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Optimal Configuration of Robotized Assembly Systems
Copyright @ IFAC Intelligent Manufacturing Systems, Vienna, Austria, 1994
OPTIMAL CONFIGURATION OF ROBOTIZED ASSEMBLY SYSTEMS M. SKUBIC· and D. NOE· • University ofLjub/jana, Faculty of Mech. Engineering, Askerceva 6, Ljub/jana, Slovenia
Abstract. One of the main concerns when planning the robot-assisted assembly cell is the selection of all equipment for assembly operations such as robot, gripper, change devices and peripheral or assembly devices. Within the boundary conditions such as product to be assembled, assembly operations sequence, workspace size and shape, the selection must be also optimized with respect to a minimum assembly cell cost or minimum cycle time. The paper describes the development of two models for the equipment of robotized assembly system selection.
Key Words: assembling; computer selection and evaluation; optimal search techniques; grippers; assembly planning; computer software
Assembly is a relatively difficult task for robotic implementation. Part of this difficulty arises from the large variety of assembled parts, and the resulting need for multiple feeders, grippers, and other mechanical interfaces which may limit the system flexibility .
I. INTRODUCTION The economic importance of assembly has led to extensive efforts for improving the efficiency and cost effectiveness of assembly systems. In automated systems, there is a need for specialization of tooling and feeding devices, which directs the division of the assembly task into a series of workstations. The individual processes must be allocated to workstations in such a way that the total assembly time required at each assembly station or cell is approximately the same. Furthermore, the cost of selected equipmemnt should be minimized. If such balance cannot be achieved, inefficiencies in the form of idle time at stations, or temporary blocking or waiting of stations will result.
2. OVERVIEW OF SELECTION PROCESS One of the main concerns when planning the robotassisted assembly cells is the selection of all equipment for the assembly operation such as robot, gripper, change devices, and peripheral or assembly devices. Within the boundary conditions imposed by planner such as product to be assembled, assembly operations sequence, workspace size and shape, the selection must be optimized also with respect to a minimum assembly cell cost or minimum cycle time.
An effective CA assembly process planning, the component selection problem, layout design of shop floor and simulation for optimization depend significantly on the quality and availability of technological data for assembly cell components, knowledge of selection and assembly process planning, and methods and tools for decision making and evaluation. An assembly process plan contains information about selected operations, operation sequences, and equipment required (Wang et al., 1993). For automation of selection tasks, suitable methods and software often become necessary to allow rapid, comprehensive fmishing of the selection phase.
Based on conditions and particular point of view, we usually select a group of components that satisfy proposed constraints. Our goal is to enhance the selection procedure with equipment ranking to achieve the fmal (optimum) solution. The objective of this attempt is to devise a method of tradeoff between alternatives to make it possible to rank them according to their suitability for the desired application. For this purpose multiple attribute decision making method (Hwang et al., 1982) has been employed. The approach allows such an analysis by providing the
297
framework for processing infonnation about relative importance of equipment attributes.
weight, shape, and other data pertaining to an object to be manipulated (assembled) and may be represented by
Another way of solving such problems is closely connected with the current trend in developing selection and evaluation systems where expert systems technology is used. This provides an excelent framework to incorporate the decision making process of the planner and make it suitable for automation. In such a system, little user interaction is required; since rules and facts are scientifically dermed, each recommendation can be logically judged by the expert system. But unfortunately this is true for machining. However, for assembly operations a kind of generally accepted categorization of them does not exist. Assembly process planning, system components selection, etc. relies heavily on the experience of the planner and the industry in which he/she is working. Thus expert systems intended for assembly applications are likely to be designend as intelligent decision support systems with the engineer having the final decision. In order to develop the selection of assembly system components, it is necessary that the actual assembly operations are clearly understood and defined. One of the ideas is that we use a list of 'standard' assembly operations, develop a system for product part grouping and a series of rules about assembly system components selection. For example, the number of grippers is detennined by the number of different components of an assembly task. It is reduced when identical or similar parts are used and be manipulated via a single gripper.
