ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 47)

Motion Library Tutorial Switch Radius Calculation
MAN-MLT (Ver 2.0)
2-26
or
rd = hd – hR – hr
(2.2.3.1-3)
and for
r
the result is
r = h(d – R)/(d + h )
(2.2.3.1-4)
Example 2-24
( Motion Mathematic Lib Samples \Circle to Line\ Section 2_2_3_1\
CircleLine_Ex_2_24 – www.elmomc.com)
The circle is defined by its radius R = 50000, init angle
α =
45
o and sweep angle
β= -45 o
and the init point (35355, 35355). The line
L
end point is (80000, 80000). The circle end
angle =
0 o
, so the line init point coordinates (50000, 0). For the coefficients A, B, C in the line
standard equation Ax + By + C = 0,
A = -(Y2 - Y1) = -0 + 80000 = 80000 , B = X2 - X1 = 80000 – 50000 = 30000,
C = X1(Y2 - Y1) - Y1(X2 - X1) = 50000(80000 – 0) – 0 = 4000000000 . The length of
h
can be calculated as:
h = |C|/(A 2 + B 2 ) 1/2 = 4000000000/(80000*80000 + 30000*30000) 1/2 = 46816.5
The length
h
of the perpendicular can be also calculated by formulas (a.16),(a1.4) and (a.17)
from Appendix1 (this approach is used in the sample program CircLine_ex_3_13a).
β = 45 o = π /4 = 0.785398, γ = arccos(h/R) = arccos (46816.5/50000) =
0.358768.
λ = β + γ = 0.785398 + 0.358768 = 1.144166.
d = h/cos(λ)
= 46816.5/cos( 1.144166) = 113136 and the for the switch radius:
r
max
= h(d – R)/(d + h) = 46816.5(113136-50000)/(113136 + 46816.5) = 18479