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Contribution to Computer-Aided Design of Flexible Assembly Systems
DESIGN METHODOLOGIES II
Copyright © IFAC Information Control Problems in Manufacturing Technology. Madrid. Spain 1989
CONTRIBUTION TO COMPUTER·AIDED DESIGN OF FLEXIBLE ASSEMBLY SYSTEMS J.
M. Henrioud, A. Bourjault and D. Chappe
Laboratoire d'Automatique de BeSatl(On, Institut de Productique, Besancon, France
Abstract . In this paper, the authors present a complete stategy to design a flexible assembly system for any product. The basic idea is to divide the assembly actions in two classes; the dedicated ones ( specific of the product) and the positional ones (specific of the assembly process). The proposed method includes an algorithm which generates all the valid combinations of the dedicated actions. in the form of assembly trees ; the awkward ones are then rejected by the introduction of some set of constraints. The remaining trees are then transformed by the assignment of equipments to its different nodes, which introduces the positional actions. A comparison of the different solutions is then achieved by the way of a simulation. Keywords . Computer-aided design; flexible manufacturing; assembling; automation; simulation.
Product modelisation
INfRODUcnON
Any industrial product resulting from the assembly of n elementary components: CI ......Cn can be considered as a set of characters which have to be created in some convenient order. These characters are listed hereafter in a classified way. - the relational characters, specific of the assembly problem. they are divided in two categories: - the liaisons, there is a liaison between two elementary components iff they have some common surface in the assembled product. - the joinin~s, each one adding cohesion to one or several liaisons. The joinings are : - welding - screwing - sticking - deformation joining
The most important problem in manufacturing appears to day to be an assembly problem; the competition is very hard with countries where manpower is cheap. The assembly tasks are generally numerous and little automatised; they contribute considerably to the cost of a product (20 - 60 %). The set of knowledge about machining is not here transferable to assembling because assembly is specific. Before the eighties. the automatisation of the assembly tasks were most of the time the substitution of a man by a robot; that is an approach called "work-station" ; the economic results were not always satisfying and today, it is preferable to have a global vision. i.e. a system-like approach. In this way. the most difficult is certainly to obtain and apply a methodology which permits to design an efficient flexible assembly system.
- the complementary characters which are mainly: - inspection and test -labelling - painting - cleaning - machining
For several years we have been working on this problem. more precisely, on the elaboration of a computer-aided workstation, to design flexible systems; whose elements could also be used to control the system on line. The resulting method is divided in two pincipal stages described in this paper: the determination of a set of assembly plans. then. for each one. the determination of several organisations; all the resulting assembly processes being compared by means of a simulation. This approach was first developped for single product assembly systems and is thus presented in this paper; recently we have begun to extend it to multi-products processes.
Being given any product p. we list the set of all its characters and we define a 5-uple: < c.r,1:.I'1,f > where -C is the set of the elementary components -r is the set of the (geometrical) liaisons, given as couples (Ci. Cj)
ASSEMBLY PLANS DETERMINA nON
-1: is the set of the joinings -1'1 is the set of the complementary characters
Up to this day, there are two efficient methods for the exhaustive determination of the assembly plans. The first one is known as the liaison-sequence method (Bourjault 1984, De Fazio and Whitney 1986); we have already described it in different papers. The second one, which could be named subassemblies decomposition method, (Homen de Mello 1986 and Henrioud 1987). is the one used in this paper and is succintly described here.
-f is a function mapping 1: u 1'1 into P(C) x P(1:) x P (l1); it defines,for each joining or each complementary character,the set of elementary parts and characters concerned. The couple [C. Il defines a graph called the liaisons graph.
461
J.
462
M. Henrioud, A. Bourjault and D. Chappe
Any sub-assembly, or part, produced in the course of the assembly process is described by a 4-uple
< X, y, cr, 0 >
Crystal (a)
with: X ~ C; Y !:: G; cr ~ S ; 0 ~ D and such that : [X, y] being the subgraph of rC, r] induced by X, it is connected and, if f(
~X;IJ.
