablty becomes more mportant from the vewpont of the ecology (Jovane et al., 99)(Harjula et al., 996)(Krause & Selger, 997)(Nsh et al., 999)(Kasa & Suga, 999)(Chodo et al., 999). Therefore, we develop a system whch can generate dsassembly sequences wth the feasblty and the effcency and can be appled to the desgn consderng the ease of dsassembly for recyclng/reuse. Frst, the method for verfyng dsassemblablty of parts s explaned based on calculaton of possble motons and detecton of confguratons where contact state transton occures. Next, n order to reduce the number of dsassembly sequences, we propose a method for estmate t wthout actually generatng dsassembly sequences and ntroduce some precedence constrants. Fnally, we mplement a dsassembly support system and some examples are shown to demonstrate ts effcency.. DISASSEMBLY SEQUENCE GENERATION. Geometrc model and contact state In ths secton, we propose a method of dsassembly sequence generaton. Frst, we assume that an assembled product s gven by the CAD system and parts have rgd bodes. Let A and a be a selected part for dsasemblablty verfcaton and one of ts shape elements, respectvely. B and b denote all other parts exceptng A and one of ther shape elements. When a product s represented by a polyhedron, the shape element s ether a vertex, an edge, or a planar surface (face). We deal wth cylndrcal surfaces whose two ends are both crcles because axal parts wth rotatonal functonalty are typcal n mechancal products. Ther radus, normalzed vector of the central axs, and poston vector of a pont on the axs, are gven by the CAD system. Contact states can be represented by the combnaton of the shape elements mentoned above, for example, vertex a contacts wth face b. In our study, the contact states ncludng a cylndrcal surface are dealt wth specfcally. We regard only the case satsfyng the followng condtons as a cylndrcal contact as shown n Fg.: Contactng elements are both cylndrcal surfaces. Ther axes are colnear. Ther rad are the same. Other contact states ncludng a cylndrcal surface are represented as those between polyhedra by polyhedral approxmaton of the cylndrcal surface.. Generaton of possble motons from contact states The moton of a part s constraned by contact wth the other
Fg.. Cylndrcal contact parts. In our study, spatal moton s separated nto translatonal moton and rotatonal moton. Ths separaton allows analytcal calculaton of the confguraton where contact states change as descrbed n Secton.. Fgure shows an example of contact of two parts. In ths fgure, a and b, a vertex of a part A and a face of B respectvely, contact wth each other. Possble translatonal drectons of A are represented by x R whch satsfes the followng condton: f T x 0 () where f denotes the outward normal vector of face b. Moreover, possble rotatonal axs drectons of A are represented by x whch satsfes the followng nequalty: ( v v c ) f [ ] T x 0 () where, v, and v c denote the outer product of vectors, the poston vector of a, and the foot of the perpendcular from v to the rotatonal axs, respectvely. Please note that v v c ( ) s normalzed. We can also generate possble motons from other contact states whch ncludes vertex-vertex, edge-face, face-face contact and so on. b v Fg.. Contact state and possble moton. Calculaton of confguraton to transt contact states Contact states of parts can be changed when one part moves. Such transton of contact states can be classfed as follows:. The sum of dmensonalty of contactng elements decreases, where dmensonaltes of a vertex, an edge, and a surface are 0,, and, respectvely. If any element and ts bounds are n contact, only the maxmum value of the sum of dmensonalty s consdered. For example, n Fg., an edge of A and a face of B, a vertex of A and a face of B, an edge of A and an edge of B are n contact at once. In ths case, the edge-face contact has the maxmum value of the sum of dmensonalty, +=, and s used. If A s translated along the drecton x as shown n Fg., the edgeface contact turns nto the vertex-edge contact whose sum of dmensonalty s. Thus the sum of dmensonalty decreases. We call ths confguraton where contact state transton occurs contact decreasng confguraton (CDC).. Contact states are changed by the collson between parts A and B. We call such a confguraton contact ncreasng confguraton (CIC). When one element of part A s n cylndrcal contact and the part rotates around ts axs, contact state does not change. Ths rotatonal moton s not requred for removng a part, and can be excluded. Both CDC and CIC can be calculated f the geometrcal shape a v c x f A 0 B Fg.. Contact states and dmensonaltes of parts and ther removng motons are gven.. Algorthm for verfyng dsassemblablty Fgure shows the algorthm for verfyng the dsassemblablty. Frst we calculate X s whch denotes a set of possble motons x sk (k=,, K) calculated from w s whch denotes any confguraton. Then, for each k, we fnd x d sk and meanng the CDC and CIC calculated wth x sk and w s, and set the nearer confguraton of them to w sk. Replacng w s by w sk and repeatng ths procedure, a tree structure s constructed whose nodes and arcs denote confguratons and possble motons of a verfed part, respectvely. When w sk does not exst for an arbtrary translatonal moton, we decde that the part s dsassemblable. An upper boundary N max s ntroduced n order to lmt the number of tmes whch a part can change the removng drecton. If a state n whch a part s dsassemblable can not be found as the result of verfyng all nodes satsfyng the upper boundary, the part s not dsassemblable. If a confguraton whch s exactly the same as that whch has already been verfed s found, t s excluded, snce possble motons calculated from them are the same. In ths procedure, the case that a verfed part moves along the same path repeatedly does not occur. The current mplementaton s based on the breadth-frst search. In Fg., w nt, N s, W, and W denote an ntal confguraton of a verfed part, the number of tmes that moton drecton changes before reachng the confguraton w s, a set of unchecked nodes, and a set of checked nodes, respectvely. x sk Pck out Start W wnt W' Ø ws N s < N max? from W Calculate X s X s Ø? k k k + Calculate w sk Dsassembly s possble. w sk s translaton w sk does not exst? x Calculate w sk w sk exsts? w sk W w sk W'? W W { } k = K? W W - { w s } W' W' { w s } Fg.. Procedure flow chart W = Ø? w sk Dsassembly s mpossble.
