perfect, maximum distance is
virtually zero. So if you want, you
can make the tooth height shorter
than the optimum dimension shown
in the tutorial. If you choose, for
instance, y = half of optimum, your
robot won’t notice any difference
with this lower height in 50% of the
hits since you came in on the short
side of the 50/50 odds. On the
other 50% (where tooth bite would
be higher than half of optimum), the
opponent will touch the body of the
drum/disk before being hit by a
tooth, resulting in a tooth bite equal
to the tooth height. Designing y less
than half of optimum is not a good
idea, as most attacks will end up
touching the drum/disk before the
tooth.
For instance, the 2008 version
of our featherweight Touro Feather
had a drum with n = 2 teeth
(Figure 3) spinning up to 13,500
rpm. Since the robot’s top speed is
14. 5 mph, then maximum bite
distance = 14 mm (calculations
shown in the tutorial). Since the
overall height of the drum needed
to be smaller than 100 mm ( 4”) by
design, a tooth height of 14 mm
would result in a drum body with
low diameter ( 72 mm or 3”). We
then chose y = 10 mm for the
tooth to stick out of the drum
body. This 10 mm height is usually
enough to grab an opponent. Also,
in 10 mm/14 mm = 71% of the
hits at full speed, the tooth height
y will be higher than the tooth bite
d. The opponent will only touch
the drum body in the remaining
29% of the hits, when the next
tooth will be able to hit the
opponent with its full 10 mm height
(unless the opponent had bounced
off immediately after hitting the
drum body).
Beware of a frontal collision
between two vertical spinning
weapons because the opponent may
be able to grab your drum or disk
body with its teeth before you can
grab it. In this case, it is a game of
chance. The robot with higher teeth
will have a better chance of
grabbing the opponent, as long as it
spins fast enough. Since a vertical
spinning bar does not have a round
inner body, it basically behaves as if
its tooth height y was equal to the
bar radius. So, usually a powerful
vertical bar will have an edge in
weapon to weapon hits against
drums or vertical disks.
FIGURE 3
Number of Teeth
An important conclusion from
the tooth bite equations is that you
must aim for a minimum number of
teeth. The lower the number of
teeth, the higher the value of the
bite distance. Disks with three or
more teeth are not a good option.
The best choice is to go for two
teeth, as with bars or two-toothed
disks. Even better is to try to develop
a one-toothed spinning weapon,
such as the disk of the vertical
spinner Professor Chaos. However,
but this requires a careful calculation
to avoid unbalancing by using (for
instance) a counterweight
diametrically opposite to that tooth.
Note that a one-toothed
weapon does not have to be too
much asymmetric, nor will it need
heavy counterweights, if you do
your math right. For instance, the
one-toothed bar pictured in Figure 4
can be made out of a symmetrical
bar, as long as the short end is
chamfered properly. (Editor’s note:
Another long, interesting, but hard
to type series of mathematical
equations was deleted here and
substituted with the word
“properly.” See the source document
if you want to do the math yourself.)
In this way, with the bar at full
speed, even if the long end barely
misses the opponent, the short end
won’t
touch it
because
during a
half turn,
it would
approach
— at most
— half of
FIGURE 4
the optimum bite. After the full turn,
it would have approached up to the
best bite distance, hitting for sure
with the long end. With just one
tooth, it is possible to move twice as
much into the opponent before
hitting it, transferring more impact
energy.
With this proposed one-toothed
bar geometry, the counterweight
wouldn’t have to be very heavy
because its mass would only have
to account for the mass of the tip
insert plus the removed mass from
the chamfers. This bar is also
relatively easy to fabricate, with
very little material loss. In fact, for
wide bars with large inserts —
which increase the value of b — it is
even possible to design the bar in a
way it’s almost symmetrical even
after chamfering. In addition, if
you perform some shape
optimization removing some
material from the long end, it is
even possible to remove the
counterweight, being careful not to
compromise the bar strength at its
most stressed region.
In our experience, to bind well
to the opponent, the tooth bite
should not be below 1/4”, no
matter if the robot is a hobbyweight
or a super heavyweight. We’ve
tested different tooth heights with
our drumbot hobbyweight Touro Jr
and featherweight Touro Feather,
and values below 1/4” made the
SERVO 11.2010 31
