ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 60)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-39
2.3.2 Each circle intersects the internal area of the second
Figure 2-33 shows another case of two circles intersecting: circle C
1
comes from inside of
the circle C
2
and circle C
2
continues inside the circle C
1
. Noting that
d =
ρ(O
1,
O
2
)
,
the
switch radius must obey the following necessary condition:
R ≤ [d – (d – R
1
) – (d – R
2
)]/2 = (R
1
+ R
2
– d)/2 (2.3.2-1)
Condition (2.3.2-1) is sufficient in case line O
1
O
2
intersects circle arc
C
1
and circle arc
C
2
.
Figure 2-33
Line O
1
O
2
does not intersect at least one of two circle segments (Figure 2-35)
Another case when line O
1
O
2
does not intersect at least one of the two circle segments. In Figure 2-35 line
(X
c1
, Y
c1
) – (X
c2
, Y
c2
)
connecting two circle centers does not intersect circle arc
C
2
. Draw a line
O
2
P
1
between the circle
C
2
center and its end point
P
1
(X
1
,Y
1
).
The center
(X
o
, Y
o
)
of the switch arc with a
maximum radius must belong to this line. To define maximum radius
r,
use the same system as in the
previous cases.
(X
1
– X
o
)/(X
1
– X
c2
) = r/R
2
(2.3.2-2)
(Y
1
– Y
o
)/(Y
1
– Y
c2
) = r/R
2
(2.3.2-3)
(X
o
– X
c1
) 2 + (Y
o
– Y
c1
) 2 = (R
1
– r) 2 (2.3.2-4)