23 Agustus 2008

Ebook Robotika buat persiapan Kontes Robot Indonesia

Buat temen-temen yang mencari referensi buat persiapan Kontes Robot Indonesia, nih saya punya ebook robotika yang bagus buat referensi. Ini saya ambil dari ebook berjudul "Robotic Demystified"

Read this document on Scribd: Bikin robot ( persiapan KRI )

For more information about this title, click here CONTENTS Preface Acknowledgments CHAPTER 1 Introduction A Brief Tour of Robotics Automata and Animatronics Factory Machines Fictional Robots Future Dreams Inside Robots Tools and Supplies Parting Words of Wisdom Mechanical Forces Introduction Energy Units of Measurement Position Time: t Length: l Mass: m Velocity: v xv xvi 1 2 2 4 7 8 9 10 11 13 13 15 16 16 17 17 18 19 v CHAPTER 2 vi CONTENTS Acceleration: a Force: F Momentum: p Energy: E Storing Energy Losing Energy Summary Quiz CHAPTER 3 Simple Machines Introduction Structural Strength Triangles and Squares Hidden Triangles Inclined Plane Wedge Screw Levers Lever Machine Pulleys Pulley Machine Wheels and Torque Gears and Sprockets Summary Quiz Electricity Introduction Pieces of Matter Electrons in Metal Electromagnetic Field Units Unit Prefixes Electrical Charge 23 24 26 26 27 29 30 30 32 32 33 33 35 36 40 41 42 42 44 45 49 51 53 53 54 54 55 56 57 59 59 60 CHAPTER 4 CONTENTS Current: I Charge Difference Electrical Energy Power: P Batteries and Generators Speed of Electricity Summary Quiz CHAPTER 5 Starting with Electronics Introduction Electronic Circuits Schematic Printed Circuit Board Circuit Assembly Prototyping Boards Dead Bug and Wire Wrapping Soldering Suppliers Resistors Resistor Ohm’s Law Resistor Networks Resistive Sensor Light Bulb Summary Quiz Control Introduction Passive Control Balancing Machine Open-Loop Control Feedback Control 61 62 63 63 63 64 65 65 66 66 67 67 68 70 70 71 72 79 80 80 81 83 87 94 94 95 96 96 97 98 98 99 vii CHAPTER 6 viii CONTENTS Centrifugal Feedback Hysteresis Mechanical Switch Summary Quiz CHAPTER 7 Sequencing and Programs Introduction Switches and Cycles Cam Control Cardboard Cam Card Control Mechanical Card Reader Programming Concepts Computer Numbers Computer Instructions Summary Quiz Joints Introduction Rotation and Bending Rotation Bearings and Bushings Bending Sliding Complex Motion Ball and Socket Universal Joint Robot Wrist Others Summary Quiz 100 102 104 105 106 107 107 108 111 113 113 115 115 117 121 122 123 124 124 125 125 126 127 128 128 128 130 131 134 134 135 CHAPTER 8 CONTENTS CHAPTER 9 Power Transmission Introduction Chains, Belts, and Cables Gears Gear Trains More Gears Couplers Directional Transmission Differential Transmission Summary Quiz Beyond Resistance: Capacitance Introduction AC/DC Oscilloscope Diodes Signal Diode Rectifier Light-Emitting Diode Zener Diode Capacitors Capacitor Capacitors and Audio Capacitor Networks RC Circuits RC Filters Diode-Capacitor Circuits Summary Quiz Inductance and Magnetism Introduction 136 136 137 141 142 145 149 150 150 154 155 156 156 157 160 161 161 162 163 163 165 165 168 170 171 172 176 178 178 179 179 ix CHAPTER 10 CHAPTER 11 x CONTENTS Electromagnets Nail Electromagnet Relay Motors Generators Servos and Steppers Inductors Behavior Component Filters Phase Transformer Summary Quiz CHAPTER 12 Semiconductors Introduction Conductor Physics Semiconductor Physics Doped Silicon Diode Physics Forward Bias Reverse Bias Electronic Switches Analog Versus Digital Transistor FET Integrated Circuits Summary Quiz Programming Introduction Programming Basics 180 181 182 182 184 184 185 186 186 187 187 188 189 189 190 190 191 192 193 195 197 198 198 198 200 202 204 205 205 207 207 208 CHAPTER 13 CONTENTS Flowcharts RCX Programming Programs Simple Timed Sequence Obstacle Avoidance Line Following Self-Calibration Summary Quiz CHAPTER 14 Shaping Motion Introduction Looking Back Single-Link Mechanisms Two Links More Links Parallel Motion Four-Bar Linkage Complex Motions Other Mechanisms Cardan Gear Quick-Return Geneva Stop Ratchet Summary Quiz Communication Introduction Telerobotics Tethered Robots Remote Control Semi-Autonomous Communication Technologies 208 211 213 213 213 218 221 221 223 224 224 225 225 228 229 229 232 234 236 236 237 237 237 238 240 241 241 241 242 243 243 245 xi CHAPTER 15 xii CONTENTS Parallel Serial Wireless Other Interfaces Summary Quiz CHAPTER 16 Languages Introduction Programming Concepts Turing Machine Choosing a Language Manufacturing Languages Custom Languages Human Language Human Intelligence Summary Quiz Intelligent Behavior Introduction Reflexive Control Thermostat PID Motor Control Serial Behaviors Layered Behaviors Logical Behavior Scripting Formal Logic Natural Computation Pattern Recognition Statistics Fuzzy Logic Neural Networks 