Β < 0 (β < 0, α < φ), Β > 0, α > φ, Γ = arccos(h/r) – ElmoMC Multi-Axis Motion Controller-Maestro Motion Control User Manual

Page 46: Λ = θ + γ = θ + arccos(h/r), D = ρ(o, H/cos(λ), R/h = (d – r – r)/d

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Motion Library Tutorial

Switch Radius Calculation

MAN-MLT (Ver 2.0)

2-25

1. Circle init radius intersects with the line

L

continued in its positive direction

(Figure 2-23);

2. Line

L

is

parallel to the init radius (Figure 2-25);

3. Line

L

continued in the reverse direction intersects init radius (Figure 2-26) (by

the init radius there a line segment that connects the circle arc center with the
circle arc init point).

2.2.3.1 Line L and init radius continued in their positive
intersecting directions

The init circle radius continuing in its positive direction intersects with the line

L

continued

in its positive direction (Figure 2-23). It takes place if the circle arc init angle with the axis

X

positive direction

α

is less than the line

L

angle with the axis

X

positive direction

φ

and the

circle arc sweep angle

β < 0 (β < 0, α < φ)

or in case:

β > 0, α > φ.

Figure

2-23

Drop a perpendicular from the circle center

O

c

on the line

L.

Its length

h

can be

calculated by (2.2.1.1-4). Now calculate the angle

γ = arccos(h/R),

where

R –

circle

arc radius. The circle arc sweep angle

θ

so

λ = θ + γ = θ + arccos(h/R).

Now calculate the distance

d = ρ(O

c

, P

2

) = h/cos(λ)

(2.2.3.1-1)

To define the switch radius

r,

use a proportion

r/h = (d – R – r)/d

(2.2.3.1-2)

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