|
Locking Layers
Recall the standard grid we discussed in Chapter 1. We showed how it leads
to easy interlocking between horizontal and vertical beams. The sequence was: 1 beam, 2
plates, 1 beam, 2 plates… You can take advantage of the plate layer between the beams
to connect two groups of stacked beams, thus getting a very simple chassis like the one in
Figure 5.1. If you actually build it, you can see how, despite its simplicity, it results
in a very solid assembly. This also proves what we asserted in Chapter 1 regarding the
importance of locking layers of horizontal beams with vertical beams. For instance, if you
remove the four 1 x 6 vertical beams, the structure becomes very easy to take apart.
NOTE
Remember to use the black pegs (or pins) when connecting beams. They fit in the holes with
much more friction than the gray ones, because they are meant to block beams. The gray
pegs, on the other hand, were designed for building movable connections, like levers and
arms. You're not compelled to place all the beams in one direction and the plates in
another. Actually, you are likely to need beams in both directions, and Figure 5.2 shows a
very robust way to mount them, locked in the intermediate layer of our example structure.
Sometimes you want to block your layers with something that stays inside the height of the
horizontal beams, maybe because you have other plates or beams above or below them. The
full beams we’ve used up to this point extend slightly above and below the structure.
The liftarms help you in such cases, as shown in the three examples of Figure 5.3
Despite our insistence on the importance of locking beams, there's no need
to go beyond the minimum required to keep your assembly together. When the horizontal
beams are short, a single vertical beam is usually enough. The example “a” in
Figure 5.4 is better than its “b” counterpart, because it reaches the same
result with fewer parts and less weight. Weight is, actually, a very important factor to
keep under control, especially when dealing with mobile robots. The greater the weight,
the lower the performance, due to the inertia caused by the mass and because of the
resulting friction the main wheel axles must endure. Figure 5.4 One Vertical Beam is
Sometimes Enough
We suggest you also support the load-bearing axles with more than a single
beam whenever possible. The three examples shown in Figure 5.6 are better than those in
Figure 5.5, with 5.6c being the best among all the solutions shown so far. The use of two
supports, one on either side of the wheel, like on a bicycle, avoids any lever-effect
created by the axle on the support, thus reducing the friction to a minimum. Figure 5.6
Two Supporting Beams Are Better than One
The position of the RCX has a strong influence on the behavior of mobile robots. It's
actually the shape and weight of the whole robot that determines how it reacts to motion,
but the RCX (with batteries) is by far the heaviest element and thus the most relevant to
balancing load. To explain why balancing load is important, we must recall the concept of
inertia. We explained earlier in the chapter that any mass tends to resist a change in
motion. In some cases, to resist acceleration. The greater the mass, the greater the force
needed to achieve a given variation in speed. The “Acrobot” model shown in the
MINDSTORMS Constructopedia works under this same principle. If you have already built and
tried it, did you wonder why it turns upside down instead of moving forward? This happens
because the inertia of the robot keeps it in its present condition—which is
stationary. Once power is supplied to the motor, the wheels try to convert that power into
motion, accelerating the robot. But the inertia is so great that the force resorts to the
path with least resistance, turning the body of the robot instead of the wheels. After
having turned upside down, the robot has the undriven wheels in front of it, preventing it
from turning again, and now can't do anything other than accelerate. You probably don't
want your robots to behave like Acrobot. More likely, you ’re looking for stable
robots that don't lose contact with the ground. You can use gravity to counteract this
unwanted effect, putting most of the weight further from the driving axles. There's no
need for complex calculations, simply experiment with your robot, running a simple program
that starts, stops, reverses, and turns the robot to see what happens. Place the RCX in
various positions until you're satisfied with the result.
