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constraint graph. Homem de Mello and Sanderson [SI took a diffexent
approach by representing all the assembly plans explicitly using an
AND/OR graph. Any feasible assembly plan cOneSpOndS to a tree in the
graph. They have proved that a complete and cOrrect set of precedence
relationships can be derived from the AND/OR graph. Since che precedence
constraints are determined by the geomq of a product, it is more desirable
to obtain the precedence relations directly from the geometry of the assem-
bly (i.e., the CAD model of the assembly) and then generate assembly
plans, rather than vice versa.
Not all of the assembly plans generated f" the precedence relation-
ships are efficient or even feasible for a particular assembly cell. Both
Homem de Mello [9] and Wolter [I61 defined criteria, such as degrees of
This work was supported in part by the National Science Found.ticn un&r Orwt
CDR 8803017 to the Engineering Research Center for Jntelligent Manufacturing
Systems and a grant ham the Ford Fund. freedom of subassemblies, and directionality of assembly maling tasks, e..
to select optimal assembly plans frun all the possible onm. But MQC of
cell, such as fixture and 001 stkctiaas. Therefac. the optimal plan UIUS
selected may still be infeasible for a given nbly cell.
~paper&scribesanautmraticasscmblyplanniqgsystun. Theiaput
to the system is a CAD desziptioa of a product and an assembly cell m
which the product is to be assembled. The output ofthe is an
efficient feasible assembly plan subject to the ltaoucc coastrun tsofthe
given BssemMy cell. The plan nat only contains the sequence of asembly
mating tasks to be done, but also the fix- con6guration end tool
speciscations for each of meSe mating tasks.
2. Assembly Planning System
these criteria is directly rem to the rcsolmx CQnstrSints of an BssQnbly
The proposed assembly planning system cax+ts of five & modules:
base, simulated world model. and sssmbly planna. The funchon of each
major module is described in the following subsections.
2.1. World Database
assembly and a model of assembly cell.
tuple, < C , R > in which
world databa% knowledge acquisition nwch" . Planning.lolowledge
The wmld database consists of two modules, a relational model of
Definition 1. A relational malcl of an ncomponent assembly is a two
C= (c1 , c2, 9.- , c.) isa set of symbolsrepmenting components in
the assembly.
R = [ rl , rz, ..- , r, ) is a set of four tuples representing relations
between components of the assembly. when? m = Ci = n(n - 1)R.
ri = < c,, , cq , A , TN >. whae cp , cq E C, A is a 4x4 homogene-
ous transformatii matrix representing spawfre~mhip between
components c,, and cq.
= {NULL, if no contacts exist between components c,, and cq
PI
< TRb , TR, , Typ, Stclbility > , XconUasmistbetarknc, mdc,