(I)
We also consider the environment E where the task is to be perfonned with attributes ZE' The environment could be an extremely hot or cold, clean room, with aggressive media, etc. The environmental attributes may also include distances between machines, ambient temperature, etc., and may be represented by (2)
Furthennore, we also have to describe parts of assembly P with different characteristics Qp that influence the selection of components such as geometrical fonn, function, accessibility, the joining method, joining direction, material, surface conditions, etc. All these attributes are expressed by (3)
The problem is to select the device in a robotized assembly cell D, with attributes XD , that can perfonn the task within the environment and for a specified group of part assemblies to be assembled on a particular assembly cell. The device attributes may be expressed by (4)
The objective function can be stated as f(XnJ ~f(YAO Z& Qp}
In order to include infonnation about assembly technology, product parts and sub-assemblies, they are described by characteristic features: a geometrical fonn of the components, a mechanical function, a accessibility, a joining direction, a connectiong and assembly method.
XI> YAO Z& Qp
where Xl) YAG Z& Qp are the robot, task, environment and product part variables. When selecting the equipment (components) for a robotized assembly cell we must consider that these components work together in order to assemble part components. This cooperative work and the relations in assembly cell is shown in figure I .
Thus for every object there is a complete description as regards its assembly: a part (name, joining positions), a sub-assembly (name, components), a operation (name, joining position, joining method, joining direction).
3. ROBOTIZED ASSEMBLY SYSTEM COMPONENTS SELECTION As an example we consider an assembly operation AD; with attributes (characteristics) YAD to be done with a robot in an assembly cell. The task may vary from a simple pick and place routine to more complex operations such as gluing, soldering, screwing etc. Additional task characteristics might include the
Fig. 1.
298
Structure of robotized assembly cell and relations between components
3.1 Knowledge for selection
created. For implementation we use a relational database system. Entity-Relationship model is transformed into relations using rules as shown in figure 3.
In order to determine precisely the particular component for a given task, further information is needed. This regards to product components to be handled and operations to be accomplished.
DB of product corrponents
Knowledge needed for component selection is presented in a form of relations in relational database management system. Therefore several parameters were defmed to perform selection procedure. For assembly operations such parameters are: D minimum number of axes, needed for individual assembly operation, D type of robot control, D preconditions and postconditions, D requirement for special tools, D positioning accuracy, D sensor requirement.
ossignng a list of assembly operations to cell (station)
knowtedtJe base about assembly operations
1 . pick and place 2 - insertF.20N
3· SCteW 4· ...
Product parts to be assembled are described by: D size of the component, D weight of the component, D joining technique, D joining direction, D material, D joining force, D operational environment D product part shape, D speed of working.
selection procedure finds
SCJtisfyinQ solutions using elimination search
evaluation and ranking procedure using
lOPSlS method
4. STRUCTURE OF SELECTION MODEL Fig. 2. The major steps involved in the development of the computer aided component selection process include the following: (a) selecting the appropriate characteristics of assembly cell components for the creation of a component descriptive database (CDD); (b) designing of a classification system using the characteristics selected from step (a); translating the task variable to those of components in CDD in order to match job requirements with the component capabilities in the CDD; (c) designing a method that can classify and select components based on a given criterion; and, (d) applying the selection model. Additionally we could also (e) apply an economic analysis for cost comparison of feasible component candidates.
Model of computer-aided selection of robotized assembly cell component
.-----,
DEVICE ([)# . description ....) 101 Robot 102 Ordering device 103 Conveyor FUNCTION (FI. [)# . description . time) 11 101 HandHng 1 11 102 Ordefing 3 12 10 1 Assembly 4 13 103 Transport 2 DEVl CE ([)#. description .... )
m11
nFUNCTlON _____(FI . description .... )
1 PERFORM (GI . FI . time)
Fig. 3.
A model for computer aided selection of components is presented in the figure 2. In this model we assume that operation (task) sequence is known and is optimally defmed. Based on the task sequence and assembly parts characteristics we generate the criteria for component selection. The selection procedure is performed using interactive work with user (planner) or in the future with methods described in chapter 5. For efficient selection of components a data base is
Transformation ofE-R model to relations
5. METHODOLOGY FOR ASSEMBLY CELL COMPONENTS SELECTION The optimum selection of assembly cell components to suit particular application and production environment is done after considering various attributes among the large number of available alternatives. This is a difficult problem because of a large number of available alternatives, and due to the fact that different
299
alternatives may be conflicting in nature. It is not possible for an individual to take all of these considerations into account without the help of computer software.
