Elmomc Multi-Axis Motion Controller-Maestro Motion Contro Uživatelský manuál stáhnout pdf (Strana 40)

Motion Library Tutorial Switch Radius Calculation

MAN-MLT (Ver 2.0)

2-19

c) The circle arc sweeps an angle less than 90

and a perpendicular dropped from the

circle init point

on the line L intersects line segment at point P

∈

(Figure 2-

15). A projection of the circle init point

)

on the line L – point P

)

and the length of the segment defined by the line init point

and projection point

: ρ

= ρ(P

) can be determined. Now calculate the maximum switch radius

with the use of the following equation:

(R – r)

= (R – ρ

)

+ r

(2.2.1.3-4)

that leads to

–2Rr = – 2Rρ

+ (ρ

)

and finally

r = [2Rρ

– (ρ

)

]/(2R)

(2.2.1.3-5)

Figure 2-15

Example 2-16

(

Motion Mathematic Lib Samples\Circle to Line\ Section 2_2_1_3\

CircleLine_Ex_2_16 – www.elmomc.com)

The circle (Figure 2-16 ) is defined by its init point P

(0, -80000), radius R = 80000, init angle

α = -90

and sweep angle β =-45

. Coordinates of the line end point (150000,150000).

Circle end point P

(line init point) coordinates are calculated as X

= 80000*cos(pi + pi/4) = -

56569 and

= 80000*sin(pi + pi/4) = -56569

Drop a perpendicular from the circle init point P

on the line L

. To define coordinates of the

projection point P

2 ,

use formulas from the Appendix 1.

k = dY/dX = (150000 + 56569)/ (150000 + 56569) = 1, q = –1/k = –1.

1 2 ... 35 36 37 38 39 40 41 42 43 44 45 ... 71 72

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