ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 42)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-21
ρ[(X
p
,Y
p
),(X
1
,Y
1
)] = r
(2.2.2.1.1-2)
The following is known:
ρ
3
= ρ[(X
p
,Y
p
),(X
f
, Y
f
)] = ρ[(X
p
,Y
p
),(X
i
, Y
i
)] + d
(2.2.2.1.1-3)
where (X
i
, Y
i
) – circle-line intersection point .
As
ρ[(X
1
,Y
1
),(X
o
, Y
o
)] = ρ[(X
p
,Y
p
),(X
f
, Y
f
)] = ρ
3
then use an equation to define r
(R + r)
2
– (ρ
3
)
2
= (ρ
1
– r)
2
(2.2.2.1.1-4)
From (2.2.2.1.1-4) for
r
there is
r = [(ρ
3
)
2
+ (ρ
1
)
2
– R
2
]/(2R + 2ρ
1
)
(2.2.2.1.1-5)
2.2.2.1.2 Line continues inside the circle (Figure 2-18)
The following is known:
ρ
3
= ρ[(X
p
,Y
p
),(X
i
,Y
i
)] – d
(2.2.2.1.2-1)
Figure 2-17