Satisfying solutions: a satisfYing solution is one whose attributes all exceed certain minimum desired levels of aspiration. A set of satisfYing solutions is composed of acceptable alternatives. Preferred solution: a preferred solution is a nondominated solution selected as the final choice through the decision maker involvement in information processing. Only nondominated solutions which are the satisfYing solutions can qualifY to be in the set from which a preferred solution is selected.
Cl
Cl
5.1 System based on Multiple Attribute Decision Making Multiple Attribute Decision Making (MADM) refers to an approach of problem solving that is employed to solve problems involves selection from among a fmite number of alternatives. A MADM is a procedure that specifies how attribute information is to be processed in order to arrive at a choice. MADM is one of the two categories of a more general problem solving approach termed Multiple Criterion Decision Making (MCDM) (Hwang et al., 1982). Although these techniques have been widely developed in fields like economics and mathematics. The method is discussed in detail in papers Hwang et. al. (1982) and Agrawal et. al. (1991). Therefore we aviod repetition and give only a brief description.
TOPS/S'method. The TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method is applied as next. In a short this algorithm can be divided in the following steps: Step I Write decision matrix Aij where row i corresponds to the component and column j corresponds to the considered attributes of the component. Step 2 Obtain information from user (or expert system) on relative importance of attributes in pairwise comparison. The relation dij=d! d;k is established and form the relative importance matrix D where importance of ,1h attribute d; = (5) J importance ofJ1h attribute Step 3 The information in the D matrix cannot be used directly in the MADM method. Using eigenvector method we seek to fmd weight matrix vector W where DW=IIW . Obtain maximum eigenvalue A. using this value of A. to find eigenvector W, where W presents the weights of each attribute as (D-A.maxI)W=O. Step 4 Construct normalized decision matrix R from decision matrix A using the relation
MCDM refers to making decisions in the presence of multiple, usually conflicting, criteria. MCDM is required when confronted with a problem that has the following characteristics: Cl Multiple objectives/attributes, Cl Conflict among criteria, Cl Incommensurable units, Cl Design/selection.
Basic definition for the MADM environment. The proposed method is characterized by: Cl Attributes: performance parameters, components, factors, characteristics and properties Cl Decision matrix: a decision matrix D is a 'm by n' matrix whose element x(i. j) indicates the value of alternative i(AJ where there are m alternatives and n attributes. Hence Ai, i = I, ..., m is denoted by !; = (x(i, I), x(i, 2), ... , xCi, n» and the column vector ~=(x(l,j), x(2,j), ... , x(m, j)? shows the contrast of each alternative with respect to attribute j . Cl Optimal solution: an optimal solution is one which results in the maximum value of each of the attributes simultaneously. That is, takingXto be a set of all alternatives, ,I* is an optimal solution if,I* eX and k*»j{,!} for all ,IeX. Cl Nondominated solutions: a feasible solution is nondominated if there exist no other feasible solutions that will yield an improvement in one attribute without causing a degradation in at least one other attribute.
rei, j)
= -;::::=a(=i,=}=~=
..
(6)
L(a(i,}W /-\
r(i. j) = an element of the normalized decision matrix a(i. j) = an element of decision matrix A
Step 5 Determine weighted normalized decision matrix V using R and W. Step 6 Determine positive ideal A * and negative ideal Asolution using the relation
(7)
and
300
{~.~~~I~) l.~~~i~l
A- •
=
'... ~:.~~iJ)l )
{V V2- •••• V,,-} I-.
(8)
The ideal solution is a hypothetical solution for which all attribute values correspond to the maximum attribute values in the database comprising the satisfying solutions; the negative ideal solution is the hypothetical solution for which all attribute values correspond to the minimum attribute values in the mentioned database. Step 7 Calculate separation measures Si' and Si· • where separation from the ideal is given by
SI·=[t(V(i.JJ-V;r~
(i=1.2 • ...• m)
(9)
J
j-I
and separation from the negative-ideal is given by
SI-
=[
t
(v(iJ)-VI-r
j-I
_~_""'_
~
~
J
(i = 1.2 •...• m)
(10)
Structure of database. As a part of knowledge-based and/or rule-based tools for automatic selection of components of robotized assembly cell we have developed a system for computer aided selection of grippers. In the database are stored information about grippers. Each gripper is stored in a form of a record in the database. As database management system a well known DBMS system Paradox was used. The software has been made 'user friendly' and the system is running under the operating system MS-Windows. Program modules were written in object based programming language ObjectPAL. that is a part of Paradox. To use this program an extensive knowledge about grippers and gripper application is not required. The database may be updated considering changes on the market. The user are given following options: Cl adding a new gripper to the database. Cl deleting an existing gripper. Cl changing attribute information of an existing gripper. Cl listing of grippers by type. force. producer. etc. In the database grippers are grouped regarding gripping principle. the groups are: fmger grippers, vacuum grippers, magnetic grippers, grippers for boss and holes, grippers with elastic elements, adhesive grippers and special grippers.