~cr
Cover (c)
;
v
Base
(b)
~o
The function f has two purposes; the first one is to define a necessary condition for the joinings and complementary characters to be set up, the second one being to define some precedence conditions between them. Thus if :
dE D and f(d) = (X, cr, 0 ) every character in cr or in 0 has to be set up before the character d. Practically, this function f is such that for any joining j we have always: f(j) = (X, $, $)
Any assembly process for a given product is a set of actions being realized in serie and/or in parallel. Among these actions we distinguish : - the dedicated actions which create some characters of the product; they are to be done whatever assembly process is involved - the positional actions, which consist in moving the different parts between the equipments ; they depend upon the assembly process. So, to evaluate the assembly plans we just consider the dedicated actions, postponing the introduction of the positional ones to the stage of process evaluation. . Figure 1 represents a quam with its liaison graph; it has: three elementary components : -a crystal (a) -a base (b) -a cover (c). two joinings : -welding of a and b : (wl) -welding of band c : (w2) and two complementary characters : -an electric control of the welding wl : (el) -a labelling of the cover c : (la) ; this labelling assigns the quartz to a cenain class of quality, depending upon the result of the electrical control, so we consider in the model that (la) is a labelling of the whole product. The function f is thus defined by : f(wl) = (la, b), $, $) f (w2) = «(b, cl. $, $) f(el) = «(a, b), (wl), $) f(la) = (la, b, cl. (wl, w2), (el))
a
•
2
b
•
c
•
Fig. 1 Quartz given as exemple with its associated liaisons graph Assembly trees An assembly tree is a tree for which : - the root represen ts the product - the nodes represent the sub-assemblies or pans - the leaves represent the elementary parts and such that each pan associated to a node Ni can be produced from the parts associated to the successors of Ni (k E (1, 2}) by the simultaneous execution of several dedicated actions.
In any assembly tree, each sub-tree including one node and its k successors defines an operation which is - geometrical if it creates some liaisons (k E (1, 2) - physical if it adds a joining (k =1) - complementary if it adds a complementary characters (k
= 1)
An assembly tree is the first description level of the assembly process, it includes it intrinsic part and doesn't involve the positional actions, which are to be added in a second stage, when the equipments and their assignment to the operations are chosen as it is shown in the second pan of this paper. Figure 2 shows the two assembly trees available for the quartz presented in Fig 1. The nodes are labeled by the character created by the associated operation.
a ---, l -w l - , b ---1 I 2-2-el--la
c _ _ _- - II
I
2_2-la
c - - - - - - - II Fig . 2 Assembly trees available for the quartz presented above
Flexible Assembly Systems
The aSsembly constraints The assembly constraints can be devided in two categories : The operative constraints: these constraints define wether any given operation is feasible; we distinguish : - the geometrical constraints : when mating two parts, there must exist at least one collision-free trajectory to bring the two parts in contact. This constraint depends only upon the product and can be automatically evaluated - the material constraints : the effective realization of any operation involves some equipments, there is at least one part to hold (two for the geometrical operations), which requires some suitable parts surfaces for the holding; moreover, since every operation involves some spatial relation between two objects: each part with its holding equipment, or some external equipment for the non geometrical operations, there is again the necessity of a free-collision trajectory. But since the equipments are not defined at this stage, it belongs to an human expert to appreciate the feasability of the considered operation - the stability constraint : each part produced in the course of the assembly process must be stable, i.e all its subparts have to keep exactly their relative positions. Stability can only be partly automatically evaluated since an unstable part can be temporarily hold by some outside device, which has to be designed. The strate~c constraints : We call strategic constraints those which deal with the operations sequencing ; they are mainly : - operations grouping, because they require the same equipments or because they use the same assembly direction; - necessity that some sub-assembly appear in the assembly process (for inspection or storage purpose) - delaying the introduction of some elementary parts (fragility, weight, volume) - choice of a serial process (there is only adding of elementary parts) or inversely of a parallel one. Assembly trees
~eneration
In order to evaluate the assembly trees available for a given product we have elaborated a software LEGA based on a topdown algorithm. Starting from the product, we define all the valid operations having the product for result, which determines one or two parts ; then we reiterate for each of these parts till we obtain all the elementary components. An operation being valid when it agree with the set of the operative constraints. The operative constraints are described by a database including a set of facts (the unfeasible operations) and a set of rules which formalize some properties of the operative constraints. For each new operation produced by the generation tree process, the database is searched in order to find if this operation is feasible; if the datas don't allow a positive or a negative answer then an human expert is questioned about this operation. His answer is used to complete the database. At the beginning of the process the database contains no fact; at the end it contains a complete description of the operative constraints for the considered product. The software LEGA has been written in PROLOG which proved perfectly adapted to the problem discussed here. Tree selection The number of available assembly-trees is usually quite important (between and 104 for products having about ten elementary components) so it is necessary to reject those
