ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 61)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-40
This system is similar to (2.3.2-2)
–
(2.3.2-4) and comes to the same solution
r = –C
7
/C
6
where
C
1
= (X
1
– X
c2
)/R
2
C
2
= (Y
1
– Y
c2
)/R
2
C
3
= X
c1
– X
1
( 2.3.2- 5)
C
4
= Y
c1
– Y
1
C
6
= 2(C
1
C
3
+ C
2
C
4
+ R
1
)
C
7
= (C
3
) 2 + (C
4
) 2 – (R
1
) 2
Figure 2-35
Example 2-36
( Motion Mathematic Lib Samples \Circle to Circle\ Section 2_3\
CircleLine_Ex_2_36 – www.elmomc.com)
Consider an example (Figure 2-36) of a maximum switch radius calculation for the case
similar to the one drawn in Figure 2-35 with the following parameters:
Coordinates of the first arc center are
X
c1
= 0 , Y
c1
= 0 .
Coordinates of the second arc
center are
X
c1
= 100000 , Y
c1
= 100000 .
Circle arc C
1
init angle
α
1
= 0 o ,
sweep angle
β
1
= 90 o ,
radius
R
1
= 100000 .
Circle
arc
C
2
init angle
α
2
= 180 o
,
sweep angle
β
2
= 30 o , radius
R
2
= 100000 .
Calculations due to (4.2-5):
X
1
= 100000 – 100000*cos(pi/6) = 13397.459622
Y
1
= 100000 – 100000*sin(pi/6) = 50000