ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 22)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-1
Chapter 2: Switch Radius Calculation
2.1 Line – line intersection
If a trajectory contains a switch from line
L
1
to line
L
2
with non-zero velocity, the direction
of the vector velocity cannot be changed at the one intersection point. To implement such a
switch, insert into a trajectory an additional element – circle arc is inserted into a trajectory
(see-Figure 2-1).
The switch arc radius must satisfy (1-1).
Figure 2-1
In the case of a line-line intersection, parameters
r
and
d
are connected by the simple
equation
r = d*tg(γ/2)
(2.1-1
where
γ = π – α (α
- angle between vectors
L
1
and
L
2
) so the pre-defined parameter
vsd = d
must satisfy
vsd ≥ (V
end
) 2 /[AC
v
tg(γ/2)]
(2.1-2)
If ΔL1 is the length of the line L1 and ΔL2 is the length of the line L2, then there is an evident
geometric constraint for the switch radius r
r
max
≤ min(ΔL
1
, ΔL
2
)*tg(γ/2)
(2.1-3)
In fact, due to additional limitations (50% of the segment length) used in ML, the following
should be used