103
463
which obviously correspond to awkward processes. To select these trees we introduce the strategie constraints; they are to be chosen in some menu and the parameters are to be defined. This step is certainly the most difficult of the method presented here ; there is still a lot of work to be done to improve its efficiency. Thus we are trying to associate a weight to each operation, according to its difficulty (presently they are weighted by 0 or 1) in order to compare the operative difficulty of the different trees. Such a weight can be evaluated by the mixing of several criterias, mainly : - stability of the involved parts - complexity of the trajectory - morphology and size of the parts handling surfaces. ASSEMBLY SYSTEM DESIGN AND SIMULAnON Each of the selected trees is transformed in a functional diagram using the symbols given in Fig 3. This step involves for each binary operation, i.e one mating two parts, the choice between the primary part (motionless) and the secondary part (moving). Some integrated rules based on the weight, the size and the shape of the two parts leads to a partial automatization of this step; when no decision can be got from these rules, then the human expert is questioned. In each diagram all the necessary transports are introduced ; there is one for each elementary part and one for each of the secondary parts involved in the binary operations. Then, equipments are assigned to the different operations; there are usually several solutions for each diagram when several operations are liable to be realized by a same equipment; moreover some buffers are introduced. This leads to a division of the assembly system into cells and work stations. A duration is roughly attributed to each operation, including the positional ones which are introduced at the same time as the equipments. Since there are several trees selected at the precedent stage (a few tens) and several organizations for each tree, that means that there are some hundred solutions to compare. In order to perform this work we have developed a software, AISE. The aim of AISE is to provide a quick simulation of each of the possible organizations defined at this stage. For each organization a Petri net is automatically deduced, which simulates its behaviour, it provides : - the cycle time (i.e the out put period of the system) - the occupation ratio of each equipment (working time / cycle time). - the size evolution of the buffers. CONCLUSION This study is a contribution to computer-aided design of flexible assembly systems . Its main object is to encompass all the possible configurations; in order to face the size of this problem, we have split it up in several steps: deteminaton of all the available assembly plans, described by assembly trees, selection of the best ones, equipments assignment. Apart from the assembly trees determinaton, which is exhaustive, the whole method is essentially heuristic. At each stage, the human expert is presented with systematic choices, which forces him to examine solutions he wouldn't have thought of. Moreover each decision is registered, which is of great help for any discussion arising between the different engineers involved in the project. Under the condition that the good solutions have been selected at each stage, the final simulation allowing a quantitative comparison of the proposed configurations, the best one can be found. The proposed method is available for products including about twelve elementary parts ; bigger products have to be split up in several sub-assemblies. It has been developped and tested in the field of mechanical industry, where the studied products were submitted to numerous operative constraints.
J. M. Henrioud, A. Bourja ult a nd D. Chap pe
464
Our main objective is now the introduction of 3 D description of the products in our software, in order to provide it with some a~ility to det~t automatically geometrical and stability constramts. We thmk that would help also to the operations evaluation and weighting, which would be very useful for the trees selection.
D -Er DB-
Work-station
Geometrical operation
Physical or complementary operation
Buffer
Positional operation
Fig . 3 Exemple of a functional diagram with symbols used
REFERENCES Bourjault, A. (1984) Contribution 11 une approche methodologique de l'Assemblage Automatise : Elaboration Automatique des Sequences Operatoires These d'Elat, Besanyon Bowjault ,A. (1987) Methodology of Assembly Automation : a new approach 2nd Int.Conf. on Robotics and Factories of the Future, San Diego De Fazio T.L., Whitney D.E. (1987) Simplified Generation of all mechanical assembly sequences IEEE Robotics and Automation, Vol. RA .3, pp 640-658, Henrioud J.M., Bourjault A ., Chappe D . (1987) Elaboration des gammes d 'assemblage : Approche composants GAMI - Les Jouroees de la Productique Henrioud J.M., Bourjault,A. (1987 ) Logic Programming Applied to Assembly Sequences Determination lASTED Robotics and Automation, Lugano
Homem de Mello, L.S., Sanderson A.C. (1986) AND/OR Graph Representation of Assembly Plans. Proceedings of AAAI-86, ppl113-1119. Morgan Kaufmann Homem de Mello,L.S. , Sanderson A .C . (1987) Task sequence Planning for Assembly IMACS World Congress on Scientific Computation Paris Meunier M ., Lhote F. (1987) Automatisation flexible de I'assemblage, Axes RobotiQues Lui, M.M. (1988) Generation and Evaluation of Mechanical Assembly Sequnces Using the Liaison-Sequence Method.Master's thesis Department of Mechanical Engineering, M.LT.