245 246 249 250 251 251 252 252 253 255 258 260 260 261 261 262 262 263 263 264 265 266 269 270 272 272 272 273 275 275 276 278 CHAPTER 17 CONTENTS Summary Quiz CHAPTER 18 Advanced Control Introduction Decisions Mapping Odometry Odometry Errors Supervised Learning Supervised Robotic Learning Unsupervised Learning Swarm Robots Agents Summary Quiz Answers Index 280 281 282 282 283 285 287 289 289 292 293 294 294 295 295 296 309 xiii This page intentionally left blank CHAPTER 1 Introduction Robot 1.a. ˇ One of the mechanical men and women in Capek’s play; hence, a machine (sometimes resembling a human being in appearance) designed to function in place of a living agent, esp. one which carries out a variety of tasks automatically or with a minimum of external impulse. b. A person whose work or activities are entirely mechanical; an automaton. Oxford English Dictionary, Online Edition ˇ Karel Capek used the word Robot in his 1921 play Rossum’s Universal Robots, derived from the Czech word robota, meaning ‘‘forced labor.’’ These Robots were created to replace man and, in their simplified form, as cheap labor. Robots had perfect memory but were incapable of thinking new thoughts. They mirrored the Hebrew legends of the golem, a clay statue that has had life breathed into to by mystical means. And, of course, this all sounds a lot like Dr. Frankenstein’s monster, reanimated from the bits and pieces dug up from the local graveyard. One thing these stories have in common is that the creation is ultimately the downfall of their creator—robots, golems, and reanimated flesh mean trouble. They are an illustration of what happens when we reach too far and are bitten by the unintended consequences. 1 2 CHAPTER 1 Introduction We, however, are interested in the robot as an agent that carries out its tasks automatically or with a minimum of external impulse rather than a recreation of life itself. A smart machine. In this chapter, we first look at some of the history behind the robot. From there we explore the technologies that make up a robot, laying the groundwork for later chapters on how these technologies work. Once we have a good sense of what a robot is, we peek into the future to see what robots might someday be like. A Brief Tour of Robotics AUTOMATA AND ANIMATRONICS An automaton is a device that has the ability to move under its own power. The mechanism of the motion is normally hidden, giving the illusion that the device is self-motivated or alive. While this definition can apply to something as mundane as a mechanical watch, automata are usually mechanisms that try to mimic the look and behavior of living creatures. We humans have long been fascinated by the workings of our own bodies and the animals around us. With this fascination has come the urge to recreate these things, to step into the role of divinity and try our hand at the game of life. The ancient Greeks, at around 400 B.C. and continuing on into the common era, are reputed to have used steam and water power to animate statues or drive various mechanisms in their temples. Automatically opening doors, statues that appear to drink offerings of wine, singing birds, self-lighting fires, and other wonders are documented in the few remaining writings of that time. There are hints of similar Egyptian and Chinese devices from that era as well. Most of these technologies, the accumulated knowledge of ancient civilizations, were lost until relatively recent times. During the Renaissance, Europe started to drag itself out of the Dark Ages and began discovering (or, in many cases, rediscovering) all manner of ideas, art, technologies, and sciences. Among these, combining both art and technology, were the automata. Some wild stories tell us about an iron fly and an artificial eagle made of wood, constructed by Johannes Muller in the 1470s. In the fourteenth and fifteenth centuries, automata were the playthings of royalty. Leonardo da Vinci made an animated lion for King Louis XII, Gianello della Tour of Cremona built a number of mechanical entertainers for Emperor Charles V, and Christiaan Huygens created a robotic army sometime around 1680. CHAPTER 1 Introduction The first documented automaton in human form, or android, was made by Hans Bullman in the early sixteenth century. Androids have been a popular subject for automata builders ever since. Inventors built machines to play musical instruments of all kinds, draw, write, and even play chess— or at least, pretend to play chess. The eighteenth century was the golden age of automata, with many intricate machines. These were driven by clockwork gears and cylinders containing hundreds, if not thousands, of complicated control tracks. These tracks were composed of