ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 53)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-32
(X
o
– X
c2
) 2 + (Y
o
– Y
c2
) 2 = (R
2
– r) 2
(2.3.1-4)
From (4.1-2)
X
o
d – X
1
d = r(X
2
– X
1
)
and for
X
o
X
o
= r[(X
2
– X
1
)/d] + X
1
= rC
1
+ X
1
(2.3.1-5)
From (4.1-3)
Y
o
d – Y
1
d = r(Y
2
– Y
1
)
and for
Y
o
Y
o
= r[(Y
2
– Y
1
)/d] + Y
1
= rC
2
+ Y
1
(2.3.1-6)
Substituting (4.5) and (4.6) into (4.4)
[rC
1
+ X
1
– X
c2
] 2 + [rC
2
+ Y
1
– Y
c2
] 2 = (R
2
– r) 2 (2.3.1-7)
or
[rC
1
+ C
3
] 2 + [rC
2
+ C
4
] 2 = (R
2
– r) 2 (2.3.1-8)
(C
1
) 2 r 2 + (2C
1
C
3
)r + (C
3
) 2 + (C
2
) 2 r 2 + (2C
2
C
4
)r + (C
4
) 2 =
(R
2
) 2 – 2R
2
r + r 2 (2.3.1-9)
Figure 2-29
r 2 [(C
1
) 2 +(C
2
) 2 – 1] + r[2C
1
C
3
+2C
2
C
4
+ 2R
2
] + (C
3
) 2 +(C
4
) 2 –(R
2
) 2 = 0
(2.3.1-10)
But when considering