Elmomc Multi-Axis Motion Controller-Maestro Motion Contro Bedienungsanleitung PDF herunterladen (Seite 47)

Motion Library Tutorial Switch Radius Calculation

MAN-MLT (Ver 2.0)

2-26

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

and sweep angle β= -45

and the init point (35355, 35355). The line L end point is (80000, 80000). The circle end

angle =

, 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

+ B

)

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

= 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:

max

= h(d – R)/(d + h) = 46816.5(113136-50000)/(113136 + 46816.5) = 18479

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Elmomc Multi-Axis Motion Controller-Maestro Motion Contro Bedienungsanleitung Seite 47