sequences of rods of different heights fixed to a cylinder, or individual cams with complex shapes, that pushed on levers that moved rods that adjusted the automaton creating a specific sequence of actions. The Turk was a world-famous automaton from this time. Built in 1770 by Wolfgang von Kepelen, and later purchased from Kepelen’s son by Johan Nepomuk Maelzel in 1804, the Turk toured Europe and America amazing audiences by playing chess! By the time the Turk was on tour, audiences were familiar with the workings of automata and had been exposed to many fine machines. But they were also confident that these machines were just that, simple collections of gears and levers whose rote actions were no challenge to the human intellect. The automata may appear to be alive, but they are only vague shadows of life. They couldn’t think. The Turk challenged this view. It played, and often won, games of chess against any number of famous figures of the time. Napolean, Charles Babbage, and Edgar Allen Poe all took their turn against this mechanical savant. Of course, it turned out that the machine could not play chess at all. Instead, it provided cramped quarters for a human chess player who in turn ran the machinery that made the Turk move. One very complex automaton wasn’t an android, but a duck. Jacques Vaucanson created this avian automaton in 1738 and then went on tour with it. At the price of a week’s wages, audiences were invited to see this creation move around, adjust its wings, preen, drink water, and even eat food, digest it, and then defecate. All of this required thousands of moving parts within both the duck and its large base. And yet, automata were just a hobby of Vaucanson’s. He sold his collection in 1743 and went on to direct the stateowned silk-mills in France. Among other innovations, he developed a way to weave silk brocade using a machine guided by perforated cards. Owing to hostility among the weavers of the time, his advances in factory automation were ignored for decades. In 1804, Joseph-Marie Jacquard improved and reintroduced the technique and was later credited with its invention. While the automatic loom was still despised by weavers, who went as far as burning down automated factories, 3 4 CHAPTER 1 Introduction its improved efficiency led to its ultimate acceptance and led the way into the industrial revolution. In the nineteenth century improved manufacturing techniques brought simple automata to the masses, typically in the form of toys, fancy clocks, and other novelties. Clockwork mechanical toys were popular well into the twentieth century. Today the springs, gears, and cams in toys have been replaced by tiny motors and electronic controls. The skills and techniques developed by the automata makers during the Renaissance provided a foundation for the industrial revolution that followed. Today, you can still find automata for sale. Automata are now in the domain of the artist and pieces from modern craftsmen and artists can be found for as little as a few dollars, up to hundreds or thousands of dollars. Another use for these magical machines is entertainment. Walt Disney introduced mechanical actors in the displays of his amusement park and christened them Audio-Animatronics. This cumbersome name is normally shortened to simply ‘‘animatronics.’’ Animatronics are machines driven by motors and hydraulics and synchronized with an audio track to give the full illusion of life. From the simplest Egyptian trick with water to the modern miracles of Disney’s animatronics, these machine all share one characteristic. They can only reproduce a preset sequence of motions. FACTORY MACHINES Ever since the advent of factories during the industrial revolution, specialized machines have had an important role in creating the products of civilization. The most common machine was the underpaid, overworked citizen—men, women, and children. Early factory conditions were dangerous, but the wages were good and nobody could argue with the efficiency factories brought. Water and steam power, and later gas and electric power, replaced and enhanced human power, allowing us to make our products even faster and cheaper. Complex machines were created to take over many aspects of manufacture. The automatic loom is well known, but even today there are specific machines for many tasks. You don’t normally think about it, but there is a complex machine whose only purpose is to bend wire into paperclips. There is another machine, perhaps in the same factory, that makes nails. Other machines perform other tasks. These machines, invaluable as they are for industry, are still forms of automata. CHAPTER 1 Introduction Factory automata start to become robots when they gain the ability to be programmed. But there is still a large gray area. Take that nail-making machine and add a bunch of controls to it so it can make nails from different sizes of wires, with different types of points, and different types of heads. Is it an automaton or a robot? Does it make a difference if the controls are mechanical levers and knobs or electronic circuits? In the early factories, working alongside a machine made your job more dangerous even if it made it less arduous. These early machines were large assemblies of spinning, whirring, moving parts that continued to spin, whir, and move even if a finger, foot, or other body part intruded into it. Even today, people working with machines in factories and food-processing plants face special risks. Machines are designed to be as safe as possible, but there are limits to what can be done to a metal sheer or punch press, for example, and have it remain useful. As machines improved into robots, they made some aspects of factory work safer. A robotic painter, spot welder, or assembly machine can operate in an empty space without any help at all. A supervisor stands safely outside its range of motion while the robot does the dirty and dangerous work (Fig. 1-1). The most visible type of factory robot is the robot arm (Fig. 1-2). These can be given any type of specialized ‘‘hand’’ needed for their job (Fig. 1-3) and programmed to perform complex activities. One arm, with a set of different hands, can be programmed to perform any number of tasks. These are the robots that we recognize as ‘‘smart’’ machines, beginning to realize the dream promised to us by Kepelen’s Turk. 5 Fig. 1-1. Welding robot (photo courtesy Motoman). 6 CHAPTER 1 Introduction Fig. 1-2. Arm with welding attachment (photo courtesy Motoman). Fig. 1-3. Cutting attachment (photo courtesy Motoman). CHAPTER 1 Introduction Robots make some exploration jobs not only safer but possible. Most humans would not be able to walk into the mouth of an active volcano, perform hazardous-waste cleanup at the site of a nuclear accident, explore the surface of Mars for months on end, or crawl through the debris of a fallen building looking for survivors. 7 FICTIONAL ROBOTS Though not robots, legends tell about the creation of artificial life through many methods, most of which are poorly defined. How can we repeat the feats of the golem makers and the Greek deities who breathed life into ˇ clay? Even the first use of the word robot by Karel Capek was referring to a creature that was more biological than mechanical, a precursor to Mary Shelley’s Frankenstein monster. Real robots are mechanical and reproducible, machines that are built following clever and complex blueprints and driven by ingenious programs. But even in the world of mechanical men, the vision of what a robot could be has always raced ahead of what we can actually build. C3PO and R2D2 from Star Wars were the robots of my generation’s dreams. More recently, expectations were raised with the cyborgs of Blade Runner and even more so with the T2000 ‘‘liquid metal’’ robot from Terminator 2 and 3. Going back in time, there were robots spanning the spectrum from the androids of West World, the flailing robot from the original Lost in Space television series (borrowed from the even older movie Forbidden Planet), or even the stumpy repair robots from Silent Running. But why stop in the 1950s? Going back even further we see mechanical servants in films as early as 1909 in the British film The Electric Servant. Or what about the Turk-like humbug in The Wizard of Oz from 1939? Hollywood is full of robots, most of which are still beyond our ability to create. Of course, it didn’t begin on the silver screen. Science fiction authors have used the robot as a staple character since the creation of that genre. Isaac Asimov had perhaps the greatest impact on robots in literature with his very human creations and their deeply ingrained Three Laws of Robotics: 1. A robot may not injure a human being or, through inaction, allow a human being to come to harm. 2. A robot must obey orders given it by human beings except where such orders would conflict with the First Law. 3. A robot must protect its own existence as long as such protection does not conflict with the First or Second Law. 8 CHAPTER 1 Introduction Of course, many of his stories involved either creative ways to work around these laws or the conflict created by following them. The robotic creations throughout fiction and movies are a two-edged sword. On the one hand, they inspire people with the promise of technology. I know that I had grand dreams of robots and the future from reading Asimov and others. These works, in whole or in part, inspired me to take a