_ _ _ _ _ _ _ _ _ _A' IDEAL SOUJllON I
~ ~ ~
5.2 Knowledge-based system for grippers selection
Cl
l?
"6
The product parts to be assembled and assembly operation characteristics are the most important factors that determine the type and characteristics of the gripper. Information about parts are saved in a parts database and includes: main shape, supplementary shape, weight of component, largest dimension, material, roughness, surface temperature.
~
u
e >J ~ ~
I
NEGA~ IDEAl - - - - - - - _;;;--.,__,c SOLl1TlON attT1bute
Fig. 4.
x, (hcreoslng preference)
Euclidean distances to the ideal and negative ideal solutions in two-dimensional space (case of two attributes)
Selection procedure. In order to select a gripper some conditions and requirements must be fulfilled. Following parameters determine the gripper selection: geometry (main and supplementary shape of the part), dimensions, tolerances, form of gripping face, weight, robot's accelerations in each way, assembly operation, assembly Goining) force, surface, temperature. material. friction . The data model for grippers selection in figure 5 shows relations between tables.
Step 8 Calculate 'relative closeness to ideal solution'. This index is a measure of the suitability of the device for the chosen application on the basis of attributes considered. A device with the largest index (according to equation) is optimum: (J J)
Step 9 Rank alternatives in accordance with the decreasing values of indices C·. indicating the most preferred and the least preferred feasible optional solutions.
Fig. 5.
301
Data model for grippers selecion
After the user specifies and describes assembly components and assembly operations a selection is performed automaticaly. Based on the shape of part component the user can choose gripping place. Using this data the direction of gripping, the shape of gripping face and way of griping (by shape or by force) are determined. The database is scanned and all possible grippers are selected. During search procedure some calculations and some queries are performed, depending on the type of gripper. Result is a report where all grippers that satisfy all conditions are listed.
Cl Cl Cl Cl
availability, management constraints, simulation of cell operation in the workplace, international market policies, etc.
6. CONCLUSION Work was concentrated on finding of methodologies for evaluation and selection of components of the assembly system. The paper present two different models for components selection (robots, grippers, peripheral devices, etc). The first methodology is based on multiple attribute decision making principle for equipment selection. As a significant development it recognize the need for, and processes the information about, relative importance of attributes for a given application. Second aproach is more knowledge based. Selection process is based on components, assembly operations and working conditions description. In the database are for now some real grippers available on the market and some hypothetical ones. In our laboratory we are now working on improvement and testing of the system. Until now many selections have been performed. MADM method was used for assembly robots selection, the other one was used, as shown, on grippers selection. After transfering MADM to grippers selection, a comparison between both techniques will be done and results will be published.
7. REFERENCES Wang, Y., Hsieh, L.H., and Seliger, G. (1993). Knowledge -Based Integration of Design and Assembly Process Planning. Manufacturing Systems, Vol. 22, 2, pp. 107-112. Pham, D.T., and Yeo, S.H. (1991). Strategies for gripper design and selection in robotic assembly. International Journal of Production Research, Vol. 29, 2, pp. 303-316. Scholz, W. (1990). Einsatz von Datenbanken bei der rechnergestiltzten Planung von montageanlagen. elM Management, 4, pp. 18-23. Hwang, C. L., and Kohli, V. (1982). Multiple Attribute Decision Making - a State of the Art Survey. In: Lecture Notes in Economics and Mathematics, Springer - Verlag, Berlin. Agrawal, V. P., Kohli, V., and Gupta, S. (1991). Computer aided robot selection: the 'multiple attribute decision making' approach. International Journal of Production Research, Vol. 29, 8, pp. 1629-1644. Zupan, I. (1994). Data Base of Grippers. B. E. Thesis (in Slovene). University of Lj ubIj ana, Faculty of Mechanical Engineering.
isl 01 sel. o~pe"
Fig. 6.
Flow chart for selection of grippers (Zupan, 1994)
Fig. 7.
