Elmomc Multi-Axis Motion Controller-Maestro Motion Contro Bedienungsanleitung PDF herunterladen (Seite 38)

Motion Library Tutorial Switch Radius Calculation

MAN-MLT (Ver 2.0)

2-17

2.2.1.3 Line intersects the center of the circle

Consider the last case of the circle – line intersection: the line goes inside the circle

through the center of the circle (Figure 2-12-2-15). The following cases are possible:

a) The length of the line

ΔL is greater than the circle radius R and the circle diameter

orthogonal to the line intersects the circle arc:

∈

(Figure 2-12). In this case an

evident geometric constraint on the switch arc radius is

r ≤ R/2 (2.2.1.3-1)

Figure

2-12

b) The length of the line

ΔL is less than the circle radius R and a perpendicular at the

line end point intersects the circle arc:

∈

(Figure 2-13). To define the

geometric limit for the switch radius

r, use the following equation:

(R – r)

= (R – ΔL)

+ r

(2.2.1.3-2)

– 2Rr = – 2RΔL + ΔL

that leads to

r = (2RΔL – ΔL

)/2R = ΔL – ΔL

/(2R) (2.2.1.3-3)

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Elmomc Multi-Axis Motion Controller-Maestro Motion Contro Bedienungsanleitung Seite 38