ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 40)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-19
c) The circle arc sweeps an angle less than 90 o and a perpendicular dropped from the
circle init point P
1
on the line L intersects line segment at point P
2
∈
C
1
(Figure 2-
15). A projection of the circle init point P
1
(X
1
,Y
1
) on the line L – point P
2
(X
2
,Y
2
)
and the length of the segment defined by the line init point P
3
and projection point
P
2
:
ρ
1
= ρ(P
3
,P
2
) can be determined . Now calculate the maximum switch radius
with the use of the following equation:
(R – r)
2
= (R – ρ
1
)
2
+ r
2
(2.2.1.3-4)
that leads to
–2Rr = – 2Rρ
1
+ (ρ
1
)
2
and finally
r = [2Rρ
1
– (ρ
1
)
2
]/(2R)
(2.2.1.3-5)
Figure 2-15
Example 2-16
( Motion Mathematic Lib Samples \Circle to Line\ Section 2_2_1_3\
CircleLine_Ex_2_16 – www.elmomc.com)
The circle (Figure 2-16 ) is defined by its init point P
1
(0, -80000), radius R = 80000, init angle
α = -90 o and sweep angle β =-45 o . Coordinates of the line end point (150000,150000).
Circle end point P
3
(line init point) coordinates are calculated as X
3
= 80000*cos(pi + pi/4) = -
56569 and
Y
3
= 80000*sin(pi + pi/4) = -56569
Drop a perpendicular from the circle init point P
1
on the line L
2
. To define coordinates of the
projection point P
2 ,
use formulas from the Appendix 1.
k = dY/dX = (150000 + 56569)/ (150000 + 56569) = 1, q = –1/k = –1.