ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 36)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-15
Figure 2-9
Projection of the circle arc init point
P
1
on the line
L
does not belong to the line segment
L.
If a projection of the circle arc init point
P
1
on the line
L
does not belong to the line
segment
L (
Figure 2-10), calculate the maximum switch radius
r
using equation
ρ 2
(O
c
,P
5
) + (r – h)
2
= (R – r)
2
(2.2.1.2-4)
or
(ρ
1
)
2
+ (r – h)
2
= (R – r)
2
(2.2.1.2-5)
(ρ
1
)
2
+ r
2
– 2rh + h
2
= R
2
– 2Rr + r
2
(2.2.1.2-6)
R
2
– (ρ
1
)
2
– h
2
= 2Rr – 2rh (2.2.1.2-7)
The results for
r
r
=
[R
2
– (ρ
1
)
2
– h
2
]/(2R – 2h) (2.2.1.2-8)
To define
ρ(O
c
,P
5
),
drop a perpendicular from the circle center
O
c
on the line
L.
The
distance from the projection point
P
4
to the line end point
P
3
is equal to
ρ(O
c
,P
5
).
As well as in case when the circle and switch arc centers belong to different half planes
values calculated by (2.2.1.2-3) and (2.2.1.2-8) are not recommended but limiting ones.
Switch radius in use must be less those values.