Page 748 - Mechatronics with Experiments

734 MECHATRONICS
knife axis (slave axis). When the controller recieves the registration mark signal, it captures
the knife position. Then it compares that captured position with the desired position that
the knife should be at in order to cut the paper at the right location. Then, the knife is
commanded to make an incremental move to make the phase correction. Let us consider
that the paper cutting machine runs at 1200 ft∕min line speed. When the registration mark
is sensed, the controller will have to capture the knife axis position within a certain finite
time. At 1200 ft∕min rate, paper moves 20 ft∕s or 240 in∕s or 240∕1000 in∕ms. If the paper
is to be cut with ±5∕1000 in accuracy, the position must be accurately captured before that
amount of paper passes. The 5∕1000 in paper movement takes about 40 μs. Therefore, the
position capture on the registration mark must be done within 40 μs. This type of response
requires dedicated axis level high speed I/O. Notice that the correction of the position error
does not (and cannot) need to be made within 4 μs, rather within the period remaining in
the cycle which is typically in the order of tens of milliseconds.

10.5.3 CAM Profile and Contouring Coordinated Motion

Consider a shaft driven by an independent actuation source (i.e., a motor-drive) and a
mechanical cam on the shaft. The cam can be on the face of the shaft or around the shaft.
A tool is connected to the cam profile through a cam follower. As the shaft rotates, the
tool moves up and down as function of the cam profile machined on the cam groove. For
every point on one revolution of the shaft, there is corresponding point on the cam, hence
there is a corresponding position of the tool (Figure 3.9). This relationship is mechanically
determined by the cam design. For every revolution of the shaft, the cam relationship
between the shaft and the tool is repeated. More than one cam can be connected to a shaft to
drive more tools as slaved to the shaft motion. The slave motion synchronization for each
tool is determined by the cam profile machined into each cam. This type of synchronization
is more complicated than a constant gear ratio relationship.
The functionality in cam synchronization is that the slave axis position is directly a
function of the master axis position. The relationship repeats every revolution of the master
axis output shaft.
The same functionality can be more flexibily achieved by electronic cam or software
cam motion coordination. Both master and slave must have their independent actuation
source (motor-amplifier). As the master axis moves, the desired (commanded) motion for the
slave axis can be derived based on the position of the master axis. The desired relationship
in this case happens to be a cam profile. The cam profile is defined only in software as a
mathematical equation or a look-up table. As the master axis moves, the position of the
master axis is periodically sampled. Usually, the sampling rate is the same as the servo
loop update rate. Then the corresponding position where the slave axis should be is derived
from the mathematical cam profile equation or from the look-up table. Furthermore, in
software implementation, the slave axis does not have to be driven by the cam relationship
throughout the whole revolution or cycle. The cam following mode can be entered and
exited at various points during a cycle based on some application dependent condition.
Contouring coordination is mostly used in machine tools and plasma cutting types
of machines. The contour coordination is a more complicated form of cam coordination.
The basic idea is that two or more axes must move in space in order to make a tool trace
a certain path. In two-dimensional x-y motion, this corresponds to drawing an arbitrary
curve in plane, in three-dimensional x-y-z motion, it corresponds to drawing an arbitrary
curve in 3D space. At any given time all of the axes have a position that they must be at
in order to trace the desired path. The way the commanded motion is generated for each
axis can vary: one alternative is that the feedrate along the path (tangential linear speed)
can be the indepedent variable. The feedrate can be planned based on application specific
requirements. Then as the tool travels along the path, the desired motion of each axis is