career in technology. On the other hand, these fictions set the bar very high. It is easy to feel let down when you see a robot in the real world if you are comparing it to C3PO or the Terminator machines. Much of the thrill comes back when you build the robot yourself. It may not look like much to others, but you know how much work went into it, the lessons you had to learn and the difficulties you had to overcome to make it work. After all this, when the machine you have crafted works perfectly time and again, it raises itself in your esteem from a few bits of metal and plastic to a status worthy of R2D2. At least until the next project. FUTURE DREAMS The big dreams are being dreamed in the universities and labs across the world. Japan has been pushing for human-like robotic helpers for years and some companies are showing some excellent results. Honda’s P5 and Asimo leap to mind, and Sony’s Aibo brought the robot to the home as a pet. The universities have been hot on the trail of robots and robot minds as well. Rodney Brooks is the director of the MIT artificial intelligence lab, as well as the founder of their humanoid robotics group. The Cog project has been exploring the boundaries of human/robot interaction ever since Brooks dreamed it up in 1993. Newer projects explore other aspects of social robots. Macaco is a dog-like head that Artur Arsenio is using to explore robot vision, while Kismet is used by Cynthia Breazeal’s team to explore social and emotional interactions between this infant-like robot and its caretakers. On a more commercial front, the robot reality of Sarcos in Salt Lake City is getting close to some of the movie dreams. Alvaro Villa’s animatronic creations are used in the movies to create more dreams—or in some cases, with his Crypt Keeper, nightmares. And there are more, many more. Scientists are modeling robots on all aspects of nature, basing their work on insects, birds, dinosaurs, and, of course, humans. A visual tour of robots can be found in the beautiful book Robosapiens, by Peter Menzel and Faith D’Aluisio. In a way, researchers are still mimicking nature like the automata builders did in the fifteenth century. Only their tools are better, and their creations are more capable. CHAPTER 1 Introduction It makes sense to mimic nature. Time and hardship have sculpted the world’s creatures, enabling them to survive and adapt in ways that roboticists still only dream about. Some researchers are not content to simply imitate nature’s results, however, but go one step behind the scenes and try to reproduce nature’s methods. These researchers are working on evolving robots, using the rules and techniques of genetics to develop machines and the brains to drive them. Machines that were not designed at all, but evolved. Other researchers are delving down into the very small, not trying to create large complex machines but instead small, simple clouds of machines. Smart dust. Nanotechnology. When we can build our robots on the scale of a single cell, we may have reached the ultimate in robotics. Of course, as stories have told us for hundreds of years, with such power there is also much responsibility and the potential for much harm. This, perhaps, is why Asimov’s three laws are so well known and well loved. They remind us that we need to keep our tools safe, so they can be used without causing harm. 9 Inside Robots When you open up a robot, what do you see? Mostly the big bits—the outer layers, like the metal or plastic skin, the framework that holds it together, the motors that make it go. Bits of wire. This is what you would see if you could see past your skin into your muscles and bones. So it seems natural to follow this analogy and compare the robot to your body. As with most analogies, it falls apart if you look too closely. Where do lungs fit into the picture? The endocrine system, or kidneys? What does a robotic liver do? Okay, maybe the kidneys would be the oil filter, and lungs could be cooling fans. But I digress. A robot is not just one thing, and the study of robotics does not cover just one area of knowledge. A robot brings together systems from many different fields, and to learn robotics is to learn many different technologies. A robot can be considered in four parts, its frame, mechanics, electronics, and control logic. The first visible piece is the robot’s structure. An animal is held together by its bones, unless you count some of our creepier cousins, in which case the bones are on the outside as an exoskeleton. A robot will have bones of a sort, the parts that give it shape and form. Sometimes the pieces are held together by the robot’s shell, or skin. Other times the robot mimics the skeleton model. 