Elmomc Multi-Axis Motion Controller-Maestro Motion Contro Instrukcja Użytkownika Pobierz pdf (Strona 52)

Motion Library Tutorial Switch Radius Calculation

MAN-MLT (Ver 2.0)

2-31

2.3.1 One of two circle arcs intersects the internal area of

the second

If the circle arc C

comes from inside of the circle C

– Figure 2-28 (or circle C

continues

inside the circle

), then the switch arc radius must satisfy the necessary condition

r ≤ (R

+ h)/2

(2.3.1-1)

where h = ρ(O

) – distance from the circle C

center O

to the intersection point

) of the line O

connecting the centers of two circles with the circle arc C

(Figure 2-28). Condition (2.3.1-1) is not always sufficient– only in cases that the points of

intersection

with C

and C

belong to C

and C

: P

)

∈

and

)

∈

(Figure 2-28).

Figure 2-28

In Figure 2-29 the case when a point of intersection of the line O

does not belong to

the circle arc

is presented. Line O

goes through the circle C

center O

and its

init point

). P

) – intersection point of the line O

with

the circle

arc C

(calculation of the circle – line intersection point coordinates can be found in

Appendix 4).

By knowing the coordinates of two points P

and P

, calculate the

distance

d = ρ(P

To define the maximum switch arc radius

r, use the following system of equations:

– X

)/(X

– X

) = r/d (2.3.1-2)

– Y

)/(Y

– Y

) = r/d (2.3.1-3)

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