ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 59)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-38
Substituting into (4.1-32)
(X
2
+ C
1
r – X
c1
) 2 + (Y
2
+ C
2
r – Y
c1
) 2 = (R
1
+ r) 2 (2.3.1-35)
(C
1
r + C
3
) 2 + (C
2
r + C
4
) 2 = (R
1
+ r) 2
(2.3.1-36)
r 2 [(C
1
) 2 +(C
2
) 2 –1] + r[2C
1
C
3
+2C
2
C
4
–2R
1
] + [(C
3
) 2 + (C
4
) 2 –(R
1
) 2 ] = 0
(2.3.1-37)
But
(C
1
) 2 +(C
2
) 2 –1 = (X
c2
– X
2
) 2 /d 2 + (X
c2
– X
2
) 2 /d 2 –1 =
d 2 /d 2 –1 = 0
(2.3.1-38)
So
r = –C
7
/C
6
(2.3.1-39)
where
C
1
= (X
c2
– X
2
)/d
C
2
= (Y
c2
– Y
2
)/d
C
3
= X
2
– X
c1
(2.3.1-40)
C
4
= Y
2
– Y
c1
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 2-32