derivative gain, it is clear that the overshoot is
severely dropped and the output position settles
much more quickly. The derivative gain acts to
slow down the motor if the motor is moving
fast, and once the position becomes close to
the desired location. The motor was set to 50
degrees, but notice that both of the controllers
still have a little bit of error at the end of the
test.
Figure 8 shows the second test, comparing
the P and PID controller. Here, the P gain was
set very low. In the P test, the controller
struggled to get the output position error less
than three degrees. The PID controller had the
integral term which integrated the error over
time. As a result, the output angle was
tightened up right to 50 degrees.
The PID and PD controllers are the most
commonly used controllers, especially for servo
control. The controllers work great for any
mass-spring-damper system, but not all systems
can be easily modeled in this form. The complexities of the
hexapod cannot make perfect use of the PID controller
because of the geometries involved, but the adjustable gains
can be set whenever the lag is either free or in contact with
the ground. Fortunately, this flexibility can help to tackle
some of the tougher optimal control strategies.
FIGURE 13.
Using the
Involute shape,
various sized
gears can be
designed.
Gears
The 3DOF head mechanism in the hexapod is rather
intricate, involving many spur and bevel gears. Not knowing
proper gear design at the time, I simply made some
arbitrary triangular cuts in a disc and meshed them in
Solidworks the best that I could get them to fit. This
resulted in improper motion and teeth colliding, and a
significant breaking-in period was necessary to make it
usable. If you look at a professionally made gear, you will
notice that the teeth seem to have a small flat part, then
curve up.
Recently, I looked into designing proper gears using the
involute curve method. Originally, I did not know why the
curve was important, but after some research the curve
finally made sense. I’ll attempt to explain why it makes
sense to use.
FIGURE 14. Again using the Involute shape, bevel gears
are created using a lofted cut.
Gear Purpose
Obviously, a gear is used to transfer circular motion to
another circular device. Figure 9a shows the general
motion. If we were to simply use circular discs, then they
would need ideal friction to fully transmit the power.
Unfortunately, ideal friction does not exist (it would cause
some wear if it did exist). Another method to transfer this
motion is to instead put a piece of string wrapped around
each disc. Figure 9b shows separating the discs and placing
a piece of string to transmit power. A nice aspect of using
the string is that the transfer of motion between each disc is
linear. This will transfer the power well, but only allows a
single direction of power transmission. A setup like the one
in Figure 9c could work for both directions, but the turning
range is limited, strings may rub, etc.
SERVO 01.2012 61