Putting It All Together: Chassis, Modularity, and Load The following example summarizes
all the concepts discussed so far in this chapter. Using only parts from the MINDSTORMS
kit, we built the chassis shown in Figure 5.7. Its apparent simplicity actually conceals
some trickiness. Let's explore this together. Figure 5.7 A Complete Platform
It's built like a sandwich, with two layers of beams that contain a level of plates. It's
robust, because vertical beams lock the layers together. Notice that for the inner part of
the robot, we used 1 x 3 liftarms instead of 1 x 4 beams. This way the top results in a
smooth surface where one can easily place the RCX or other components. The load-bearing
axles are two #8 axles that support both the outer and inner beams (#8 means that the axle
is 8 studs long), while the wheels are as close as possible to their supports. Figure 5.8
Bottom View
The motors have been mounted with the 1 x 2 plates with rail, as explained in Chapter 3
(look back to Figure 3.4). They are kept in place by two 2 x 4 plates on their bottom
(Figure 5.8), but by removing those plates you can quickly and easily take out the motors
without altering the structure (Figure 5.9). Figure 5.9 Easily Removing the Motors
You can also remove the pivoting wheel and the two main wheels in a matter of seconds to
reuse them for another project (Figure 5.10). We should mention here that the pivoting
wheel is quite special, since it's what makes a two-wheeled robot stable and capable of
smooth turns. The technique of making a good pivoting wheel has its own design challenges,
of course, which we'll explore in Chapter 8. Figure 5.10 …and the Wheels
The truth is that if you own only the Robotic Invention System, you probably won't have
enough parts to build another robot unless you dismantle the whole structure. If you have
more LEGO TECHNIC parts, however, you can leave your platform intact and reuse wheels and
motors in a new project. Now we can experiment with load and inertia. If you have the LEGO
remote control, you don't need to write any code. If not, we suggest you write a very
short program that moves and turns the robot. You don't need anything more complex than
the following pseudo-code example, which will drive your robot briefly forward then
backward, and make it turn in place: start left & right motors forward
wait 2 seconds
stop left & right motors
wait 2 seconds
start left & right motors reverse
wait 2 seconds
stop left & right motors
wait 2 seconds
start left motors forward
start right motors reverse
wait 2 seconds
stop left & right motors
Place your RCX in different locations and test what happens. When it is
just over the main wheel axles (Figure 5.11), the robots tend to behave like the Acrobot
and overturn easily. Figure 5.11 Poor Positioning of the Load (RCX) Makes This Robot Very
Unstable
As you move the RCX toward the pivoting wheel, the robot becomes more stable (Figure
5.12). It still jumps a bit on sudden starts and stops, but it doesn't flip over anymore.
Figure 5.12 Better Positioning Improves Stability
Summary
The content of this chapter may be summarized in three words: layering, modularity, and
balancing. These are the ingredients for optimal structural results. Thinking of your
robot in terms of layers will help you in building solid, well-organized structures.
Recall the lessons you learned in Chapter 1 about layering beams and plates and bracing
them with vertical beams to get a solid but lightweight structure. A robust chassis comes
more from a good design than from using a large number of parts. Modularity can save you
time, allowing you to reuse components for other projects. This is especially important
when it comes to the “noble” parts of your MINDSTORMS system—the sensors,
motors and, obviously, the RCX—because they are more difficult and expensive to
replicate. You should put this concept into operation not only for single parts, but for
whole subsystems (for example, a pivoting wheel), which you can transfer from one robot to
another.
Balancing is the key to stable vehicles. Keep the overall mass of your mobile robots as
low as possible to reduce inertia and its poor effects on stability. Experiment with
different placements of the load, mainly in regards to the RCX, to optimize your
robot’s response to both acceleration and deceleration. We will look more deeply into
this matter in Chapter 15, when we learn how to build walking robots (where management of
balance is a strict necessity). Unfortunately, these goals are not always reachable;
sometimes other factors force you to compromise. Compactness, for example, doesn’t
mesh well with modularity. Certain imposed shapes, like those used in the movie-inspired
droids of Chapter 18, can force you to bypass some of the rules stated here. We
aren’t saying they can’t be violated. Use them as a guide, but feel free to
abandon the main road whenever your imagination tells you to do so.
Table of Contents
Part I Tools
Chapter 1 Understanding LEGO Geometry
Chapter 2 Playing with Gears
Chapter 3 Controlling Motors
Chapter 4 Reading Sensors
Chapter 5 Building Strategies
Chapter 6 Programming the RCX
Chapter 7 Playing Sounds and Music
Chapter 8 Becoming Mobile
Chapter 9 Expanding Your Options with Kits and Creative Solutions
Chapter 10 Getting Pumped: Pneumatics
Chapter 11 Finding and Grabbing Objects
Chapter 12 Doing the Math
Chapter 13 Knowing Where You Are
Part II Projects 247
Chapter 14 Classic Projects
Chapter 15 Building Robots That Walk
Chapter 16 Unconventional Vehicles
Chapter 17 Robotic Animals
Chapter 18 Replicating Renowned Droids
Chapter 19 Solving a Maze
Chapter 20 Board Games
Chapter 21 Playing Musical Instruments
Chapter 22 Electronic Games
Chapter 23 Drawing and Writing
Chapter 24 Simulating Flight
Chapter 25 Constructing Useful Stuff
Part III Contests
Chapter 26 Racing Against Time
Chapter 27 Hand-to-Hand Combat
Chapter 28 Searching for Precision
Appendix A Resources
Appendix B Matching Distances
Appendix C Note Frequencies
Appendix D Math Cheat Sheet
Sensors
Averages
Interpolation
Gears, Wheels, and Navigation
Index
|
