ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 34)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-13
Figure 2-7
This condition is not always sufficient. Adequacy depends on arc and line lengths. If the
circle’s center projection on the line
L
belongs to the line segment (
P
1
∈
L ) and an
intersection point of the continued perpendicular with the circle arc belonging to the
circle segment
P
2
∈
C
then (2.2.1.2-1) is sufficient
.
If projection of the circle init point
P
1
belongs to the line segment -
P
5
∈
L
(Figure 2-
8), use the following proportion
h/r = ρ(P
3
, O
c
)/[ρ(P
1
, P
3
) – r] = ρ
1
/(ρ
2
– r)
(2.2.1.2-2)
where
P
3
is the point of intersection of the line
(P
1
,O
c
)
with the line
L.
As init point of
the circle
P
1
and a circle center are known,
P
3
can be determined
.
The length
h
of the
perpendicular dropped from the circle center
O
c
on the line
L
can be also found by
(2.2.1.2-4) or another method.
From (2.2.1.2-2) the results are
hρ
2
– hr = rρ
1
=> r = hρ
2
/(ρ
1
+ h)
(2.2.1.2-3)