ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 49)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-28
Figure 2-25b
Maximum switch radius is perpendicular to the line L at the line end point.
h
– the length of
the perpendicular dropped from the circle center on the line. We can calculate an angle
γ
between the perpendicular at the line end point and the line that connect the centers of the
init circle and a switch arc
γ = 180 – 90 – (180 – θ) = θ – 90
(2.2.3.2-1)
To define max switch radius we can use an equation
(R + r)cosγ = r + h (2.2.3.2-1)
that produces
r = (Rcosγ – h)/(1 – cosγ)
(2.2.3.2-1)
2.2.3.3 Line L and init radius continued in their reverse
directions intersect
This case is shown in Figure 2-26.
1. Find the coordinates
P
1
(X
1
,Y
1
)
– intersection point of two lines init circle radius
(O
c
,P
2
)
and a line
L
.
2. Knowing the coordinates of circle arc center
O
c
(X
c
,Y
c
)
and intersection point
P
1
(X
1
,Y
1
)
makes
ρ
1
= ρ(P
1
,O
c
) = [(X
1
- X
c
) 2 + (Y
1
- Y
c
) 2 ] 1/2
known
.