2 line continues inside the circle (figure 2-18), Ρ[(x, R + r) – ElmoMC Multi-Axis Motion Controller-Maestro Motion Control User Manual
Page 42: R = [(ρ, 2r + 2ρ
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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
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