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290 CHAPTER ELEVEN
within the moving parts. The energy needed to accelerate the parts to the speeds in ques-
tion will be greater than the estimate.
NATURAL FREQUENCIES
We’ve already covered natural vibration in a previous chapter. All mechanical structures
will vibrate easily at specific “natural” frequencies. The materials and the structure con-
tribute to this particular type of vulnerability. At worst, the robot may shake apart. At
best, the robot may make noise as it moves. The best way to eliminate this problem is
to vary the design in ways that make cooperative vibrations less likely. Notice that the
solutions for damping out vibrations are much the same as adding friction to our sec-
ond-order control system.
Here are a couple web sites about natural frequency vibrations:

www.ideers.bris.ac.uk/resistant/vibrating_build_natfreq.html
www.newport.com/Vibration_Control/Technical_Literature/Fundamental_of_
Vibration/Fundementals_of_Vibration/

HEAT TRANSFER

A couple of short notes must be made about heat transfer. Often heat must be taken out
of a component. Heatsinks, for example, remove heat from integrated circuits like
microprocessors. Although heat transfer is a general problem, we can use a processor
and a heatsink in our example without a loss of generality. Heat flows from the proces-
sor, through the heatsink, and into the ambient air. Each component has a well-specified
thermal impedance that can be used to measure its effectiveness. Low thermal imped-
ance means the component can transfer heat more effectively. Here’s how the calcula-
tions are done.
Suppose the processor dissipates 20 watts, that the ambient air is at 25 degrees
Celsius, and that the thermal impedance of the heatsink is 2 degrees Celsius per watt.
The processor will rise to a temperature of

25 2 20 65 degrees Celsius
This temperature may be too high for the processor. If that’s the case, then lower the
temperature of the ambient air, get a heatsink with a lower thermal impedance, or find
a lower-energy processor.