. ESTIMATION OF DISASSEMBLY SEQUENCE NUMBER p p As mentoned n the prevous secton, We can verfy on a computer whether one part of a product can be dsassembled or not. By repeatng ths verfcaton for all parts, we can generate possble assembly sequences. But f the number of parts becomes larger, a great amount of computaton may be requred to generate assembly sequences because the number of them also becomes larger. Therefore, we must elmnate napproprate dsassembly sequences by gvng some precedence constrants n advance. In order to utlze for ths elmnaton, we propose a method for estmatng the number of dsassembly sequences. It allows desgners to decde whether other constrants should be gven. Precedence constrants for dsassembly can be represented by a bnomal relaton between two parts. For example, ( p, p j ) () means that part p must be removed before part p j. The assumpton that drectons for removng each part can be gven, allows us to represent the precedence constrants wth only logcal-and connectons, wthout usng logcal-or. They can be also expressed by ether an adjacency matrx or a drected graph. For convenence, we classfy such graphs nto as follows: out-tree graph n-tree graph (c) dsconnected graph consstng of out-tree graphs and n-tree graphs (d) others Frst, we consder only precedence constrants that can be represented by a type graph after they are transformed nto a non-transtve graph as shown n Fg.. We transform the non-transtve type graph nto a transtve graph as shown n Fg.. The graph shown n Fg.6 s a subgraph of the transtve graph as shown n Fg. where node p s a ntal node of arcs whose termnal nodes correspond to all other parts. It means that precedence constrants for dsassembly between p and all other parts, the number of them s r, are determned, whereas precedence constrants between other parts except part p are not determned. Hence, the number of dsassembly sequences from the graph as shown n Fg.6 s n! r! () ( r +)! where n denotes the total number of parts. Smlarly, as shown n Fg.6, p s the ntal node of arcs whose termnal nodes are and. Ths mples that sequences between p and the two parts are determned, whereas sequence between the two parts s not determned. The number of dsassembly sequences becomes n! r! r! ( r +)! ( r +)!. () Repeatng ths procedure for all parts, we n! r! r!lr n! ( r +)! ( r +)!L ( r n +)! = n! ( r +) ( r +)L( r n +). (6) r j s the out degree of each node and t s equal to the sum of components of the jth column of the matrx correspondng to the drected graph. The transtve graph as shown n Fg. can be represented by a matrx as shown n Fg.7. The number of feasble sequences calculated from the matrx s 6! = 0. (7) 6 Fgure 7 shows the feasble sequences satsfyng the matrx. These propertes can be readly extended to precedence constrants represented by ether type or type(c) graphs. p p Fg.. n-transtve and transtve graphs p p p Fg.6. Calculatng of dsassembly sequence number for precedence constrants represented by out-tree 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 + + + + + +. 6 7 8 9 0 6 7 8 9 0 sequence p p p p6 p p p p p6 p p p p p p p6 p p p p p6 p p p p p p6 p p p p p6 p p p p p p6 p p p p p p6 p p p p p p p p6 p p p p p6 p p p p p p6 p p p p p6 p p p p p p6 p p p p p p6 p p p p p6 p p p p p p6 p p p p p p6 p p p p p p6 p p p p p p6 p p p p p p6 p p p p p Fg.7. Calculatng of dsassembly sequence number for graph as shown n Fg. At present, we do not know how to calculate the number of the sequences from type(d) graph. We solve ths problem by calculatng the upper and the lower boundares of the sequences. The number gven by eq.(6) s smaller than the actual number for type(d) graphs. We call ths smaller number the lower boundary. We calculate the upper boundary by removng several arcs from the type(d) graph, whch transforms the graph nto another type. Thus, we can estmate the upper and the lower boundares of the number of dsassembly sequences wthout calculaton of possble motons or geometrcal confguratons of parts.. REDUCTION OF DISASSEMBLY SEQUENCE NUMBER In order to reduce the number of dsassembly sequences, we defne three operatons as follows: () ntroducton of the assembly feature
