Elmomc Multi-Axis Motion Controller-Maestro Motion Contro Instrukcja Użytkownika Pobierz pdf (Strona 60)

Motion Library Tutorial Switch Radius Calculation

MAN-MLT (Ver 2.0)

2-39

2.3.2 Each circle intersects the internal area of the second

Figure 2-33 shows another case of two circles intersecting: circle C

comes from inside of

the circle

and circle C

continues inside the circle C

. Noting that

d = ρ(O

), the switch radius must obey the following necessary condition:

R ≤ [d – (d – R

)

– (d – R

)]/2 = (R

+ R

– d)/2

(2.3.2-1)

Condition (2.3.2-1) is sufficient in case line

intersects circle arc C

and circle arc

Figure 2-33

Line

does not intersect at least one of two circle segments (Figure 2-35)

Another case when line O

does not intersect at least one of the two circle segments. In Figure 2-35 line

, Y

) – (X

, Y

)

connecting two circle centers does not intersect circle arc C

. Draw a line O

between the circle

center and its end point P

). The center (X

, Y

) of the switch arc with a

maximum radius must belong to this line. To define maximum radius

r, use the same system as in the

previous cases.

– X

)/(X

– X

) = r/R

(2.3.2-2)

– Y

)/(Y

– Y

) = r/R

(2.3.2-3)

– X

)

+ (Y

– Y

)

= (R

– r)

(2.3.2-4)

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