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will block the won Tij and none of them can be performed simultane-
ously with Tip [Wi), I = I, 2. . , mlij. is the set of mating tasks (ilud-
ing real and pseudo) such that the esrabllshing of any one of them will block
the operation Tij and all of them can be performed simultaneously with Tij.
Then the pt-condition of operation Tij is
Rij=MP( Tij , zlSy )ANL( Tij, V Vi). (6)
For task Tij to be performed successfully, at least one of its opemtions is not
blocked; i.e..
”* .. I”*
1-1
is the postcondition of task Ti. Its equivalent disassembly form is
Equations (7) and (8) an two formulas representing pmedence
knowledge of assembly and disassembly respectively. It can be shown that
they can be derived from each other. The equivalence of (7) and (8) sug-
gests that either assembly approach or disassembly appaach can be used in
acquiring precedence knowledge of an embly. Following is a prowdm
which obtains the assembly postconditions for mating tasks, it can easily
be modified to obtain disassembly preconditions.
Algorithm ACQUISITION-FOSr (Acquire assembly post-
conditions). Given an assembly with ne components and n real mating
tapirs and the number ofopaaio~ for each nal matins Ti is 4.
i = 1,2, *- , n. this a@” obtains the ansanbly postanditions fix the
product with the time complexity to be a polymmialof the number of mat-
ing tasks of the product It is assumed that Ti’s with i gmte~ than n am
pseudomatingtasks.
Al. ~~tspLindex.lSetit1.RtTRUE.
A2.
A4. [Loop2fa~operstiOna]Ifjisg~?aterthan~,then (iti+l.
AS. [Initialize relaion indcx.] Sett t 1. Rj?’ t TRUE , Rd t TRUE.
A6. [Loop 3 form rela1ions.1 Ift is g” than I)! =(ne - 1 ) n, 12. thea [
Ri tRi V (RY ARd ) . j t j + Land go to
A7. rrajectory is blocked.] If T is blocked by Sf and cannot be pa-
formed simularneously with $, thenRr +R* AMP( 4, s!); else
if Tij is blocked by Wi but can be performed imultaneowly wth w,
thenR$ t R# AM( Ti/, Wi ).
1 for n tasks.] Ifi isg” than n, then exit
AX Fitializc-On indcx.1 Seti t 1,Ri t TRUE.
R t R ARi 1, and go (0 step A2
1.
AS. End of loop 3.1 A t A + 1 and go to step A6.
END ACQvrSmON_POST.
The result and output of this algorithm will be the expressiOn shown in
(7). There are three loops in the algorithm, at steps A2. A4. and A6. The
loop in step A2 has n iterations; the hp in step A4 has mi Mons; and
the loop in step A6 has (ne - 1 ) n, I2 iterstions. The total number of itera-
tions in this algorithm is then n (h- 1)n, mi n. Suppose M = max (mi ),
then the total number of iterations in the above algorithm is less than