Page 191 - Modular design for machine tools

Application of Machine Tool Description to Engineering Design 151

Y X Y
X s s s s

Set X Set Y
s
X s Y s s
X s Y s

R(X )
s
x 1 y y 1
X s x 2 y 2 Y s
X s x 3 y 3 Y s
x 4 y 4 Figure 4-17 Definition of rate of
x 5 y 5 6 commonness.
R(Y )
s

where |R(X )| is the number of vertices in |Y | connecting with those
s
s
in |X |, |R(Y )| is the number of vertices in |X | connecting with those
s
s
s
in |Y |, and in general |R(X )| |R(Y )|.
s
s
s
In the calculation, the evaluation criteria are as follows, when the
second, third, and fourth figures within the GT codes for both structural
modules can be written as (B , C , D ) and (B
, C
, D
).
s
s
s
s
s
s
1. When B B
, C C
, and D D
, both modules are identical, and
s
s
s
s
s
s
the evaluation value is unit.
2. When B B
, C C
, and D D
, the evaluation value is 0.5
s
s
s
s
s
s
3. In other cases, the evaluation value is nil.
Actually, in the evaluation procedure, the reference matrix is pro-
duced by allocating the vertices of both sets to the line and row, and by
determining the (i, j) component using the evaluated value obtained
from the above-mentioned criteria, accordingly, the pattern similarity
can be calculated by using the information for the adjacency relation-
ships between both modules, starting and terminal vertices within
FOF, and pattern of FOF in the structural pattern. Considering the
structural pattern is that of the directed graph, the pattern similarity
yields to the identical evaluation of a couple of adjacency matrices
derived from both structural patterns. In fact, the calculation procedure
is as follows.
1. Arrangement of the structural pattern on the disposition plane [X, Y],
using the converse directed graph and rooted-directed tree, as shown
in Fig. 4- 18.
2. Determination of the arranging order of [X, Y] coordinates on the
row and column of the adjacency matrix. As shown on the far left