ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 51)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-30
By (a3.6)-(a3.7) from Appendix 3.
q
1
= ΔX
1
/ΔY
1
= (34641-0)/(20000-0) = 1.73205
Y
1
= ((q
1
*Y
1
+ X
21
– X
11
)*ΔY
2
–Y
21
ΔX
2
)/(q
1
*ΔY
2
– ΔX
2
) =
((1.73205*0 + 40000 –0)*(25000-0) - 0)/( 1.73205*(25000-0) - (130000-40000)) =
-21414X
1
= X
11
+ q
1
(Y
1
– Y
11
) = X1 = 0 + 1.73205(-21414- 0) = -37090
To get the length of the perpendicular h from the circle center on the line L, line L is needed.
Figure 2-26
standard equation in a form Ax + By + C = 0. For A,B,C we have
A = -(Y
22
– Y
21
) = 25000, B = 130000 – 40000 = 90000, C =
C = X
21
(Y
2
– Y
21
) - Y
1
(X
22
– X
21
) = 40000(25000-0) = 10 9 .
h = (0*25000 + 0*90000 + 10 9 )/( 25000 2 + 90000 2 ) 1/2 = 10706 ρ
1
= [(-37090) 2 + (-
21414) 2 ] 1/2 = 42828
ρ
2
= [(-37090 – 34641) 2 + -21414– 20000) 2 ] 1/2 =82828
and for maximum switch radius we get
r = hρ
2
/(ρ
1
– h) = 10706*82828/(42828– 10706) = 27605
2.3 Circle – circle intersection
Note:
C
1
– first circle arc,
C
2
– second circle arc,
P
i
– point of two circle arcs intersection,
C
o1
– first circle center point,
C
o2
– second circle center point.