Delta Tau GEO BRICK LV User Manual
Turbo PMAC User Manual
290
Writing and Executing Motion Programs
Turbo PMAC computes intermediate “way-points” WP
i
for each axis for each point along the spline by
taking a weighted average of the specified point P
i
and the specified points on either side. For the
uniform spline, this is done according to the equation:
6
1
i
P
i
P
4
1
i
P
i
WP
+
+
+
−
=
Turbo PMAC also computes the velocity V
i
for each axis at each way-point along the spline. In the
uniform spline, it does this by taking the velocity halfway between the average velocities of the segments
on either side of the way point:
on either side of the way point:
(
) (
)
T
2
1
i
P
1
i
P
T
2
1
i
P
i
P
i
P
1
i
P
i
V
−
−
+
=
−
−
+
−
+
=
Similar calculations are done for the non-uniform spline.
Having computed exact positions and velocities at segment boundaries, Turbo PMAC calculates the
unique cubic position equation (parabolic velocity profile) that meets these constraints, and uses this
equation for interpolation.
Having computed exact positions and velocities at segment boundaries, Turbo PMAC calculates the
unique cubic position equation (parabolic velocity profile) that meets these constraints, and uses this
equation for interpolation.
Added Pieces
At the beginning and end of a series of splined moves, Turbo PMAC automatically adds a zero-distance
segment of the same segment time for each axis, and performs the spline between this segment and the
adjacent one. This results in S-curve acceleration to and from a stop.
segment of the same segment time for each axis, and performs the spline between this segment and the
adjacent one. This results in S-curve acceleration to and from a stop.
Quantifying the Position Adjustment
The difference between the splined commanded position and the pre-splined (program-line) commanded
position for an axis at the end of segment i in the uniform spline can be calculated according to the simple
equation:
position for an axis at the end of segment i in the uniform spline can be calculated according to the simple
equation:
6
i
Dist
1
i
Dist
i
Diff
−
+
=
where Dist
i
is the programmed distance for segment i of the spline (whether in absolute or incremental
mode), and Dist
i+1
is the programmed distance for segment i+1.
5-Point Spline Correction
In contouring applications, it is often desired to pass through the series of points as closely as possible. In
these applications, the error introduced by the standard spline algorithm may be too large to tolerate.
However, in the uniform spline, a simple pre-compensation can reduce the splining errors dramatically.
For each point P
these applications, the error introduced by the standard spline algorithm may be too large to tolerate.
However, in the uniform spline, a simple pre-compensation can reduce the splining errors dramatically.
For each point P
i
in the spline, replace with a point P’
i
with the following formula before sending to
Turbo PMAC:
6
1
i
P
i
P
8
1
i
P
i'
P
+
−
+
−
−
=
Non-Uniform Spline
Turbo PMAC’s SPLINE2 mode is similar to the SPLINE1 mode, except that the requirement that the
TA spline segment time remain constant is removed. The removal of this constraint makes the SPLINE2
mode a non-uniform non-rational cubic B-spline, whereas the SPLINE1 mode is a uniform non-rational
cubic B-spline. The “non-rational” specification indicates that there are no independent weightings
(ratios) of the different points in the spline.
TA spline segment time remain constant is removed. The removal of this constraint makes the SPLINE2
mode a non-uniform non-rational cubic B-spline, whereas the SPLINE1 mode is a uniform non-rational
cubic B-spline. The “non-rational” specification indicates that there are no independent weightings
(ratios) of the different points in the spline.
The added segment at the beginning of a spline has the same time as the first programmed segment; the
added segment at the end of a spline has the same time as the last programmed segment.
added segment at the end of a spline has the same time as the last programmed segment.
The combined time of any three consecutive segments in a SPLINE2 continuous spline must be less than
8,388,608 msec, or about 2 hours and 20 minutes.
8,388,608 msec, or about 2 hours and 20 minutes.