Selection module of programme
The fmal decision of gripper selection after browsing may be made on the basis of other factors which have not been taken into account earlier, such as: Cl economic considerations,
302
OPTIMAL CONFIGURATION OF ROBOTIZED ASSEMBLY SYSTEMS M. SKUBIC· and D. NOE· • University ofLjub/jana, Faculty of Mech. Engineering, Askerceva 6, Ljub/jana, Slovenia
Abstract. One of the main concerns when planning the robot-assisted assembly cell is the selection of all equipment for assembly operations such as robot, gripper, change devices and peripheral or assembly devices. Within the boundary conditions such as product to be assembled, assembly operations sequence, workspace size and shape, the selection must be also optimized with respect to a minimum assembly cell cost or minimum cycle time. The paper describes the development of two models for the equipment of robotized assembly system selection.
Key Words: assembling; computer selection and evaluation; optimal search techniques; grippers; assembly planning; computer software
Assembly is a relatively difficult task for robotic implementation. Part of this difficulty arises from the large variety of assembled parts, and the resulting need for multiple feeders, grippers, and other mechanical interfaces which may limit the system flexibility .
I. INTRODUCTION The economic importance of assembly has led to extensive efforts for improving the efficiency and cost effectiveness of assembly systems. In automated systems, there is a need for specialization of tooling and feeding devices, which directs the division of the assembly task into a series of workstations. The individual processes must be allocated to workstations in such a way that the total assembly time required at each assembly station or cell is approximately the same. Furthermore, the cost of selected equipmemnt should be minimized. If such balance cannot be achieved, inefficiencies in the form of idle time at stations, or temporary blocking or waiting of stations will result.
2. OVERVIEW OF SELECTION PROCESS One of the main concerns when planning the robotassisted assembly cells is the selection of all equipment for the assembly operation such as robot, gripper, change devices, and peripheral or assembly devices. Within the boundary conditions imposed by planner such as product to be assembled, assembly operations sequence, workspace size and shape, the selection must be optimized also with respect to a minimum assembly cell cost or minimum cycle time.
An effective CA assembly process planning, the component selection problem, layout design of shop floor and simulation for optimization depend significantly on the quality and availability of technological data for assembly cell components, knowledge of selection and assembly process planning, and methods and tools for decision making and evaluation. An assembly process plan contains information about selected operations, operation sequences, and equipment required (Wang et al., 1993). For automation of selection tasks, suitable methods and software often become necessary to allow rapid, comprehensive fmishing of the selection phase.
Based on conditions and particular point of view, we usually select a group of components that satisfy proposed constraints. Our goal is to enhance the selection procedure with equipment ranking to achieve the fmal (optimum) solution. The objective of this attempt is to devise a method of tradeoff between alternatives to make it possible to rank them according to their suitability for the desired application. For this purpose multiple attribute decision making method (Hwang et al., 1982) has been employed. The approach allows such an analysis by providing the
297
framework for processing infonnation about relative importance of equipment attributes.
weight, shape, and other data pertaining to an object to be manipulated (assembled) and may be represented by
Another way of solving such problems is closely connected with the current trend in developing selection and evaluation systems where expert systems technology is used. This provides an excelent framework to incorporate the decision making process of the planner and make it suitable for automation. In such a system, little user interaction is required; since rules and facts are scientifically dermed, each recommendation can be logically judged by the expert system. But unfortunately this is true for machining. However, for assembly operations a kind of generally accepted categorization of them does not exist. Assembly process planning, system components selection, etc. relies heavily on the experience of the planner and the industry in which he/she is working. Thus expert systems intended for assembly applications are likely to be designend as intelligent decision support systems with the engineer having the final decision. In order to develop the selection of assembly system components, it is necessary that the actual assembly operations are clearly understood and defined. One of the ideas is that we use a list of 'standard' assembly operations, develop a system for product part grouping and a series of rules about assembly system components selection. For example, the number of grippers is detennined by the number of different components of an assembly task. It is reduced when identical or similar parts are used and be manipulated via a single gripper.
