ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 45)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-24
2.2.2.3 Circle center (Xc,Yc) Є L1 (line L1 intersects the center of
the circle)
2.2.2.3.1 Line goes outside of the circle (Figure 2.11).
An equation for r
(R + r)2 = (R + d)2 + r2 (2.2.2.3.1-1)
r = (2Rd + d2)/(2R) (2.2.2.3.1-2)
2.2.2.3.2 Line goes inside the circle (Figure 2.12)
(R – r)2 = (R – d)2 + r2 (2.2.2.3.2-1)
r = (2Rd – d2)/(2R ) (2.2.2.3.2-2)
Figure 2-22
2.2.3 Line goes outside the circle
If the line goes outside of the circle, the switch arc radius is limited by the length of the line
segment and the length of the circle arc segment. The connection between the switch arc
radius and distance
d
between intersection point and a last point of the switch arc on the
line
L
was considered in section 3.2. The maximum switch radius for the given line
segment
ΔL
can be calculated by formulas (2.2.2.1.1-5) or (2.2.2.2.1-3) from 2.2.2.1.1 where
d = ΔL
.
When considering the limitations imposed by the length of the circle arc (defined by the
sweep angle and a circle radius), three cases are possible: