User Manual
Chapter 7
GFK-1742F
Jan 2020
Programmed Motion
215
7.7.11
Calculating Acceleration, Velocity and Position Values
One method of determining the value for APM or DSM motion program variables such as
Acceleration, Velocity or Position is to plot the desired move or move segment as a velocity
profile. A velocity profile plots time on the horizontal axis of a graph and velocity on the
vertical axis. The key to understanding profile generation is to break the complete move into
smaller segments that may be analyzed geometrically. Most applications will use the
economical trapezoidal move, velocity profile as illustrated below. To move as quickly as
possible, use a triangular velocity profile if the servo has sufficient speed range. A triangular
move would accelerate half the distance then decelerate the remaining half. Another
alternative is to use a trapezoidal profile with a shorter slew segment.
Kinematic Equations
Kinematics is the branch of mechanics that studies the motion of a body or a system of
bodies without consideration given to its mass or the forces acting on it. The following table
includes transformations of the basic linear equations as applied to the acceleration portion
of motion profiles. Use these formulae to calculate the velocity and acceleration for the
acceleration portions of the move.
Table 50: Linear Equation Transformations
Given
Solve For
A, X
A, V
A, t
V, t
V, X
X, t
Acceleration
V/t
V
2
/2X
2X/t
2
Velocity
At
2X/t
X (Distance)
V
2
/2A
At
2
/2
Vt/2
time
V/A
2X/V
Figure 91 provides an example of a trapezoidal move. Beginning at zero velocity the axis
accelerates in a positive direction (ta), run (slew) at velocity for some time (t
s
), then
decelerate back to zero velocity (td). That’s a complete move or move segment. By looking
at the figure, you can easily separate the different portions of the move. A common rule of
thumb is to divide the trapezoidal move into three-time portions, one-third for acceleration,
one-third at slew velocity and the remaining third to decelerate. The slew (X
s
) section of an
equally divided trapezoidal velocity profile represents ½ of the distance moved and the
acceleration and deceleration portions each represent ¼ of the total distance. The rule of
thirds minimizes the RMS torque current in the motor and is the most economical use of
energy.