ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 28)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-7
Figure 2-2
Example 2-2
(Motion Mathematic Lib Samples\Circle to Line\ Section 2_2_1_1\
CircleLine_Ex_2_2 – www.elmomc.com)
Circle arc is defined by its init position X
from
= 0, Y
from
= 100000, radius R = 100000, init
angle α = 90 o (with axis X positive direction), and sweep angle = 180 o . Line end point X
to
= -140000, Y
to
= 100000.
Circle center coordinates
Xc = X
from
– Rcos(απ/180) = 0 – 100000cos(π/2) = 0
Yc = Y
from
– Rsin(απ/180) = 100000 – 100000sin(π/2) = 0
Circle end points
X
1
= Xc + Rcos(α + β) = 0 + 100000cos(π/2 + π) = 0
Y
1
= Yc + Rcos(α + β) = 0 + 100000sin(π/2 + π) = -100000
Projection of the circle center on the line (Appendix )
K
1
= (Y
2
– Y
1
)/(X
2
– X
1
) = (100000+100000)/(-140000-0)=-1.4286
K = -1/K
1
= 0.7
Xp=(Yc – Y
1
+ K
1
*X
1
- KXc)/(K
1
- K) =
(0+100000 + 0.7*0 +1.4286*0))/(-1.4286 - 0.7) = -46979