ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 55)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-34
(rC
1
+ C
3
) 2 + (rC
2
+ C
4
) 2 = (R
2
– r) 2
(2.3.1-20)
where
C
3
= X
1
– X
c2
and C
4
= Y
1
– Y
c2
From (2.3.1-20),
r 2 C
12
+ 2C
1
C
3
r + C
32
+ r 2 C
22
+ 2C
2
C
4
r + C
42
= R
22
– 2R
2
r + r 2
(2.3.1-21)
r 2 (C
12
+ C
22
– 1) + r(2C
1
C
3
+ 2C
2
C
4
+ 2R
2
) + (C
32
+ C
42
– R
22
) = 0
(2.3.1-22)
but
C
12
+ C
22
= [(X
c1
– X
1
) 2 + (Y
c1
– Y
1
) 2 ]/R
12
= 1
(2.3.1-23)
so we get
rC
6
+ C
7
= 0
(2.3.1-24)
r = – C
7
/C
6
(2.3.1-25)
where
C
1
= (X
1
– X
c1
)/R
1
C
2
= (Y
1
– Y
c1
)/R
1
C
3
= X
1
– X
c2
C
4
= Y
1
– Y
c2
C
6
= 2C
1
C
3
+ 2C
2
C
4
+ 2R
2
C
7
= C
32
+ C
42
– R
22
(2.3.1-26)
Example 2-30
( Motion Mathematic Lib Samples \Circle to Circle\ Section 2_3\
CircleCircle_Ex_2_30 – www.elmomc.com)
Circle C1 (Figure 2-30) is defined by its radius R1 = 40000, init point P
1
(-40000, 0), center
coordinates (0,0), init 180 o angle and a 90 o sweep angle.
Circle C2 is defined by the radius R2 = 100000, init point (0, -40000) center coordinates (-
65000, 35000) and -180
o sweep angle.
Coordinates of point P
1
: X1 = -40000, Y1 = 0;
To get the coordinates of the point P
2
, use the circle C
2
equation:
(X + 65000) 2 + (Y – 35000) 2 = 100000 2
Know that Y2 = 0, for X
2
use the following equation: