Elmomc Multi-Axis Motion Controller-Maestro Motion Contro Uživatelský manuál stáhnout pdf (Strana 67)

Appendix A: Projection of a point on a

line defined by the end points

The line L is defined by its end points P

) and P

). Drop a perpendicular

from some point

) on the line L and find coordinates (X

, Y

) of the projection

point and the length of the perpendicular

a) X

= X

= Y

h = |X

– X

b) Y

= Y

= X

= Y

h= |Y

– Y

c) X

≠ X

and Y

≠ Y

Line equation

(X– X

)/(X

– X

) = (Y – Y

)/(Y

– Y

) (a1.1)

That can be transformed into

(Y – Y

)∆X = (X – X

)∆Y

Y = (Y

dX + X∆Y – X

∆Y)/∆X = Y

+ k(X – X

) (a1.2)

Where

k = ∆Y/∆X = (Y

– Y

)/(X

– X

)

An equation of the perpendicular dropped from (Xo,Yo) on L can be written in a form

(Y - Y

) = (-1/k)(X – X

) = q(X – X

) (a1.3)

Y = Y

+ q(X – X

) (a1.4)

Substituting (a1.4) into (a1.2) the results are

Yo + q(X – Xo) = Y

+ k(X – X

) (a1.5)

That produces for X coordinate

X = (Y

– Y

+ kX

– qX

)/(k – q) (a1.6)

Maestro Software Manual

MAN-MLT(Ver. 2.0)

A-1

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