ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 29)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-8
Yp = Yc + K*(Xp – Xc) = 0 +0.7*(-46979 - 0) = -32885
And the perpendicular length
h = [(Xc – Xp) 2 + (Yc - Yp) 2 ] 1/2 = [(0 + 46979) 2 + (0 + 32885) 2 ] 1/2 = 57345
Max switch radius calculated by (2.2.1.1-1)
Rmax = (R – h)/2 = (100000 – 57345)/2 = 21328
Rmin = 100000 2 /(2800000*0.9) = 396.8
As a switch radius we can take any value Rswitch that satisfies
Rmin < Rswitch < Rmax
We take Rswitch = (Rmin + Rmax)/2 = (21328 + 396.8)/2 = 10862
In Figures 2-3 and 2-5, two possible cases are presented when the projection of the circle
center on the line
L
does not belong to the line segment.
In Figure 2-3, perpendicular at the Line
L
end point
P
2
intersects with the circle
C
at point
P
3
that belongs to the circle arc
P
3
∈
C.
In Figure 2-3, observe the switch arc with the
maximum possible radius
r.
This limit value can be calculated.
Figure 2-3
Since the coordinates of point P
1
(X
1
,Y
1
) – projection of the circle center point
O(X
c
,Y
c
) on line L and line end point P
2
(X
2
,Y
2
) are known, the distance is
ρ(P
1
,P
2
) = u = [(X
2
– X
1
)
2
+ (Y
2
– Y
1
)
2
]
1/2
(2.2.1.1-2)