() consderaton of removng drectons for dsassembly () groupng parts Frst, we ntroduce the assembly feature. For example, bolts have the functon to fx one part to another part. So t s obvous that they must be removed before these two parts for dsassembly. Furthermore, the drecton of moton for ther removng s predetermned. We call such a set of parts whose dsassembly sequence can be predetermned by consderng ther functon the assembly feature. If a desgner adds some nformaton wth respect to the assembly feature to a product, the number of dsassembly sequences can be reduced. In our study, only three types of the assembly feature as shown n Fg.8 are prepared. They can be appled to a bolt, a knd of plug, and a key, respectvely..80 0 < N <.8 0 6. (9) As the number s stll large, we consder removng drectons. In ths case, we assume that dsassembly of parts whose translatonal drecton for removng s parallel to z-axs precedes that of any other parts. Then, the number becomes 8,870 < N < 0,880. (0) Fnally, we group some parts. In ths case, part 7, 8, 9, 0,, and can be grouped and they are represented by g. Then, the number becomes < N < 0. () Ths s suffcently small for generatng dsassembly sequences. Consequently, 8 sequences are generated as shown n Table. After that, the system can calculate dsassembly sequences of grouped parts. bolt-type plug-type (c) key-type Fg.8. Examples of assembly feature part 8 part part part 9 part 7 part part 0 part Next, precedence constrants between removng drectons for dsassembly are consdered. In general, the assembly/dsassembly of parts whose drectons for assembly/dsassembly are the same precedes that of parts whose drectons are dfferent. Therefore, precedence constrants wth respect to removng drectons can be gven. Fnally, we can reduce the number of dsassembly sequences by groupng parts. A set of parts g can be grouped f drectons for dsassembly of all grouped parts are the same and no parts satsfy both of the condtons below: p s not an element of g p corresponds to an ntermedate node on the path between any two parts whch are both elements of g. part 7 part Front vew part part 8 part 0 part 9 part part part By applyng above three operatons, we can add some precedence constrants for dsassembly to a product. Increase of the number of precedence constrants leads to decrease of the number of dsassembly sequences. For example, a product whch s added 8 precedence constrants as shown n Fg. has 0 dsassembly sequences, whle that whch s added constrants as shown n Fg.6 has 0 sequences. Thus, we can reduce the number of dsassembly sequences by addng precedence constrants to a product. When t becomes suffcently small, we can calculate actual dsassembly sequences usng the method explaned n Secton.. EXAMPLE OF DISASSEMBLY We mplemented a dsassembly support system on a UNIX workstaton n order to demonstrate the effcency of our proposed methods. In ths secton, some case studes of. Dsassembly sequence generaton for all parts We apply our developed system to a practcal mechancal product consstng of parts as shown n Fg.9. Frst, we generate precedence constrants from the vewpont of geometrc nterference. Then the system calculates the number of dsassembly sequences from generated precedence constrants. The number N becomes.90 0 6 < N <. 0 6. (8) Next, we consder the assembly feature n order to reduce the number N. Part 9, 0,, and have bolt-type assembly feature and part and 6 have plug-type assembly feature. By addng precedence constrants wth respect to these features, The number becomes part 6 part part Rear vew Fg.9. Example of product to dsassemble. Dsassembly sequence generaton for partcular part Our system can also generate dsassembly sequences n order to dsassemble a partcular part. By consderng dsassembly of one part, we can classfy parts nto three types as follows: type-i : a set of parts whch must be removed before the part s dsassembled type-ii : a set of parts whch can not be dsassembled untl the part s removed type-iii : a set of parts whch are nether ncluded n type-i nor type-ii. When one part to dsassemble s desgnated, the system checks whether t can be dsassembled or not. If t can not be dsassembled, type-i parts wth respect to the desgnated part are searched and ther dsassemblabltes are verfed one by one. If one type-i part can be dsassembled, the system removes t and verfes dsassemblablty of the desgnated part agan. These operatons are repeated untl the desgnated part can be dsassembled. If type-i parts can not be dsassembled, the system searches parts whch must be removed before these parts are dsassembled, that s, new type-i parts wth respect to
