User's Manual

PMAC User Manual
Writing Programs for PMAC 181
384
4
R
3
R384
4
T
4
V
E
θ
==
where V is the vector velocity, T is the segment time, R is the local radius of curvature, and
θ is the
subtended angle.
Splined Moves
PMAC can perform two types of cubic splines (cubic in terms of the position vs time equations) to blend
together a series of points on an axis. Its SPLINE1 mode is a uniform non-rational cubic B-spline and its
SPLINE2 mode is a non-uniform non-rational cubic B-spline. It can, of course, do either spline for all of
the axes simultaneously. Splining is particularly suited to odd (non-cartesian) geometries, such as radial
tables and rotary-axis robots, where there are odd axis profile shapes even for regular tip movements.
C
i
R
i
V
i
P
i
V
X
i
V
Y
i
P
i-1
R
i+1
C
i+1
P
i+1
P
i+2
P
i+3
C
i+2
V
i+2
R
i+2
V
i+1
4
To compute axis velocities at point P :
1. Find common center of P , P , P
2. Compute velocity vector as normal
to radius vector
3. Resolve velocity vector into components
i
i-1 i i+1
Figure 34 PVT Segment Shapes
TA
P
V =
c
TA
(added)
TA
(added)
TA TA TA TA
No velocity or acceleration
discontinuities at segment
boundaries
If segment were
done at constant
velocity:
VEL
TIME
etc.
etc.
INCREMENTAL
SPLINE
TA500
X10000
X9000
X10500
X12000
Figure 35 Splined Moves (All Segments at Same Time)