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
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