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Calculating Jerk
Zero Acceleration
Zero Velocity
Ø
t
1
(zero)
A
A
t
=
1
J
A
V
A
-
t
=
2
AA
J
A
V
t
=
3
AA
NOTE: t
- t
= t
3
2
1
2
J
* t
A
1
V
=
=
1
2
2 * J
2
A
V
= V -
2
2 * J
A
Starting at a Non-Zero Velocity: If starting the acceleration profile with a non-zero
initial velocity, the move comprises two components: a constant velocity component, and
an s-curve component. Typically, the change of velocity should be used in the S-curve
calculations. Thus, in the calculations above, you would substitute "(V F - V O )" for "V"
(V F = final velocity, V O = initial velocity). This is shown in the jerk equation (right).
A
(Programmed Accel)
V
(Programmed Velocity)
V
2
V
1
t
t
2
3
B
C
≥ t ≥ Ø
A
t
1
≥ t > t
B
t
2
2
A
A
≥ t > t
C
t
3
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Rules of Motion:
=
Jerk
dv
=
a
dt
dx
=
v
dt
Assuming the accel profile starts
when the load is at zero velocity and
the ramp to the programmed velocity
is not compromised:
Jerk = J
=
A
A
= programmed acceleration
(A, AD, HOMAD, etc.)
AA = average acceleration
(AA, ADA, HOMAA, etc.)
V
= programmed velocity
(V, HOMV, etc.)
a (t) = J
* t
A
2
J
* t
A
v (t) =
2
3
J
* t
A
d (t) =
6
a (t) = A
1
2
A
v (t) =
+ A * (t - t
2J
A
3
J
* t
A * (t - t
A
1
d (t) =
+
6
a (t) = A - (J
* (t - t
A
2
2
J
* (t
- t)
A
3
v (t) = V -
2
2
V
J
(t
A
d (t) =
+
2AA
Jerk = J
Introduction
da
dt
(x = distance)
2
A
* AA
V (A-AA)
a (t) = acceleration at time t
v (t) = velocity at time t
d (t) = distance at time t
)
1
2
)
1
+ V
* (t - t
)
1
1
2
))
2
3
- t)
3
- V * (t
- t)
3
6
2
A
* AA
=
A
(V
- V
) (A-AA)
F
O
17
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