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the state of an assembly.
The state of an assembly is an instance of the conditions of all its tasks.
SupposeanassemblyhasmtasksTi.i=1.2, .m. TaskT1 throughTi
are done and therestare not done yet. Then the state of this assembly can
be repremM as
i m
S,=( A =I DONE(Tj))A( ,-+I ,A -DONE(Tj)). (1)
That is. S, represents the state whose interpretation of S, is TRUE. Ndcc
that a formula can also represent a set of states. For example, by omitting 4
in S,,
i-1 )I
S', = ( A DONE( Tj ))A ( j$+l -DONE( Tj )) . (2)
J -1
can represent a set of two states, one with Ti having been Qne and the other
with Ti not done yet because bofh states will give S', a TRUE intapetation
tion of current subassemblies. Since at any time instance., an assembly
presents as a collection of subassemblies and components. This collection
is a partition of the set of all components and can also fully describe assem-
bly states. Suppose Ci's. i = 1,2, *. , A, are a cdlection of subassem-
blies, then
The second representation describa assembly states by listing a
Sc=(C,.C2, *'* .C&), (3)
k
14
where uCi=C and CinCj=O, ifi+j. (4)
is a representation of an assembly state. and C is the complete set of com-
ponents of an assembly.
Whiie both representations described above are equivalent in repsent-
ing assembly states, the first one is a better representation for precedence
knowledge while the second one is more suitable for assembly plan genera-
tion. Both of them will be used in our assembly planning system. For brev-
ity, we shall refer the tirst representation as relational fonn of state
representation and denote it by S,. and refex the second representation as
componentfonn of state repmentation and denote it by Se. It is not difficult
to transform these two representation forms from one to the other. Suppose
task Ti relates two components cp E C, and cq E Cy, then
That is, if Ti is done. then the components related by Ti belong to the same
subassembly; likewise if two components belong to the same subassembly,
then the task relating them is done.
During an assembly process a subassembly is usually fixed by a fixture
to maintain the spatial relationships among component. Before being
assembled, a component is kept in a patt feeder which can also be viewed
as a type of fixture. The association between fixture and subassemblies is
described by the following predicate in the system.
DONE(Ti)=TRUE ifandonlyif u=v. (5)
('"" ifC,isfkedbyafixhmf
C"RRm-Fm"RE( '1 1 f )= FALSE. XC, is not fixed by a fixbuef
where Ci is a component a subassanbly. andfis a vrriable
fixture,
if Ci has no 6xtllrc with it
ifCiisfixedbyafixtllrc
if Ci is a component in apart f-.
Tofullydesdbethefixture . . lsjtuatiOnh~asslmhlycC~,ach