R)/ρ – ElmoMC Multi-Axis Motion Controller-Maestro Motion Control User Manual
Page 31
Motion Library Tutorial
Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-10
Figure
2-4
In our calculations was not taken in account additional requirement that the switch arc
should not take more than 50% of the segment length. So the calculated switch arc with the
radius 22917 takes the whole line segment.
If in the calculations, some point on the line is used, for example (65000, 50000), instead of
the line end point, then u = 65000 and the result is:
r
= 0.5*(
100000
2
–
50000
2
–
65000
2
)
/
(100000 + 50000)
=
10917
Perpendicular to the Line
L
end point
P
2
does not intersect the circle
arc
C
In Figure 2-5, there is an intersecting geometric figure showing that a perpendicular line at
Line
L
end point
P
2
does not intersect the
circle
arc
C.
The switch arc drawn in Figure 2-5
is a switch arc with a maximum possible radius
r.
By knowing the coordinates of a circle center
O(X
c,
,Y
c
)
and a circle init point
P
6
(X
6
,Y
6
)
it is possible to find an intersection point
P
3
of two lines:
(X
c
,Y
c
) – (X
6
,Y
6
)
and
L
and
the length of the line segment
P
3
P
6
: ρ
1
= ρ(P
3
, P
6
).
Drop a perpendicular from point
P
6
on the line
L
and by (2.2.1.1-4) define its length
ρ
2
= ρ(P
6
,
P
4
)
.
To define
r,
use a proportion
r/ρ
2
= (ρ
1
– r)/ρ
1
(2.2.1.1-9)
and finally