ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 35)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-14
Figure 2-8
Example 2-9
( Motion Mathematic Lib Samples \Circle to Line\ Section 2_2_1_2\
CircleLine_Ex_2_9 – www.elmomc.com)
The circle arc (Figure 2-9) is defined by its radius
R
= 100000, init angle α = 0 o and sweep
angle
β = - 45 o , init point P
1
(100000, 0). Line target position (-40000, 0).
In this case
ρ
1
= 40000
,
ρ
2
= 140000 - line (P
1
,P
3
)
coincide with axis X.
Circle center coordinates Xc = 100000 - Rcos(0) = 0, Yc = 0 - Rsin(0) 0.
Line init point coordinates X1 = 0 + 100000cos(0 - 45) = 70711, Y1 = 0 + 100000sin(0-
45) = -70711
To calculate the length of perpendicular h dropped from the circle center (Xc,Yc) on the
line, use formulas (a1.6), (a1.4) and (a1.7) from Appendix 1.
k = (Y2-Y1)/(X2-X1)=(0+70711)/(-40000-70711)= -0.6387, q = -1/k = 1.5657
Xpr = (y - Y1 + k*X1 - q*x)/(k - q) = -11589.6, Ypr = y + q*(Xpr - x) = - 18145.7
h= [(-11589.6 - 0) 2 + (- 18145.7 - ) 2 ] 1/2 = 21531
r = hρ
2
/(ρ
1
+ h) = (21531* 140000)/( 40000 + 21531) = 48989