User`s manual
Programmed Motion
GFK-1742A Chapter 7 Programmed Motion 7-47
7
Trapezoidal Move
•Limits max motor speed
•Higher accel torque than triangle move
•Symmetrical profile (1/3, 1/3, 1/3 time)
maximizes power transfer to load
•Most common for long moves
Torque
A = acceleration
D = deceleration
X = distance
V
pk
= velocity peak
t
a
= time acceleration
t
s
= time at slew velocity
t
d
= time deceleration
T
a
= acceleration Torque
T
d
= deceleration Torque
X
a
= acceleration distance
X
s
= slew distance
X
d
= deceleration distance
t
a
t
d
V
pk
time
time
T
a
A
A
D
D
X
X
t
s
T
d
Velocity
X
a
X
s
X
d
()
()
t
d
V
D
t
V
a
t
d
tt
x
V
t
d
ttVx
pk
a
pk
sa
pk
sapk
=⇒=
++
=
++=
5.05.0
5.05.0
Equations
Equations
Figure 7-23. Trapezoidal Move
Once the move segment outline is drawn, we need to examine specifications or physical
restrictions applicable to the move. For instance the move may have to complete in a certain time
interval (t
a
+ t
s
+ t
d
) or move a fixed distance (X). The maximum velocity (V
pk
) of the servomotor
is one example of a physical limitation. Given any two known values of the acceleration portion
of the move segment, a remaining variable can be found using the kinematic equations as
illustrated in the example below.
Trapezoidal Velocity Profile Application Example
Let’s assume that a complete move of 16 inches must be made in three seconds and the maximum
motor velocity, translated through the gearing is 15 inches per second. Using our rule of thumb,
we divide the move’s time into thirds: t
a
= 1sec, t
s
= 1sec and t
d
= 1sec. We can also subdivide the
16-inch move into three distances. The slew (X
s
) section of an equally divided trapezoidal
velocity profile represents ½ of the distance moved and the acceleration (X
a
) and deceleration (X
d
)
portions each represent ¼ of the total distance: X
a
=4 in, X
s
=8 in and X
d
=4 in.
To calculate peak Velocity (V
pk
), the first acceleration portion of the move must travel a given
distance (X
a
) in a given time (t
a
). From the above Kinematic Velocity formula (2X/t) using the
given, X
a
=4 inches and t
a
= 1 second, (2*4 inches) / 1 second = 8 inches/second.
To calculate Acceleration the simplest formula is (V/T)=(8 inches/second / 1 second)=8
inches/second/second.
The Position (Distance = X) is the entire distance moved (X
a
+ X
s
+ X
d
) or 16 inches