(I)
We also consider the environment E where the task is to be perfonned with attributes ZE' The environment could be an extremely hot or cold, clean room, with aggressive media, etc. The environmental attributes may also include distances between machines, ambient temperature, etc., and may be represented by (2)
Furthennore, we also have to describe parts of assembly P with different characteristics Qp that influence the selection of components such as geometrical fonn, function, accessibility, the joining method, joining direction, material, surface conditions, etc. All these attributes are expressed by (3)
The problem is to select the device in a robotized assembly cell D, with attributes XD , that can perfonn the task within the environment and for a specified group of part assemblies to be assembled on a particular assembly cell. The device attributes may be expressed by (4)
The objective function can be stated as f(XnJ ~f(YAO Z& Qp}
In order to include infonnation about assembly technology, product parts and sub-assemblies, they are described by characteristic features: a geometrical fonn of the components, a mechanical function, a accessibility, a joining direction, a connectiong and assembly method.
XI> YAO Z& Qp
where Xl) YAG Z& Qp are the robot, task, environment and product part variables. When selecting the equipment (components) for a robotized assembly cell we must consider that these components work together in order to assemble part components. This cooperative work and the relations in assembly cell is shown in figure I .
Thus for every object there is a complete description as regards its assembly: a part (name, joining positions), a sub-assembly (name, components), a operation (name, joining position, joining method, joining direction).
3. ROBOTIZED ASSEMBLY SYSTEM COMPONENTS SELECTION As an example we consider an assembly operation AD; with attributes (characteristics) YAD to be done with a robot in an assembly cell. The task may vary from a simple pick and place routine to more complex operations such as gluing, soldering, screwing etc. Additional task characteristics might include the
Fig. 1.
298
Structure of robotized assembly cell and relations between components
3.1 Knowledge for selection
created. For implementation we use a relational database system. Entity-Relationship model is transformed into relations using rules as shown in figure 3.
In order to determine precisely the particular component for a given task, further information is needed. This regards to product components to be handled and operations to be accomplished.
DB of product corrponents
Knowledge needed for component selection is presented in a form of relations in relational database management system. Therefore several parameters were defmed to perform selection procedure. For assembly operations such parameters are: D minimum number of axes, needed for individual assembly operation, D type of robot control, D preconditions and postconditions, D requirement for special tools, D positioning accuracy, D sensor requirement.
ossignng a list of assembly operations to cell (station)
knowtedtJe base about assembly operations
1 . pick and place 2 - insertF.20N
3· SCteW 4· ...
Product parts to be assembled are described by: D size of the component, D weight of the component, D joining technique, D joining direction, D material, D joining force, D operational environment D product part shape, D speed of working.
selection procedure finds
SCJtisfyinQ solutions using elimination search
evaluation and ranking procedure using
lOPSlS method
4. STRUCTURE OF SELECTION MODEL Fig. 2. The major steps involved in the development of the computer aided component selection process include the following: (a) selecting the appropriate characteristics of assembly cell components for the creation of a component descriptive database (CDD); (b) designing of a classification system using the characteristics selected from step (a); translating the task variable to those of components in CDD in order to match job requirements with the component capabilities in the CDD; (c) designing a method that can classify and select components based on a given criterion; and, (d) applying the selection model. Additionally we could also (e) apply an economic analysis for cost comparison of feasible component candidates.
Model of computer-aided selection of robotized assembly cell component
.-----,
DEVICE ([)# . description ....) 101 Robot 102 Ordering device 103 Conveyor FUNCTION (FI. [)# . description . time) 11 101 HandHng 1 11 102 Ordefing 3 12 10 1 Assembly 4 13 103 Transport 2 DEVl CE ([)#. description .... )
m11
nFUNCTlON _____(FI . description .... )
1 PERFORM (GI . FI . time)
Fig. 3.
A model for computer aided selection of components is presented in the figure 2. In this model we assume that operation (task) sequence is known and is optimally defmed. Based on the task sequence and assembly parts characteristics we generate the criteria for component selection. The selection procedure is performed using interactive work with user (planner) or in the future with methods described in chapter 5. For efficient selection of components a data base is
Transformation ofE-R model to relations
5. METHODOLOGY FOR ASSEMBLY CELL COMPONENTS SELECTION The optimum selection of assembly cell components to suit particular application and production environment is done after considering various attributes among the large number of available alternatives. This is a difficult problem because of a large number of available alternatives, and due to the fact that different
299
alternatives may be conflicting in nature. It is not possible for an individual to take all of these considerations into account without the help of computer software.
