Siemens SIMOTION

Basics of Path Interpolation
2.5 Path interpolation types
TO Path Interpolation
28 Function Manual, 11/2010
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
0
+ A
1
• p + A
2
• p
2
+ A
3
• p
3
+ A
4
• p
4
+ A
5
• p
5
, p ∈ [0,1]
● vector1: A
2
● vector2: A
3
● vector3: A
4
● vector4: A
5
● A
0
and A
1
result from the start point and end point, and the predefined coefficients. For
the parameter area indicated above, this means:
– A
0
= start point
– A
1
= end point - start point - A
2
- A
3
- A
4
- A
5
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:
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Figure 2-18 Example of a polynomial path with explicit specification of the starting point data
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.