10 CHAPTER 1 Introduction The skeleton may give the robot shape but, as in animals, the muscles give it motion. Electric motors make fine muscles, but compressed air and pumped oil are also used to power muscles. For motion, there must also be joints, like your hip or elbow, and a way to attach the muscles to the frame, matching your tendons and ligaments. There are many other pieces to the mechanical puzzle—gears, levers, wheels, and the various forces that they manipulate. All of these fall under this category. Roughly a third of this book is devoted to the technology of mechanics. With mechanical knowledge in place, we can build automata. To provide sensory input and to send control signals to the muscles, we need electronics. Electronics correspond to the biological nervous system. Your eyes provide visual input, your sense of touch tactile. Internally, we can sense hunger, cold, heat, pain. These signals are routed to our brain along biological wires, our nerves. Commands are sent from the brain to our muscles and organs using these same nerves. Roughly a third of this book is devoted to the electronics that tie the robot together and let it interact with the world around it. The single greatest thing that separates you from a cockroach (no offense meant) is your brain. Even if your body was that of a giant insect, if you still possessed your mind you would still be you. Remove your head and you become a rather messy meat machine. It is our brain that collects all of the sensory data, organizes it, records it, and then sends out commands in response to it. This is the control center. Inside of your own head, it probably all feels quite simple and easy. However, this is the hardest of all aspects of robotics and the one that has made the least progress. Artificial intelligence is a new field and it has worked very hard to make its mark in the world. While roughly a third of this book is devoted to the control of the robots, we can’t make them intelligent by any stretch of the imagination. Tools and Supplies You will get more from this book if you have the following supplies, in addition to your own creativity and imagination. The mechanical examples are all performed using the LEGO Mindstorms robotic invention system, version 2.0. CHAPTER 1 Introduction Table 1-1 Supplies LEGO Mindstorms Robotic Invention System Resistors (10 k , 100 k , 10 k potentiometer) Capacitors (0.1 mF, 1 mF, 10 mF) Inductors (various) 9-volt battery and battery clip Solid wire (22 gauge, high-gauge bell wire) 22 gauge solid wire Breadboard Solder Nail, large Tools Multimeter Pliers Soldering iron Speaker Stereo Tools and supplies 11 For the electronics experiments, it will help to have a soldering iron and solder, a prototyping breadboard, 22 gauge wire, small pliers, and a handful of resistors and capacitors, as well as a 9-volt battery and battery clip. Table 1-1 lists these supplies. Parting Words of Wisdom Once you turn to the next page, you will be immersed in a great sea of information. I have tried to make it all as simple as possible and, hopefully, no simpler. 12 CHAPTER 1 Introduction If you find the information too simple, keep going; it gets more complicated later. If you find the information confusing and difficult, remember this. A complex thing is just a collection of simple things working together. Learning how to build a robot is like eating an elephant, you have to ingest it one small piece at a time. The first few chapters provide a flood of new terms and their definitions. You don’t have to memorize them! Feel free to refer back to the chapter as you need. CHAPTER 2 Mechanical Forces Introduction Mechanics is not so much the study of the physical pieces of machines as it is the study of the forces that machines apply. Force is the result of some physical action and it does work. When you push something, such as a LEGO brick (Fig. 2-1), you are moving it, and this is work. While you are pushing the brick, you are also adding energy to it. Once in motion, the brick will remain in motion until some force pushes it in the other direction, taking energy away from the brick until it stops. If your brick is on a very smooth surface like ice, it continues to move after you stop pushing (Fig. 2-2). This is because the brick still has the energy that you put into it. The motion is in fact energy. A particular form of energy called kinetic energy. But why does the brick slow down and stop? Because it is rubbing against the ice and this takes energy away from it. This rubbing is called friction. We talk about all of these ideas in more detail soon. 13 Copyright © 2005 by The McGraw-Hill Companies, Inc. Click here for terms of use. 14 CHAPTER 2 Mechanical Forces Fig. 2-1. Pushing a