KE-750_MAINTE.pdf - 第112页
When these equations are concluded in re lation to the X axis and the Y axis, the following four simultaneous equations can be obtained. xp - x1 = B (x 3 - x1) + A (x2 - x1) ⑦ yp - y1 = B (y3 - y1) + A (y2 - y1) ⑧ X - x1…
which is the mount coordinate of the mount data.
In this case, if it is assumed that the board is moved and deformed evenly,
obtain the coordinate of the rectangle coordinate which has origin (○)of point P'
on the angular coordinate made with M1', M2', and M3' with response to M1,
M2, and M3 which are equivalent to the coordinate of point P on the angular
coordinate which has two coordinate axes out of the straight lines which pass
two points out of three points, M1, M2, and M3.
In this case, a point of intersection of the two straight lines; one is drawn from P
in parallel with the angular coordinate axis and the other drawn from M1 to M2
is defined as P12, and another point of intersection of the two straight lines: one
is also drawn from P in parallel with the angular coordinate axis and the other
drawn from M1 to M3 is defined as P13. In the same manner, for P', a point of
intersection made by the straight line from M1' to M2' is defined as P12' and
made by the straight line from M1' to M3' is defined as P13'. Then, the
equations below can be obtained.
(M1→P) = (M1→P13) + (M1→P12) ①
(M1’→P’) = (M1’→P13’) + (M1’→P12’) ②
According to the definition of P', the following equations can be obtained.
|M1→P12|
|M1→M2|
|M1'→P12'|
|M1'→M2'|
=
|M1→P13|
|M1→M3|
|M1'→P13'|
|M1'→M3'|
=
Equations q and w can be as shown below when the result of equation e is A,
and that of equation r is B.
(M1→P) = B (M1→M13) + A (M1→M2) ⑤
(M1’→P’) = B (M1’→M3’) + A (M1’→M2’) ⑥
In the equations ⑤ and ⑥ on the previous page, vector coordinates M1, M2,
M3, P, M1', M2', M3', and P' on the rectangle coordinate whose origin is (
○) are
defined (x1, y1), (x2, y2), (x3, y3), (xp, yp), (x1', y1'), (x2', y2'), (x3', y3'), and (X,
Y), respectively. Then, the following equations can be obtained.
(xp, yp) - (x1, y1) = B ((x3, y3) - (x1, y1)) + A ((x2, y2) - (x1, y1))
(X, Y) - (x1’, Y1’) = B ((x3’, y3’) - (x1’, y1’)) + A ((x2’, y2’) - (x1, y1’))
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When these equations are concluded in relation to the X axis and the Y axis,
the following four simultaneous equations can be obtained.
xp - x1 = B (x3 - x1) + A (x2 - x1) ⑦
yp - y1 = B (y3 - y1) + A (y2 - y1) ⑧
X - x1’ = B (x3’ - x1’) + A (x2’ - x1’) ⑨
Y - y1’ = B (y3’ - y1’) + A (y2’ - y1’) ⑩
In this case, the values of the functions other than A, B, X, and Y are known.
Therefore, vector coordinate (X, Y) of P' where the origin is (K) can be obtained
from the answer of these simultaneous equations.
According to equations u and i, the following equations can be obtained.
xp - x1 - B (x3 - x1)
x2 - x1
yp - y1 - B (y3 - y1)
y2 - y1
=A =
xp - x1 - A (x2 - x1)
x3 - x1
yp - y1 - A (y2 - y1)
y3 - y1
=B =
When B and A are obtained from equations !1 and !2, the following equations
can be obtained.
(yp - y1) (x2 - x1) - (xp - x1) (y2 - y1)
(y3 - y1) (x2 - x1) - (x3 - x1) (y2 - y1)
B =
(yp - y1) (x3 - x1) - (xp - x1) (y3 - y1)
(y2 - y1) (x3 - x1) - (x2 - x1) (y3 - y1)
A =
When answers A and B in the above equations are substituted for equations ⑨
and ⑩, X and Y can be obtained easily. In equations ⑬ and ⑭, if the
denominator is 0, A and B become infinite. In this case, in both equations, the
following equation is true.
(y3 -y1) (x2 - x1) = (x3 -x1) (y2 - y1)
When both sides are divided by (x2 - x1) (x3 - x1), the following equation can be
obtained.
(y3 - y1)
(x3 - x1)
(y2 - y1)
(x2 - x1)
=
This means that M1, M2, and M3 are inline on a straight line. In this case, the
result is regardless as a data error because it is meaningless for the BOC mark
to be three points.
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Angular correction value θ can be obtained as the angle made by vectors
(M1→P) and (M1'→P'). So, it can be obtained as follows:
(x' - x1')
(Y' - y1')
(xp - x1)
(yp - y1)
- atan ( )θ = atan ( )
For the BOC mark of two points (the same for IC mark)
As shown in the figure above, the theoretical coordinate of the BOC mark of two
points is defined M1 and M2, and the coordinate where each mark is detected is
defined M1' and M2'. In this case, coordinate Mv is where point M2 is rotated
by 90° with point M1 set at the center, and coordinate Mv' is where point M2' is
rotated by 90° with point M1' set at the center. Using Mv and Mv' as the
theoretical coordinate of the 3rd BOC mark which is virtual point, and using M1,
M2, M1', and M2' as the physical coordinate, in the same manner as the BOC
mark of three points, coordinate correction can be made by obtaining the
coordinate of point P' from the coordinate of point P.
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