Satisfying solutions: a satisfYing solution is one whose attributes all exceed certain minimum desired levels of aspiration. A set of satisfYing solutions is composed of acceptable alternatives. Preferred solution: a preferred solution is a nondominated solution selected as the final choice through the decision maker involvement in information processing. Only nondominated solutions which are the satisfYing solutions can qualifY to be in the set from which a preferred solution is selected.
Cl
Cl
5.1 System based on Multiple Attribute Decision Making Multiple Attribute Decision Making (MADM) refers to an approach of problem solving that is employed to solve problems involves selection from among a fmite number of alternatives. A MADM is a procedure that specifies how attribute information is to be processed in order to arrive at a choice. MADM is one of the two categories of a more general problem solving approach termed Multiple Criterion Decision Making (MCDM) (Hwang et al., 1982). Although these techniques have been widely developed in fields like economics and mathematics. The method is discussed in detail in papers Hwang et. al. (1982) and Agrawal et. al. (1991). Therefore we aviod repetition and give only a brief description.
TOPS/S'method. The TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method is applied as next. In a short this algorithm can be divided in the following steps: Step I Write decision matrix Aij where row i corresponds to the component and column j corresponds to the considered attributes of the component. Step 2 Obtain information from user (or expert system) on relative importance of attributes in pairwise comparison. The relation dij=d! d;k is established and form the relative importance matrix D where importance of ,1h attribute d; = (5) J importance ofJ1h attribute Step 3 The information in the D matrix cannot be used directly in the MADM method. Using eigenvector method we seek to fmd weight matrix vector W where DW=IIW . Obtain maximum eigenvalue A. using this value of A. to find eigenvector W, where W presents the weights of each attribute as (D-A.maxI)W=O. Step 4 Construct normalized decision matrix R from decision matrix A using the relation
MCDM refers to making decisions in the presence of multiple, usually conflicting, criteria. MCDM is required when confronted with a problem that has the following characteristics: Cl Multiple objectives/attributes, Cl Conflict among criteria, Cl Incommensurable units, Cl Design/selection.
Basic definition for the MADM environment. The proposed method is characterized by: Cl Attributes: performance parameters, components, factors, characteristics and properties Cl Decision matrix: a decision matrix D is a 'm by n' matrix whose element x(i. j) indicates the value of alternative i(AJ where there are m alternatives and n attributes. Hence Ai, i = I, ..., m is denoted by !; = (x(i, I), x(i, 2), ... , xCi, n» and the column vector ~=(x(l,j), x(2,j), ... , x(m, j)? shows the contrast of each alternative with respect to attribute j . Cl Optimal solution: an optimal solution is one which results in the maximum value of each of the attributes simultaneously. That is, takingXto be a set of all alternatives, ,I* is an optimal solution if,I* eX and k*»j{,!} for all ,IeX. Cl Nondominated solutions: a feasible solution is nondominated if there exist no other feasible solutions that will yield an improvement in one attribute without causing a degradation in at least one other attribute.
rei, j)
= -;::::=a(=i,=}=~=
..
(6)
L(a(i,}W /-\
r(i. j) = an element of the normalized decision matrix a(i. j) = an element of decision matrix A
Step 5 Determine weighted normalized decision matrix V using R and W. Step 6 Determine positive ideal A * and negative ideal Asolution using the relation
(7)
and
300
{~.~~~I~) l.~~~i~l
A- •
=
'... ~:.~~iJ)l )
{V V2- •••• V,,-} I-.
(8)
The ideal solution is a hypothetical solution for which all attribute values correspond to the maximum attribute values in the database comprising the satisfying solutions; the negative ideal solution is the hypothetical solution for which all attribute values correspond to the minimum attribute values in the mentioned database. Step 7 Calculate separation measures Si' and Si· • where separation from the ideal is given by
SI·=[t(V(i.JJ-V;r~
(i=1.2 • ...• m)
(9)
J
j-I
and separation from the negative-ideal is given by
SI-
=[
t
(v(iJ)-VI-r
j-I
_~_""'_
~
~
J
(i = 1.2 •...• m)
(10)
Structure of database. As a part of knowledge-based and/or rule-based tools for automatic selection of components of robotized assembly cell we have developed a system for computer aided selection of grippers. In the database are stored information about grippers. Each gripper is stored in a form of a record in the database. As database management system a well known DBMS system Paradox was used. The software has been made 'user friendly' and the system is running under the operating system MS-Windows. Program modules were written in object based programming language ObjectPAL. that is a part of Paradox. To use this program an extensive knowledge about grippers and gripper application is not required. The database may be updated considering changes on the market. The user are given following options: Cl adding a new gripper to the database. Cl deleting an existing gripper. Cl changing attribute information of an existing gripper. Cl listing of grippers by type. force. producer. etc. In the database grippers are grouped regarding gripping principle. the groups are: fmger grippers, vacuum grippers, magnetic grippers, grippers for boss and holes, grippers with elastic elements, adhesive grippers and special grippers.
