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The output of this compass is comprised of two sine waves, one of which is 90 degrees out of phase with the other (see the sine-cosine configuration in Fig. 5.32). The amplitude of each wave correlates to direction. If a 90-degree portion of a sine wave is measured with an 8-bit A/D converter, a compass directional resolution of 1 degree is obtained.

However, there is also potential chemical and electrical energy in a battery, and a di erent look at potential energy is found in a stretched rubber band or spring. Let s look at potential energy in more detail, since it provides a way to store energy for later use.

Using a global positioning system (GPS), a robot can know precisely where on Earth it s located. While the need for a GPS is not obvious for amateur robotists, the cost of GPS systems are coming down if the need arises.

While an object in motion has kinetic energy, there are ways other than motion to store mechanical energy, such as in springs. Of course, you can store types of energy other than mechanical; batteries, for example, use stored chemical energy to move electricity. There are di erent types of springs: long at leaf springs, round disk springs, coil springs that you pull on to stretch and coil springs that you press on, or compress, to squish, and even rubber bands. These all do roughly the same thing and store energy by converting the force applied to the spring into potential energy. The force applied to the spring is called stress, and the change it creates in the spring is called strain. Force, as described above, is still mass times acceleration. Strain is the internal change of position of the atoms in the spring. Each atom inside the spring is attracted to the other atoms by the atomic forces. These forces are like gravity, except they are much stronger and are only e ective at extremely small distances. Note that there are other atomic forces that push the atoms apart.

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The human ear has an auditory range from 10 to 15,000 Hz. Sound can be picked up easily using a microphone and amplifier. Microphones typically have an auditory range that surpasses that of human hearing. Sound is a useful tool for robotists. We use hearing primarily for communication (language). Speechrecognition systems are a hot topic in robotics. Because of this, we devote an entire chapter (see Chap. 7) to building a speechrecognition circuit and interfacing. But don t skip over the following information. Robotic sound systems are pretty useful.

Between the pushing and pulling of the atomic forces, it is as if each atom is connected to its neighboring atom by a spring. The spring is made up of millions of smaller atomic springs, in the same way that an apple is pulled toward the Earth by the force of the gravity spring. Of course, these aren t tiny physical springs inside our big spring. They are the forces that keep our universe together. Strain occurs when you pull or push the atoms in an object against the atomic forces that are working to keep them in place. The object then changes shape, or deforms. This deformation is the visible manifestation of the strain inside an object. You feel the strain by the force of the object trying to return to its original shape. Of course, if you put too much strain into something, the atoms can be pushed and pulled too far and break their internal springs. Then the object bends or breaks, and its stored potential energy is rearranged so we can t use it anymore. When you stretch or compress a spring, it pushes back with the force of: F k l 2-7