Copyright © IFAC Information Control Problems in Manufacturing Technology. Madrid. Spain 1989
CONTRIBUTION TO COMPUTER·AIDED DESIGN OF FLEXIBLE ASSEMBLY SYSTEMS J.
M. Henrioud, A. Bourjault and D. Chappe
Laboratoire d'Automatique de BeSatl(On, Institut de Productique, Besancon, France
Abstract . In this paper, the authors present a complete stategy to design a flexible assembly system for any product. The basic idea is to divide the assembly actions in two classes; the dedicated ones ( specific of the product) and the positional ones (specific of the assembly process). The proposed method includes an algorithm which generates all the valid combinations of the dedicated actions. in the form of assembly trees ; the awkward ones are then rejected by the introduction of some set of constraints. The remaining trees are then transformed by the assignment of equipments to its different nodes, which introduces the positional actions. A comparison of the different solutions is then achieved by the way of a simulation. Keywords . Computer-aided design; flexible manufacturing; assembling; automation; simulation.
Product modelisation
INfRODUcnON
Any industrial product resulting from the assembly of n elementary components: CI ......Cn can be considered as a set of characters which have to be created in some convenient order. These characters are listed hereafter in a classified way. - the relational characters, specific of the assembly problem. they are divided in two categories: - the liaisons, there is a liaison between two elementary components iff they have some common surface in the assembled product. - the joinin~s, each one adding cohesion to one or several liaisons. The joinings are : - welding - screwing - sticking - deformation joining
The most important problem in manufacturing appears to day to be an assembly problem; the competition is very hard with countries where manpower is cheap. The assembly tasks are generally numerous and little automatised; they contribute considerably to the cost of a product (20 - 60 %). The set of knowledge about machining is not here transferable to assembling because assembly is specific. Before the eighties. the automatisation of the assembly tasks were most of the time the substitution of a man by a robot; that is an approach called "work-station" ; the economic results were not always satisfying and today, it is preferable to have a global vision. i.e. a system-like approach. In this way. the most difficult is certainly to obtain and apply a methodology which permits to design an efficient flexible assembly system.
- the complementary characters which are mainly: - inspection and test -labelling - painting - cleaning - machining
For several years we have been working on this problem. more precisely, on the elaboration of a computer-aided workstation, to design flexible systems; whose elements could also be used to control the system on line. The resulting method is divided in two pincipal stages described in this paper: the determination of a set of assembly plans. then. for each one. the determination of several organisations; all the resulting assembly processes being compared by means of a simulation. This approach was first developped for single product assembly systems and is thus presented in this paper; recently we have begun to extend it to multi-products processes.
Being given any product p. we list the set of all its characters and we define a 5-uple: < c.r,1:.I'1,f > where -C is the set of the elementary components -r is the set of the (geometrical) liaisons, given as couples (Ci. Cj)
ASSEMBLY PLANS DETERMINA nON
-1: is the set of the joinings -1'1 is the set of the complementary characters
Up to this day, there are two efficient methods for the exhaustive determination of the assembly plans. The first one is known as the liaison-sequence method (Bourjault 1984, De Fazio and Whitney 1986); we have already described it in different papers. The second one, which could be named subassemblies decomposition method, (Homen de Mello 1986 and Henrioud 1987). is the one used in this paper and is succintly described here.
-f is a function mapping 1: u 1'1 into P(C) x P(1:) x P (l1); it defines,for each joining or each complementary character,the set of elementary parts and characters concerned. The couple [C. Il defines a graph called the liaisons graph.
461
J.
462
M. Henrioud, A. Bourjault and D. Chappe
Any sub-assembly, or part, produced in the course of the assembly process is described by a 4-uple
< X, y, cr, 0 >
Crystal (a)
with: X ~ C; Y !:: G; cr ~ S ; 0 ~ D and such that : [X, y] being the subgraph of rC, r] induced by X, it is connected and, if f(
~X;IJ.
