Page 55 - Anatomy of a Robot

02_200256_CH02/Bergren 4/17/03 11:23 AM Page 40
40 CHAPTER TWO
HOW THE DESIGN OF THE CONTROL SYSTEM
DETERMINES HOW THE ROBOT WILL REACT
We have made a model of a second-order system and have the closed equation describ-
ing how the model behaves. If we know m, K, and B, we can graph the theoretical
behavior of the system. Here’s a step-by-step method of doing just that:
1. If you have values for m, K, and B, skip ahead to step 2.
a. Mass To measure the mass m, just weigh it in kilograms and divide by the
gravitational acceleration of 9.8 m/sec . It should be mentioned here that
2
kilograms is not a measure of weight. The actual unit of weight in the metric
system is the Newton! It is not correct to report weight in kilograms. You
should be aware that mass is not the same thing as weight. Mass is a measure
of the amount of “stuff” in the object. Weight is a force and is a measure of
the force exerted by the mass in the presence of the gravity created by another
mass like the earth. Mass in orbit is weightless, yet retains its mass. Mass on
Earth becomes weight because it’s acted upon by the acceleration of gravity
(F m g). Here’s a web site about this matter:http://feenix.metronet.com/
gavin/physics/wgt_mass.html.
This brings up an important point. The calculations for the model’s second-
order system are partially dependent upon gravity. The robot might not work
the same way in orbit. The friction we diagrammed in the model’s mechan-
ical second-order system depends on the friction of the mass resting on a sur-
face. Without gravity, there will be no such frictional coefficient B to speak
of. You can introduce other friction elements into your robot design that
would work in orbit, such as a piston with a viscuous fluid within it (like a
shock absorber).
b. Spring constant To measure the spring constant K, hang a known weight
from the spring without stretching it too far. The ratio of the displacement of
the spring to the weight will give you K using the formula

m g K displacement
2
where g 9.8 m/sec , the acceleration of gravity. The example given at the
web site www.iit.edu/ smile/ph9013.html cites a 250-gram weight sus-
pended from the spring.
Solving m g K displacement
2
250 grams 9.8 m>sec K displacement
2
K 12.4 kgm>sec 2>displacement
K 2.4 newtons>displacement