ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 43)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-22
Figure 2-18
so an equation can be written
(R – r) 2 – (ρ
1
– r) 2 = (ρ
3
) 2 (2.2.2.1.2-2)
that produces for
r
r = [R
2
– (ρ
3
)
2
– (ρ
1
)
2
]/(2R – 2ρ
1
) (2.2.2.1.2-3)
2.2.2.2 Initial circle center and switch arc center belong to two
half planes defined by the line L.
2.2.2.2.1 Line continues outside the circle (Figure 2-19)
In this case
ρ
3
= ρ[(X
p
,Y
p
),(Xi,Yi)] + d
(2.2.2.2.1-1)
Equation for r
(ρ
1
+ r)
2
= (R + r)
2
– (ρ
3
)
2 (2.2.2.2.1-2)
From (2.2.2.2.1-2) we have
r = [(ρ
1
)
2
+ (ρ
3
)
2
– R
2
]/(2R – 2ρ
1
) (2.2.2.2.1-3)
2.2.2.2.2 Line continues inside the circle (Figure 2-20)
ρ
3
= ρ[(X
p
,Y
p
),(Xi,Yi)] – d (2.2.2.2.2-1)
Equation for r
(R – r)
2
– (ρ
3
)
2
= (ρ
1
+ r)
2 (2.2.2.2.2-2)