ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 65)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-44
r
2
C
5
+ rC
6
+ C
7
= 0 (2.3.3-7)
But
1 – (C
1
)
2
– (C
2
)
2
= 1 – (X
1
– X
c1
)
2
/(R
1
)
2
– (Y
1
– Y
c1
)
2
/(R
1
)
2
= 0 (2.3.3-8)
So for r the results are:
r = – C
7
/C
6
(2.3.3-9)
Similarly in the case when l
2
> l
1,
use the following system:
(X
o
– X
2
)/(X
2
– X
c2
) = r/R
2
(2.3.3-10)
(Y
o
– Y
2
)/(Y
2
– Y
c2
) = r/R
2
(2.3.3-11)
(X
o
– X
c1
)
2
+ (Y
o
–Y
c1
)
2
= (R
1
+ r) (2.3.3-12)
Equations (2.3.3-1) - (2.3.3-2) can be written in the following format
X
o
= X
2
+ r(X
2
– X
c2
)/R
2
= X
2
+ rC
1
, C
1
= (X
2
– X
c2
)/R
2
(2.3.3-13)
Y
o
= Y
2
+ r(Y
2
– Y
c2
)/R
2
= Y
2
+ rC
2
, C
2
= (Y
2
– Y
c2
)/R
2
(2.3.3-14)
And substituting into (2.3.3-3), the results are:
(X
2
+ rC
1
– X
c1
)
2
+ (Y
2
+ rC
2
– Y
c1
)
2
= (rC
1
+ C
3
)
2
+ (rC
2
+ C
4
)
2
= (R
2
+ r)
2
(2.3.3-15)
where C
3
= X
2
– X
c1
C
4
= Y
2
– Y
c1
.
Simplifying (2.3.3-15), the results are:
r
2
[1 – (C
1
)
2
– (C
2
)
2
] + r[2R
2
– 2C
1
C
3
– 2C
2
C
4
] +[(R
2
)
2
– (C
3
)
2
– (C
4
)
2
] =
r
2
C
5
+ rC
6
+ C
7
= 0 (2.3.3-16)
But
1 – (C
1
)
2
– (C
2
)
2
= 1 – (X
2
– X
c2
)
2
/(R
2
)
2
– (Y
2
– Y
c2
)
2
/(R
2
)
2
= 0 (2.3.3-17)