brick. Fig. 2-2. The brick keeps moving on ice. Even something as simple as a flagpole (Fig. 2-3) is about force. What does the pole do except hold up the flag against gravity, and keep it from blowing away in the wind? Notice how these forces are all exactly balanced and the flag, except for its flapping, doesn’t go anywhere. This chapter introduces the important mechanical forces that we shall be working with. This is an important chapter, because we use these ideas and terms in later chapters as we describe machines. We also introduce a new way of thinking about numbers. Numbers are just numbers, right? And these numbers are used to describe things like the weight and length of an object, or the time it takes to cook a cake. CHAPTER 2 Mechanical Forces 15 Fig. 2-3. Flagpole forces. However, when you push something, you are pushing it in a particular direction. On a flat desk, this direction needs two numbers to describe it and together these two numbers, which each measure one piece of the direction, are called a vector. Directionless numbers, like time, are called scalars. Energy There are many different kinds of energy. The two we are interested in here are kinetic energy and potential energy. There is no such thing as energy. While an object can have energy, nothing can be energy. Even light and electricity are not energy. So what is energy? Kinetic energy is the energy of an object in motion. Kinetic energy is defined in terms of the object’s speed, or velocity, and how much stuff is in the object, or its mass. Mass is typically felt as an object’s weight. Potential energy is when an object doesn’t have kinetic energy yet, but could if it fell off the shelf. There are different kinds of potential energy. 16 CHAPTER 2 Mechanical Forces This type of energy is stored in the object, as height above ground, in the stretch of a spring, or in a chemical reaction waiting to happen. We’ll come back to these energies in a minute. First we need to define a few more fundamental concepts. Once we start putting these concepts together into mathematical equations, the names are going to get a bit bulky. Instead of using names, we identify each concept by its symbol. We shall be using one- and two-letter symbols for most terms, and sometimes these symbols are even going to be English letters. Greek letters, however, are very popular in math, so hopefully they don’t scare you too much. Note that we use the ‘Â’ for our multiplication symbol and division is represented by ‘/’ or, more often, by placing n the numerator above the denominator like . d Not only do we get new symbols to refer to things by, but these symbols are defined in particular units, which have their own symbols. You are already familiar with many units. For example, time can be measured in seconds, distance in inches, and weight in pounds. Units of Measurement Mechanics is a form of applied physics, and physicists don’t always use the units of measurement that we are familiar with. Before we define kinetic energy, let’s detour through the basic units we need to know. We look at both the metric and English systems of units here, to get a feel for how they relate. We use metric for all of our actual work. Units can be confusing. Even the names for the systems of units can be confusing! What we often call metric units are more correctly called the International System of Units, or SI from the French Syste`me International d’Unite´s. English units are also known as Imperial units, after the British Empire. Ironically, the United Kingdom has now moved almost entirely over to metric. We aren’t even going to think about the third system of measurement, Chinese units or Shı`zhı`. POSITION Everything has a position in both space and time. There isn’t a unit of measurement for position; however, many of the other units relate to the forces needed to change something’s position. CHAPTER 2 Mechanical Forces The position of an object is based on a measurement, the distance of that object from a fixed point of reference called the origin. Each measurement is taken in a particular direction, called an axis. For example, the distance to the right of the origin might be along the X-axis, and the distance behind the origin might be along the Y-axis. These measurements make up a coordinate, describing the position of the object. These concepts are explored in more detail when we discuss velocity. 17 TIME: t Seconds: s In both Imperial and SI units, time is measured in seconds. One second is one tick of your average analog clock, sixty seconds go in a minute, you know. A second. If you want to get really technical, a second is the duration defined by 9,192,631,770 oscillations of the light from glowing cesium 133 atoms, which can be really tricky to measure. LENGTH: l (Also, Distance: d ) Foot: ft Meter: m Closely related to position is length, or distance. Distance is the measurement in space between two different positions (Fig. 2-4). Fig. 2-4. Distance measurement. 