Page 303 - Anatomy of a Robot

11_200256_CH11/Bergren 4/10/03 12:07 PM Page 288
288 CHAPTER ELEVEN
would be to find a similar part of roughly the same shape and extrapolate the parame-
ters. Here’s one example.
Suppose you want to know the compression strength of an L-shaped beam made of
a specific type of plastic. If the manufacturer has already specified the compression
strength of a single slab of material with the same thickness, you have enough infor-
mation to make an estimate. Simply add together the compression strength of the two
flat portions of the L-beam. This estimate of the compression strength for the L-beam
will probably be low, but that’s just fine.

Dynamic Mechanics

The field of dynamics is vast and complicated. Even without the complications of rel-
ativistic motion, the physics and math are difficult and beyond the scope of this text.
However, a couple of useful tips must be passed on.

ENERGY CALCULATIONS
It’s useful to be able to estimate the energy required to make parts move within the
robot. The calculations required for making these estimates vary with the types of
motions involved.
Consider a bicycle. How much energy does it take to accelerate a bike to a fixed
speed? Let’s assume the following: The bike chassis, without the wheels, has a mass of
W1. Each wheel has a mass of W2 and has a radius of R. The bike will accelerate to a
speed of V. The energy of a mass moving in a straight line is

0.5 m v 2
where m is the mass and v is the velocity. Notice the similarity here with Einstein’s
2
famous E mc formula!
Now, if the wheels were not spinning, the energy of the bike would be

E 0.5 1W1 W2 W22 V 2

But the tires are indeed spinning and contain energy as well. The energy in a mass
constrained to rotate about a central point is
2
E 0.5 m r 1du>dt2 2