_ _ _ _ _ _ _ _ _ _A' IDEAL SOUJllON I
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5.2 Knowledge-based system for grippers selection
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The product parts to be assembled and assembly operation characteristics are the most important factors that determine the type and characteristics of the gripper. Information about parts are saved in a parts database and includes: main shape, supplementary shape, weight of component, largest dimension, material, roughness, surface temperature.
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NEGA~ IDEAl - - - - - - - _;;;--.,__,c SOLl1TlON attT1bute
Fig. 4.
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Euclidean distances to the ideal and negative ideal solutions in two-dimensional space (case of two attributes)
Selection procedure. In order to select a gripper some conditions and requirements must be fulfilled. Following parameters determine the gripper selection: geometry (main and supplementary shape of the part), dimensions, tolerances, form of gripping face, weight, robot's accelerations in each way, assembly operation, assembly Goining) force, surface, temperature. material. friction . The data model for grippers selection in figure 5 shows relations between tables.
Step 8 Calculate 'relative closeness to ideal solution'. This index is a measure of the suitability of the device for the chosen application on the basis of attributes considered. A device with the largest index (according to equation) is optimum: (J J)
Step 9 Rank alternatives in accordance with the decreasing values of indices C·. indicating the most preferred and the least preferred feasible optional solutions.
Fig. 5.
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Data model for grippers selecion
After the user specifies and describes assembly components and assembly operations a selection is performed automaticaly. Based on the shape of part component the user can choose gripping place. Using this data the direction of gripping, the shape of gripping face and way of griping (by shape or by force) are determined. The database is scanned and all possible grippers are selected. During search procedure some calculations and some queries are performed, depending on the type of gripper. Result is a report where all grippers that satisfy all conditions are listed.
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availability, management constraints, simulation of cell operation in the workplace, international market policies, etc.
6. CONCLUSION Work was concentrated on finding of methodologies for evaluation and selection of components of the assembly system. The paper present two different models for components selection (robots, grippers, peripheral devices, etc). The first methodology is based on multiple attribute decision making principle for equipment selection. As a significant development it recognize the need for, and processes the information about, relative importance of attributes for a given application. Second aproach is more knowledge based. Selection process is based on components, assembly operations and working conditions description. In the database are for now some real grippers available on the market and some hypothetical ones. In our laboratory we are now working on improvement and testing of the system. Until now many selections have been performed. MADM method was used for assembly robots selection, the other one was used, as shown, on grippers selection. After transfering MADM to grippers selection, a comparison between both techniques will be done and results will be published.
7. REFERENCES Wang, Y., Hsieh, L.H., and Seliger, G. (1993). Knowledge -Based Integration of Design and Assembly Process Planning. Manufacturing Systems, Vol. 22, 2, pp. 107-112. Pham, D.T., and Yeo, S.H. (1991). Strategies for gripper design and selection in robotic assembly. International Journal of Production Research, Vol. 29, 2, pp. 303-316. Scholz, W. (1990). Einsatz von Datenbanken bei der rechnergestiltzten Planung von montageanlagen. elM Management, 4, pp. 18-23. Hwang, C. L., and Kohli, V. (1982). Multiple Attribute Decision Making - a State of the Art Survey. In: Lecture Notes in Economics and Mathematics, Springer - Verlag, Berlin. Agrawal, V. P., Kohli, V., and Gupta, S. (1991). Computer aided robot selection: the 'multiple attribute decision making' approach. International Journal of Production Research, Vol. 29, 8, pp. 1629-1644. Zupan, I. (1994). Data Base of Grippers. B. E. Thesis (in Slovene). University of Lj ubIj ana, Faculty of Mechanical Engineering.
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Fig. 6.
Flow chart for selection of grippers (Zupan, 1994)
Fig. 7.
Selection module of programme
The fmal decision of gripper selection after browsing may be made on the basis of other factors which have not been taken into account earlier, such as: Cl economic considerations,
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