~cr
Cover (c)
;
v
Base
(b)
~o
The function f has two purposes; the first one is to define a necessary condition for the joinings and complementary characters to be set up, the second one being to define some precedence conditions between them. Thus if :
dE D and f(d) = (X, cr, 0 ) every character in cr or in 0 has to be set up before the character d. Practically, this function f is such that for any joining j we have always: f(j) = (X, $, $)
Any assembly process for a given product is a set of actions being realized in serie and/or in parallel. Among these actions we distinguish : - the dedicated actions which create some characters of the product; they are to be done whatever assembly process is involved - the positional actions, which consist in moving the different parts between the equipments ; they depend upon the assembly process. So, to evaluate the assembly plans we just consider the dedicated actions, postponing the introduction of the positional ones to the stage of process evaluation. . Figure 1 represents a quam with its liaison graph; it has: three elementary components : -a crystal (a) -a base (b) -a cover (c). two joinings : -welding of a and b : (wl) -welding of band c : (w2) and two complementary characters : -an electric control of the welding wl : (el) -a labelling of the cover c : (la) ; this labelling assigns the quartz to a cenain class of quality, depending upon the result of the electrical control, so we consider in the model that (la) is a labelling of the whole product. The function f is thus defined by : f(wl) = (la, b), $, $) f (w2) = «(b, cl. $, $) f(el) = «(a, b), (wl), $) f(la) = (la, b, cl. (wl, w2), (el))
a
•
2
b
•
c
•
Fig. 1 Quartz given as exemple with its associated liaisons graph Assembly trees An assembly tree is a tree for which : - the root represen ts the product - the nodes represent the sub-assemblies or pans - the leaves represent the elementary parts and such that each pan associated to a node Ni can be produced from the parts associated to the successors of Ni (k E (1, 2}) by the simultaneous execution of several dedicated actions.
In any assembly tree, each sub-tree including one node and its k successors defines an operation which is - geometrical if it creates some liaisons (k E (1, 2) - physical if it adds a joining (k =1) - complementary if it adds a complementary characters (k
= 1)
An assembly tree is the first description level of the assembly process, it includes it intrinsic part and doesn't involve the positional actions, which are to be added in a second stage, when the equipments and their assignment to the operations are chosen as it is shown in the second pan of this paper. Figure 2 shows the two assembly trees available for the quartz presented in Fig 1. The nodes are labeled by the character created by the associated operation.
a ---, l -w l - , b ---1 I 2-2-el--la
c _ _ _- - II
I
2_2-la
c - - - - - - - II Fig . 2 Assembly trees available for the quartz presented above
Flexible Assembly Systems
The aSsembly constraints The assembly constraints can be devided in two categories : The operative constraints: these constraints define wether any given operation is feasible; we distinguish : - the geometrical constraints : when mating two parts, there must exist at least one collision-free trajectory to bring the two parts in contact. This constraint depends only upon the product and can be automatically evaluated - the material constraints : the effective realization of any operation involves some equipments, there is at least one part to hold (two for the geometrical operations), which requires some suitable parts surfaces for the holding; moreover, since every operation involves some spatial relation between two objects: each part with its holding equipment, or some external equipment for the non geometrical operations, there is again the necessity of a free-collision trajectory. But since the equipments are not defined at this stage, it belongs to an human expert to appreciate the feasability of the considered operation - the stability constraint : each part produced in the course of the assembly process must be stable, i.e all its subparts have to keep exactly their relative positions. Stability can only be partly automatically evaluated since an unstable part can be temporarily hold by some outside device, which has to be designed. The strate~c constraints : We call strategic constraints those which deal with the operations sequencing ; they are mainly : - operations grouping, because they require the same equipments or because they use the same assembly direction; - necessity that some sub-assembly appear in the assembly process (for inspection or storage purpose) - delaying the introduction of some elementary parts (fragility, weight, volume) - choice of a serial process (there is only adding of elementary parts) or inversely of a parallel one. Assembly trees
~eneration
In order to evaluate the assembly trees available for a given product we have elaborated a software LEGA based on a topdown algorithm. Starting from the product, we define all the valid operations having the product for result, which determines one or two parts ; then we reiterate for each of these parts till we obtain all the elementary components. An operation being valid when it agree with the set of the operative constraints. The operative constraints are described by a database including a set of facts (the unfeasible operations) and a set of rules which formalize some properties of the operative constraints. For each new operation produced by the generation tree process, the database is searched in order to find if this operation is feasible; if the datas don't allow a positive or a negative answer then an human expert is questioned about this operation. His answer is used to complete the database. At the beginning of the process the database contains no fact; at the end it contains a complete description of the operative constraints for the considered product. The software LEGA has been written in PROLOG which proved perfectly adapted to the problem discussed here. Tree selection The number of available assembly-trees is usually quite important (between and 104 for products having about ten elementary components) so it is necessary to reject those
