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Introduction 17
Calculating Jerk
V
2
A
(Programmed Accel)
V
(Programmed Velocity)
V
1
t
1
t
2
t
3
Zero Velocity
Zero Acceleration
Ø
(zero)
A B C
Rules of Motion:
Jerk
dt
da
=
a
dt
dv
=
v
dt
dx
=
(x = distance)
Assuming the accel profile starts
when the load is at zero velocity and
the ramp to the programmed velocity
is not compromised:
A
2
* AA
V (A-AA)
Jerk = J
A
=
A = programmed acceleration
(
A
,
AD
,
HOMAD
, etc.)
AA = average acceleration
(
AA
,
ADA
,
HOMAA
, etc.)
V = programmed velocity
(
V
,
HOMV
, etc.)
A
J
A
t
1
=
V
AA
-
t
2
=
A
J
A
V
AA
t
3
=
NOTE: t
3
- t
2
= t
1
2
J
A
* t
1
2
V
1
=
2 * J
A
A
2
=
V
2
= V -
2 * J
A
A
2
A
t
1
≥
t
≥
Ø
a (t) = J
A
* t
2
J
A
* t
2
v (t) =
6
J
A
* t
3
d (t) =
B
t
2
≥
t > t
1
a (t) = A
2J
A
A
2
v (t) = + A * (t - t
1
)
6
J
A
* t
1
3
d (t) = + + V
1
* (t - t
1
)
2
A * (t - t
1
)
2
C
t
3
≥
t > t
2
a (t) = A - (J
A
* (t - t
2
))
v (t) = V -
2
J
A
* (t
3
- t)
2
2AA
V
2
d (t) = + - V * (t
3
- t)
6
J
A
(t
3
- t)
3
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 “
(VF
-
VO)
” for “
V
”
( VF = final velocity, VO = initial velocity). This is shown in the jerk equation (right).
A
2
* AA
(V
F
-
V
O
) (A-AA)
Jerk = J
A
=
a (t) = acceleration at time t
v (t) = velocity at time t
d (t) = distance at time t
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