ICPDAS
I-8092F Software User Manual
100
Partial S-curve Description
Partial S-curve is composed of three segments (1, 2, 3): one straight line and two S-curve
lines. S-curve is the (1), (3) segments for S-curve acceleration, the straight line is (2) segment for
linear acceleration; the total motion time is defined
TA
, and the time of the linear acceleration
is
)
2
(
TS
TA
×
−
. However there is the same acceleration value in the join of the three segments.
Velocity equation of segment (1):
TS
t
t
C
t
V
<
=
,
)
(
2
1
(1-8)
Velocity equation of segment (2):
TS
TA
t
TS
t
C
t
V
−
<
<
=
,
)
(
2
(1-9)
Velocity equation of segment (3):
TA
t
TS
TA
t
TA
C
V
t
V
<
<
−
−
−
=
,
)
(
)
(
2
1
(1-10)
The constant value
2
C
is the slope of the line:
TS
TA
VS
V
C
2
2
2
−
−
=
(1-11)
Boundary condition of the connection for (1), (2):
2
)
(
'
C
TS
V
=
(1-12)
We can find that
))]
2
(
(
[
2
2
1
TS
TA
TS
TS
V
C
−
×
+
=
(1-13)
Fig. A-19 Partial S-curve planning
In case of S-curve acceleration / deceleration driving, the acceleration profile is not linear. The
