Gemini GV6K and Gemini GT6K Programmer's Guide

Calculating Jerk
Zero Acceleration
A
(Programmed Accel)
Rules of Motion:
da
Jerk =
dt
dv
a =
dt
dx
v = (x = distance)
dt
V 2
V
(Programmed Velocity)
Assuming the accel profile starts
when the load is at zero velocity and
the ramp to the programmed velocity
is not compromised:
Zero Velocity
Ø
(zero)
V 1
t 1 t 2 t 3
A B C
Jerk = J A =
A 2 * AA
V (A-AA)
A = programmed acceleration
(A, AD, HOMAD, etc.)
AA = average acceleration
(AA, ADA, HOMAA, etc.)
V = programmed velocity
(V, HOMV, etc.)
A
A
t 1 =
t1 ≥ t ≥ Ø a (t) = J A * t
a (t) = acceleration at time t
v (t) = velocity at time t
J A
J A * t 2 d (t) = distance at time t
v (t) =
V A
2
t 2 = -
AA J A
J A * t 3
d (t) =
V
6
V 2 = V -
A 2
2 * J A
C t3 ≥ t > t2 a (t) = A - (J A * (t - t 2 ))
t 3 =
AA
NOTE: t 3 - t 2 = t 1
B t2 ≥ t > t1 a (t) = A
A 2
v (t) =
2J A
+ A * (t - t 1 )
V 1 =
2
J A * t 1 A 2
3
J A * t 1 A * (t - t 1 ) 2
=
d (t) = +
2 2 * J
6
2
A
+ V 1 * (t - t 1 )
J A * (t 3 - t) 2
2
v (t) = V -
V 2 J A (t 3 - t) 3
d (t) =
2AA
+
6
- V * (t 3 - t)
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). For example, the jerk equation would be:
Jerk = J A =
A 2 * AA
(V F - V O ) (A-AA)
138 Gem6K Series Programmer’s Guide