ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 57)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-36
From (2.3.1-27)
Figure 2-31
X
o
R
1
– X
1
R
1
= r(X
c1
– X
1
)
(2.3.1-30)
or
X
o
= X
1
+ r[(X
c1
– X
1
)/R
1
] = X
1
+ rC
1
(2.3.1-31)
where
C
1
= (X
c1
– X
1
)/R
1
(2.3.1-32)
From (2.3.1-28)
Y
o
R
1
– Y
1
R
1
= r(Y
c1
– Y
1
)
(2.3.1-33)
or
Y
o
= Y
1
+ r[(Y
c1
– Y
1
)/R
1
] = Y
1
+ rC
2
(2.3.1-34)
where
C
2
= [(Y
c1
– Y
1
)/R
1
(2.3.1-35)
Substituting X
o
and Y
o
into (2.3.1-29)
[X
1
+ rC
1
– X
c2
] 2 + [Y
1
+ rC
2
– Y
c2
] 2 = (r + R
2
) 2
(2.3.1-36)
If we note that X1 – Xc2 = C3 and Y1 – Yc2 = C4, then (2.3.1-37) can be written in a format
[rC
1
+ C
3
] 2 + [rC
2
+ C
4
] 2 = (r + R
2
) 2
or