Special Motion Commands
4.5 Polynomial interpolation (POLY, POLYPATH, PO, PL)
Job planning
Programming Manual, 07/2010, 6FC5398-2BP40-0BA0
255
Description
The equation used to express the polynomial function is generally as follows:
f(p)= a
0
+ a
1
p + a
2
p
2
+. . . + a
n
p
n
with: a
n
: Constant coefficients
p: Parameter
In the control, polynomials up to a maximum of the 5th degree can be programmed:
f(p)= a
0
+ a
1
p + a
2
p
2
+ a
3
p
3
+ a
4
p
4
+ a
5
p
5
By assigning concrete values to these coefficients, it is possible to generate various curve
shapes such as line, parabola and power functions.
A straight line is generated using a
2
= a
3
= a
4
= a
5
= 0:
f(p) = a
0
+ a
1
p
The following still applies:
a
0:
Axis position at the end of the preceding block
p = PL
a
1
= (x
E
- a
0
- a
2
*p
2
- a
3
*p
3
)/p
It is possible to program polynomials without the polynomial interpolation having been
activated using the G command
POLY. In this case, the programmed polynomials are not
interpolated, but instead, all of the programmed end points of the axis are linearly
approached (
G1). The programmed polynomials are only moved as such as after explicitly
activating polynomial interpolation in the part program (
POLY).
Special feature: Denominator polynomial
Command PO[]=(…) can be used to program a common denominator polynomial for the
geometry axes (without specifying an axis name), i.e., the motion of the geometry axes is
then interpolated as the quotient of two polynomials.
With this programming option, it is possible to represent forms such as conics (circle, ellipse,
parabola, hyperbola) exactly.
Example:
Program code Comment
POLY G90 X10 Y0 F100 ; Geometry axes traverse linearly to
position X10 Y0.
PO[X]=(0,–10) PO[Y]=(10) PO[]=(2,1) ; Geometry axes traverse along the
quadrant to X0 Y10.
The constant coefficient (a
0
) of the denominator polynomial is always assumed to be 1. The
programmed end point is independent of
G90 / G91.
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