AMCI SMD34K, User Manual

Page: 48 / 100

C
ALCULATING
M
OVE
P
ROFILES
SMD34K User Manual
ADVANCED MICRO CONTROLS INC.
48
S-Curve Acceleration Equations (continued)
Determining Waveforms by Values
If your programmed acceleration and deceleration values are the same, then your move’s acceleration and
decelerations will be identical. If these two programmed values are different, use the above methods to deter-
mine the Acceleration Jerk parameter for either the move’s acceleration or deceleration phases and use the
following calculations to determine the shape of the other phase.
Two examples are given below. Both assume a change in speed between the Starting Speed and Programmed
Speed of 30,000 steps/sec and an acceleration of 58,000 steps/sec
2
. The first example uses an Acceleration
Jerk parameter value of 20 and the second a value of 400.
Triangular or Trapezoidal S-curve accelerations are always symmetrical. We’ll use this fact to calculate the
profile up to one-half of the change in speed. At that point, doubling the time and distance will yield the total
time and distance traveled.
Example 1, Jerk = 20
Because a
f
is less than or equal to the programmed acceleration of 58,000 steps/sec
2
, the resulting accelera-
tion is a Triangular S-curve. Total time to accelerate is twice the value calculated above, or 3.216 seconds.
S
m
30,000 steps/sec
2
--------------------------------------- 15,000 steps/sec = = S
m
= midpoint of change in speed
J
100 j
a
-----------
j
Ja
100
--------- =

=
J Acceleration Jerk parameter =
j physical jerk property =
a
f
calculated final acceleration =
j
20 58,000 steps/sec²
 
100
---------------------------------------------------- =
j 11,600 steps/sec³ =
Just as displacement
1
2
---
at
2
, Speed
1
2
---
jt
2
= =
15,000 steps/sec
11,600 steps/sec³ t
2
 
2
-------------------------------------------------- =
t
2
15,000 steps/sec
5,800 stesp/sec³
--------------------------------------- =
t 1.608 seconds =
Just as speed = at, acceleration = jt
a
f
11,600 steps/sec³ 1.608 sec
 
=
a
f
18,655 steps/sec² =