103
463
which obviously correspond to awkward processes. To select these trees we introduce the strategie constraints; they are to be chosen in some menu and the parameters are to be defined. This step is certainly the most difficult of the method presented here ; there is still a lot of work to be done to improve its efficiency. Thus we are trying to associate a weight to each operation, according to its difficulty (presently they are weighted by 0 or 1) in order to compare the operative difficulty of the different trees. Such a weight can be evaluated by the mixing of several criterias, mainly : - stability of the involved parts - complexity of the trajectory - morphology and size of the parts handling surfaces. ASSEMBLY SYSTEM DESIGN AND SIMULAnON Each of the selected trees is transformed in a functional diagram using the symbols given in Fig 3. This step involves for each binary operation, i.e one mating two parts, the choice between the primary part (motionless) and the secondary part (moving). Some integrated rules based on the weight, the size and the shape of the two parts leads to a partial automatization of this step; when no decision can be got from these rules, then the human expert is questioned. In each diagram all the necessary transports are introduced ; there is one for each elementary part and one for each of the secondary parts involved in the binary operations. Then, equipments are assigned to the different operations; there are usually several solutions for each diagram when several operations are liable to be realized by a same equipment; moreover some buffers are introduced. This leads to a division of the assembly system into cells and work stations. A duration is roughly attributed to each operation, including the positional ones which are introduced at the same time as the equipments. Since there are several trees selected at the precedent stage (a few tens) and several organizations for each tree, that means that there are some hundred solutions to compare. In order to perform this work we have developed a software, AISE. The aim of AISE is to provide a quick simulation of each of the possible organizations defined at this stage. For each organization a Petri net is automatically deduced, which simulates its behaviour, it provides : - the cycle time (i.e the out put period of the system) - the occupation ratio of each equipment (working time / cycle time). - the size evolution of the buffers. CONCLUSION This study is a contribution to computer-aided design of flexible assembly systems . Its main object is to encompass all the possible configurations; in order to face the size of this problem, we have split it up in several steps: deteminaton of all the available assembly plans, described by assembly trees, selection of the best ones, equipments assignment. Apart from the assembly trees determinaton, which is exhaustive, the whole method is essentially heuristic. At each stage, the human expert is presented with systematic choices, which forces him to examine solutions he wouldn't have thought of. Moreover each decision is registered, which is of great help for any discussion arising between the different engineers involved in the project. Under the condition that the good solutions have been selected at each stage, the final simulation allowing a quantitative comparison of the proposed configurations, the best one can be found. The proposed method is available for products including about twelve elementary parts ; bigger products have to be split up in several sub-assemblies. It has been developped and tested in the field of mechanical industry, where the studied products were submitted to numerous operative constraints.
J. M. Henrioud, A. Bourja ult a nd D. Chap pe
464
Our main objective is now the introduction of 3 D description of the products in our software, in order to provide it with some a~ility to det~t automatically geometrical and stability constramts. We thmk that would help also to the operations evaluation and weighting, which would be very useful for the trees selection.
D -Er DB-
Work-station
Geometrical operation
Physical or complementary operation
Buffer
Positional operation
Fig . 3 Exemple of a functional diagram with symbols used
REFERENCES Bourjault, A. (1984) Contribution 11 une approche methodologique de l'Assemblage Automatise : Elaboration Automatique des Sequences Operatoires These d'Elat, Besanyon Bowjault ,A. (1987) Methodology of Assembly Automation : a new approach 2nd Int.Conf. on Robotics and Factories of the Future, San Diego De Fazio T.L., Whitney D.E. (1987) Simplified Generation of all mechanical assembly sequences IEEE Robotics and Automation, Vol. RA .3, pp 640-658, Henrioud J.M., Bourjault A ., Chappe D . (1987) Elaboration des gammes d 'assemblage : Approche composants GAMI - Les Jouroees de la Productique Henrioud J.M., Bourjault,A. (1987 ) Logic Programming Applied to Assembly Sequences Determination lASTED Robotics and Automation, Lugano
Homem de Mello, L.S., Sanderson A.C. (1986) AND/OR Graph Representation of Assembly Plans. Proceedings of AAAI-86, ppl113-1119. Morgan Kaufmann Homem de Mello,L.S. , Sanderson A .C . (1987) Task sequence Planning for Assembly IMACS World Congress on Scientific Computation Paris Meunier M ., Lhote F. (1987) Automatisation flexible de I'assemblage, Axes RobotiQues Lui, M.M. (1988) Generation and Evaluation of Mechanical Assembly Sequnces Using the Liaison-Sequence Method.Master's thesis Department of Mechanical Engineering, M.LT.