20 Gear Drive, Plymouth Ind. Park, Terryville, CT 06786
Tel: (860) 585-1254 Fax: (860) 584-1973 http://www.amci.com
SMD23E2 and SMD24E2 User’s Manual
C
ALCULATING
M
OVE
P
ROFILES
49
S-Curve Acceleration Equations (continued)
Trapezoidal S-Curve Acceleration (continued)
The value of the Acceleration Jerk parameter can now be easily calculated.
This value represents the ideal Acceleration Jerk parameter value for a trapezoidal S-curve acceleration with
a constant acceleration for half of the phase. Setting the value lower than this will result in a shorter constant
period, while setting the value greater than this will result in a longer constant period.
Another example of a trapezoidal S-curve acceleration is when the linear acceleration occurs for one third of
the time. In this case, the programmed acceleration must be the constant acceleration value multiplied by 3/2
and the Acceleration Jerk parameter must be set to 300/t.
When a
s
= a
c
The above examples assume that you can increase the programmed acceleration value to keep the time of the
acceleration phase the same. If your constant acceleration value is the maximum your system will allow, then
using S-curve accelerations will lengthen the time needed to accelerate to your desired speed.
In the case of trapezoidal S-curve accelerations, calculating the percentage increase in time is shown in figure
R3.6. The time added to the acceleration phase is equal to the time spent increasing the acceleration during
the phase. As shown in the figure, when the Trapezoidal S-curve is programmed to spend 50% of its time at
the programmed acceleration value, the time spent in the acceleration phase will be 133.33% of the time spent
if a constant acceleration were used.
Figure R3.6 Trapezoidal S-curve Time Increase Example
In this case the value of the Acceleration Jerk parameter should be based on the new, longer time. For exam-
ple, assume an equivalent constant acceleration of 15,000 steps/sec
2
that is applied for 2.0 seconds. If the
acceleration value must remain at 15,000 steps/sec
2
, then the acceleration phase will take 2.667 seconds
(2.0
1.333) and the Acceleration Jerk parameter should be set to 150 (400/2.667)
Similarly, if the Trapezoidal S-curve acceleration is to spend 33.3% of its time at constant acceleration, and
the programmed acceleration value cannot be increased, the time spent accelerating will increase by 50% and
the Acceleration Jerk parameter should be adjusted accordingly.
j
a
s
t
4
--------
=
j
a t
=
j
4
a
s
t
--------
=
Ja
s
100
---------
4
a
s
t
--------
=
j
Ja
100
---------
=
Ja
s
t
400
a
s
=
J
400
t
---------
=
Acceleration Jerk Parameter = 400 / acceleration time
t
a = a
c
s
Time
Constant
Acceleration
Trapezoidal S-Curve Acceleration
0.25n + 0.25t
t + n
a (t) = a (.5n +.5t) + a (.25n + .25t)
c
c
c
a (t) = a ((.5n +.5t) + (.25n + .25t))
c
c
t = .75n +.75t
0.25t = .75n
t = 3n
t/3 = n
t+n = t + t/3 = 4/3t = 1.3333t