Table. Result of dsassembly sequence generaton. sequence 6 7 8 9 0 6 7 8 9 0 6 7 8 p6 g p p p p p p6 g p p p p p p6 g p p p p p p6 g p p p p p p6 g p p p p p p6 g p p p p p p6 g p p p p p p6 g p p p p p g p p p p6 p p g p p p6 p p p g p p p6 p p p g p p p p6 p p g p p p6 p p p g p p p6 p p p g p p6 p p p p g p p6 p p p p g p p6 p p p p g p p6 p p p p g p p6 p p p p g p p6 p p p p g p6 p p p p p g p6 p p p p p g p6 p p p p p g p6 p p p p p g p6 p p p p p g p6 p p p p p g p6 p p p p p g p6 p p p p p type-i parts, and contnues dsassemblablty verfcaton. When any type-i parts do not exst, the system requres the operator to select one type-iii part n order to verfy ts dsassemblablty. If any type-iii parts also do not exst, t s found that the desgnated part can be dsassembled. Fgure 0 shows dsassembly sequences of the product as shown n Fg.9 n order to dsassemble part whch s emphaszed wth whte color n Fg.0. Thus, dsassembly sequences for not only one part but also a set of parts can be generated. By usng the developed system, desgners/process planners can verfy dsassemblablty of the whole parts or partcular parts of. sequence p p p8 p p p8 a product. Furthermore, desgners can check whether t s easy to dsassemble the product or not when ts mantenance, repar, recyclng, and dsposal are consdered and they can mprove ther desgn f necessary. 6. CONCLUSION A system whch can generate dsassembly sequences of mechancal parts was developed. Frst, methods to calculate possble motons of parts and to detect confguratons where contact state transton occurs were presented. Based on them, an algorthm for verfyng dsassemblablty of parts was explaned. Next, a method to estmate the total number of feasble dsassembly sequences wthout actually generatng them was proposed. In order to reduce the number of dsassembly sequences, precedence constrants such as the assembly feature were ntroduced. Fnally, a dsassembly sequence generaton system was mplemented and ts effcency was demonstrated. We expect that the developed system wll be useful for not only the desgn verfcaton or the assembly plannng but also the desgn evaluaton consderng recyclng/reuse. 7. ACKNOWLEDGEMENT Ths study has been supported n part by a Grant-n-Ad for Scentfc Research of Japan Socety for the Promoton of Scence.007 n 999. 8. REFERENCES Ara E., Uchyama N., Igosh M. (99). "Dsassembly Path Generaton to Verfy the Assemblablty of Mechancal Products", JSME Int. Journal, Seres C, Vol.8,., pp80-80. Boothroyd G., Dewhurst P., Knght W. (99). "Product Desgn for Manufacture and Assembly", Marcel Dekker. Chodo J.D., Bllett E.H., D.J.Harrson D.J. (999). "Prelmnary Investgatons of Actve Dsassembly Usng Shape Memory Polymers", Proc. of st Internatonal Symposum on Envronmentally Conscous Desgn and Inverse Manufacturng, pp90-96. Harjula T., Knght W.A., Boothroyd G. (996). "Desgn for Dsassembly and the Envronment", Annals of the CIRP, Vol.-, pp09-. Jovane F., Armllotta A., Feldmann K. (99). "A Key Issue n Product Lfe Cycle: Dsassembly", Annals of the CIRP, Vol.-, pp6-68. Kasa D., Suga T. (999). "Actve Dsassembly of Bonded Wafers", Proc. of st Internatonal Symposum on Envronmentally Conscous Desgn and Inverse Manufacturng, pp88-89. Krause F.L., Selger G. (997). "Lfe Cycle Networks", Chapman & Hall. Nsh T. et al. (999). "Study on TV Recyclablty", Proc. of st Internatonal Symposum on Envronmentally Conscous Desgn and Inverse Manufacturng, pp78-80. Uchyama N., Ara E., Igosh M. (99). "Testng the stablty of Subassembles Usng Geometrc Model for Mechancal Assembly Plannng (Japanese) ", Trans. of JSME, Seres C, Vol.6,.8, pp-9. Uchyama N., Ara E., Igosh M. (99). "Generaton of Mechancal Assembly Sequences Consderng Dfferent Evaluaton Vewponts", Advancement of Intellgent Producton, pp70-706. Fg.0. Example of desgnated part dsassembly