Elmomc Multi-Axis Motion Controller-Maestro Motion Contro Manual do Utilizador descarregar pdf (Página 30)

Motion Library Tutorial Switch Radius Calculation

MAN-MLT (Ver 2.0)

2-9

The length of the perpendicular h should also be calculated. By knowing the line equation

in a form

Ax + By + C = 0 (2.2.1.1-3)

then

h can be calculated by

h = |AX

+ BY

+ C|/(A

+ B

)

1/2

(2.2.1.1-4)

If line

L is defined by its starting point (X

) and end point (X

), coefficients

A,B,C can be calculated by formulas in Appendix 2 or Appendix 1.

To define

r we can use an equation

(R – r)

= (h + r)

(2.2.1.1-5)

– 2Rr + r

= h

+ 2hr + r

+ u

(2.2.1.1-6)

max

= (R

– h

– u

)/(2R + 2h) (2.2.1.1-7)

This means that the parameter vsr that defines switch arc radius must obey the following

constraints:

(vse)

/vac

< vsr < (R

– h

– u

)/(2R + 2h)

(2.2.1.1-8)

The switch arc with parameter vsr calculated by (2.2.1.1-7) takes up the whole line segment.

To satisfy additional requirement that switch arc cannot take more than 50% of the segment

length instead of the line end point we should use in calculations some other point

′

that

belongs to the line segment. The distance between this point and the intersection point

2 =

ρ(P

) must be equal k*l (where k < 0.5 , l – the length of the line). If the distance from the

intersection point Pi to P

is defined as ρ(P

), then (2.2.1.1-7) can be presented as a

function of the used partial length k*l of the line L.

max

= [R

– h

– (ρ(P

) – k*l)

]/(2R + 2h)

(2.2.1.1-9)

Example 2-4

(Motion Mathematic Lib Samples\Circle to Line\ Section 2_2_1_1\

CircleLine_Ex_2_4 – www.elmomc.com)

Circle arc (Figure 2-4) is defined by its init position X

from

= 0, Y

from

= 0, radius R = 100000,

init angle α = –90

(with axis X positive direction), and sweep angle = +60

. Line end

point X

= 25000, Y

= 50000. Circle end point [Xc + Rcos(-30), Yc + Rsin(-30)] = (86603,

50000) so the line L is parallel to the axis X. From Figure 2-4, h = 50000, u = 25000. The

switch radius is calculated by (2.2.1.1-7).

r = 0.5*(100000

– 50000

– 25000

)/(100000 + 50000) = 22917

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