4.INTERPOLATION FUNCTIONS PROGRAMMING B-63324EN/03
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4.14 SPLINE INTERPOLATION (G06.1)
Spline interpolation produces a spline curve connecting specified
points. When this function is used, the tool moves along the smooth
curve connecting the points. The spline interpolation command
eliminates the need to approximate the smooth curve with minute
straight lines or arcs. A machining program coded with this command
requires less tape than that including the approximation.
- Spline curve
A spline curve connecting n + 1 points consists of n parametric cubic
curves. The general formula f(t) of the cubic curve is expressed as:
where P is the position vector at a point on the curve, t is a parameter,
and A, B, C, and D are vector coefficients.
The CNC unit performs spline interpolation by calculating the
coefficients according to the specified points and changing t.
- Conditions of specified points
In the spline interpolation mode, two curves joining at a point satisfy
the following conditions at that point. This results in a smooth spline
- The two curves have an identical joining point (specified point).
- The two curves have an identical tangential vector at the joining
point. (The two curves have an identical first-order differential
vector obtained for t.)
- The two curves have an identical curvature at the joining point.
(The two curves have an identical second-order differential vector
obtained for t.)
As the feedrate in spline interpolation mode, specify a tangential
feedrate using the F code.
This tangential feedrate is found in the Cartesian coordinate system
generated by the specified axes. During spline interpolation, the
feedrate component on each axis changes with time. Let Fx, Fy, and Fz
be the feedrate components on the axes at a given point of time. Then,
tangential feedrate F is obtained as follows:
)( FzFyFxF ++=
The following command sets spline interpolation mode:
In the G06.1 block, a tangent vector at the start point can
G06.1 X_ Y_ Z_ ;
X_ : X-axis component of the tangent vector
Y_ : Y-axis component of the tangent vector
Z_ : Z-axis component of the tangent vector