Polynomial Path - Direct Specification Of The Polynomial Coefficients; Polynomial Paths - Explicit Specification Of The Starting Point Data - Siemens SIMOTION Function Manual

Basics of Path Interpolation
2.5 Path interpolation types
2.5.5.2

Polynomial path - direct specification of the polynomial coefficients

For the polynomial specification using (polynomialMode:=SETTING_OF_COEFFICIENTS() )
polynomial coefficients, the polynomial path is determined using a function of the fifth
degree:
P = A
● vector1: A
● vector2: A
● vector3: A
● vector4: A
● A
2.5.5.3

Polynomial paths - explicit specification of the starting point data

For the polynomialMode:=SPECIFIC_START_DATA setting and the explicit specification of
the starting point data, the two geometric derivatives at the start point must also be specified
for the derivatives at the end point of the polynomial.
The derivatives must be specified as follows:
● vector1: First geometric derivative/tangential vector in start point
● vector2: Second geometric derivative/curvature vector in start point
● vector3: First geometric derivative/tangential vector in end point
● vector4: Second geometric derivative/curvature vector in end point
Example of a polynomial path with explicit specification of the starting point data
This example connects a linear path and a circular path:
Figure 2-18
The two derivatives in the starting point of the polynomial must be calculated first. The
_getLinearPathGeometricData() function used for this purpose calculates the two derivatives
for the end point of the straight line (starting point of the polynomial) using the coordinates of
the straight line.
28
+ A • p + A • p + A
2
0 1 2
2
3
4
5
and A result from the start point and end point, and the predefined coefficients. For
0 1
the parameter area indicated above, this means:
– A = start point
0
– A = end point - start point - A
1
Example of a polynomial path with explicit specification of the starting point data
• p + A • p + A • p
3 4 5
3 4 5
- A - A - A
2 3 4 5
, p ∈ [0,1]
Function Manual, 11/2010
TO Path Interpolation