working voltage Vinput, connect
the motor (without loads on its
shaft) to the appropriate battery —
the same that will be used in
combat — and measure Ino_load.
Note that the value of Ino_load
does not depend much on Vinput.
However, it is always a good
idea to measure it at the working
voltage. If you have an optical
tachometer (which uses strobe
lights, such as the one in Figure
1), you can also measure the
maximum no-load motor speed
ω no_load. A cheaper option is to
attach a small spool to the motor
shaft, and to count how long it
takes for it to roll up. For
instance, take 0 meters or 30
feet of nylon thread. The angular
speed in rad/s will be the length
of the thread divided by the radius
of the spool; all this is divided by
the measured time (the thread
needs to be thin, so that when it’s
rolled up around the spool the
effective radius doesn’t vary
significantly).
• Attach the motor shaft to a vise
grip, hold both the motor and the
vise grip well, and connect the
battery. Be careful because the
torque can be large. The
measured current will be
Istall, associated with the circuit
resistance Rsystem = Rbattery +
Rmotor, so Istall = Vinput / Rsystem;
then, calculate Rbattery = (Vinput/
Istall) - Rmotor. Do not leave the
motor stalled for a long time; it
will overheat
and possibly get
damaged. Also,
take care not to
dent the motor
body while
holding it (for
instance, with
a C-clamp) as
shown in
Figure 2.
• Repeat the
procedure above,
but supporting
one end of the
vise grip by a
scale or spring dynamometer (with
the vise grip in the horizontal
position; see Figure 2). Then,
measure the difference between
the weights with the motor stalled
and with it turned off, and
multiply this value by the lever arm
of the vise grip to obtain the
maximum torque of the motor,
τstall. For instance, if the scale
reads 0.1 kg with the motor
turned off (because of the vise
grip weight) and 0.8 kg when it is
stalled, and the lever arm
(distance between the axis of the
motor shaft and the point in the
vise grip attached to the scale) is
150 mm, then τstall = (0.8kg –
0.1kg) × 9.81m/s2 × 0.150m =
1.03N×m.
• Because τstall = Kt × (Istall – Ino_load),
you can obtain the motor torque
constant by calculating Kt = τstall /
(Istall – Ino_load).
FIGURE 2
• Alternatively, if you were able to
measure ω no_load with a
tachometer or spool, then you can
calculate the motor speed
constant using Kv = ω no_load /
(Vinput – Rsystem × Ino_load). Check if
the product Kt × Kv is indeed equal
to 1, representing Kt in N×m/A
and Kv in (rad/s)/V. This is a
redundancy check that reduces
the measurement errors. If you
weren’t able to measure ω no_load,
there is no problem. Simply
calculate Kv = 1 / Kt, taking care
with the physical units.
• Finally, once you have the values
of Vinput, Kt (and/or Kv), Rsystem,
and Ino_load, you can obtain all
other parameters associated with
your motor + battery system using
the previously presented equations
(don’t forget to later add the
resistance of the electronics, as
well). SV
Aff rdable 2. 4 GHz
● by Pete Smith
number of channels available and
controlling the use of those channels
in a major event.
The arrival of the Spektrum DX6
changed all that. It uses 2. 4 GHz
and each radio “binds” to and can
control only one RX at a time
without any possibility that it can
interfere with (or be interfered by)
another transmitter. This removed —
The principal radio frequency for many years in USA combat
robotics was 75 MHz PCM. This
worked well enough, but the
transmitters (TX) and receivers (RX)
for PCM were both expensive, and
the receivers were both bulky and
not particularly reliable under
combat conditions. The main
problem, however, was the limited
in a stroke — many of the radio
concerns at events. Organizers no
longer had to worry about competitors
interfering with each other or with
other RC sets being used nearby,
affecting safe control of the robots.
SERVO 01.2011 23
