ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 38)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-17
2.2.1.3 Line intersects the center of the circle
Consider the last case of the circle – line intersection: the line goes inside the circle
through the center of the circle (Figure 2-12-2-15). The following cases are possible:
a) The length of the line
ΔL
is greater than the circle radius R and the circle diameter
orthogonal to the line intersects the circle arc: P
1
∈
C
1
(Figure 2-12). In this case an
evident geometric constraint on the switch arc radius is
r ≤ R/2 (2.2.1.3-1)
Figure 2-12
b) The length of the line
ΔL
is less than the circle radius R and a perpendicular at the
line end point intersects the circle arc: P
1
∈
C
1
(Figure 2-13). To define the
geometric limit for the switch radius r, use the following equation:
(R – r)
2
= (R – ΔL)
2
+ r
2
(2.2.1.3-2)
or
– 2Rr = – 2RΔL + ΔL
2
that leads to
r = (2RΔL – ΔL
2
)/2R = ΔL – ΔL
2
/(2R) (2.2.1.3-3)