ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 50)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-29
3. Know trajectory init point
P
2
(X
2
,Y
2
)
, calculate
ρ
2
= ρ(p
2
, p
1
) =
[(X
2
– X
1
) 2 + (Y
2
– Y
1
) 2 ] 1/2
4. Drop a perpendicular from the circle center O
c
on the line
L
and calculate its
length h by (2.2.1.1-4)
5. To get switch arc radius, use a proportion
ρ
1/(
ρ
2
+ r) = h/r
or
(2.2.3.3-1)
ρ
1
r = hρ
2
+ hr
(2.2.3.3-2)
and finally the value for
r
is:
r = hρ
2
/(ρ
1
- h)
(2.2.3.3-3)
Figure 2-25
Example 2-27
( Motion Mathematic Lib Samples \Circle to Line\ Section 2_2_3_3\
CircleLine_Ex_2_27 – www.elmomc.com)
The circle arc is defined by its radius R = 40000, init angle α = 30 o and sweep angle β = -30 o ,
init point (34641, 20000) – Figure 2-27.
Line L target point (130000, 25000).
Coordinates of the circle center O
c
: X
c
= 34641 – 40000cos(π/6) = 0, Y
c
= 20000 –
40000sin(π/6) = 0;
Define the coordinates of the intersection point P
1
(X
1
, Y
1
). For X
1
and Y
1
, use expressions