18 CHAPTER 2 Mechanical Forces Imperial units define distance as the foot, which is in turn twelve inches long. A yard is three feet long. Your foot is that thing attached to the tip-end of your leg and, in fact, the original measurement of a foot was based on the average size of feet. SI units prefer to use the meter. The meter was originally defined as 1/10,000,000 of the distance around the Earth. One meter is 3.2808 feet long, or roughly a yard. Owing to the difficulty of getting an accurate measurement of the size of the Earth by walking around it, the meter was redefined as the distance between two very carefully marked lines on a particular bar of platinum– iridium metal in France. Today, the meter is defined as the distance that light can travel through a vacuum in 1/299,792,458 of a second. This relates distance m to time s, since light moves through a vacuum at the same constant speed everywhere in the universe. One of the great discoveries of science was that light moves away from you at the same apparent speed, no matter how fast you yourself are moving. This phenomenon is described in Einstein’s theory of relativity, and isn’t something we need to worry about for our relatively slow-moving robots. MASS: m Pound: lb Kilogram: kg The mass of something is, roughly, how much stuff it is made of. Technically, the count of the ‘‘stuff,’’ or molecules, in an object is the mole, used in chemistry. In the presence of gravity, mass is felt as weight. Without gravity, mass can be felt as an object’s resistance to pushing. The more mass something has, the harder you have to push to move it. To get a feel for mass, try rolling a bowling ball and then a marble. Neither object has much friction, but each one has a different mass resisting the push. Imperial measurement defines mass in pounds. One pound avoirdupois, to get really picky, is sixteen ounces. Troy pounds are different. And there are different definitions for ounce, as well. It can be really confusing, but usually when anyone talks about pounds of mass they all mean the same thing, our familiar sixteen-ounce pound avoirdupois. Mass in SI units is defined by the gram. Since grams are annoyingly small for everyday use, we use the kilogram, one thousand grams. ‘‘Kilo’’ is the prefix in SI that means ‘‘one thousand.’’ One kilogram is 2.2046 pounds. CHAPTER 2 Mechanical Forces 19 Fig. 2-5. Center of mass. The current definition of kilogram is defined by a carefully protected bar of platinum–iridium metal in France. Scientists would like to replace this bar of metal with a more universally accurate definition but haven’t been able to come up with a good one yet. An object has mass spread all over and through it. Since objects can be in all sorts of awkward shapes, it can be difficult to calculate how they will behave when pushed, unless we simplify them. For every object, there is a single point in space where the mass of the object is balanced in every direction. This is called its center of mass. In the presence of gravity, this is also known as the center of gravity, or COG. For a sphere, square, box, or other well-behaved and symmetrical object, this point is in the very center of the object. For more unusual shapes, such as the letter ‘‘C,’’ it takes a bit more math to find the center of gravity (Fig. 2-5). Once found, however, the object can be treated as a single mathematical point for many calculations. VELOCITY: v Feet per second: ft/s Meters per second: m/s Velocity is a derived unit. This means it doesn’t represent anything new, but combines base units to come up with a new concept. Time, length (or distance), and mass are base units. Velocity describes the change in position of something over time (Fig. 2-6). To describe velocity you need both a distance, in meters or feet, and the time measurement in seconds. Velocity is also known as speed. A velocity of 3 m/s means the object has traveled three meters in one second. It could also mean it moved six meters in two seconds, nine meters in 20 CHAPTER 2 Mechanical Forces Fig. 2-6. Velocity. Fig. 2-7. Single axis. six seconds, and so on. You assume the measurement is made across one second unless otherwise specified. Once an object is moving, it stays moving until another force acts on the object to make it stop moving. This is Newton’s first law of motion: A body must continue in its state of rest or of uniform motion in a straight line, unless acted on by some external force. Note that an object doesn’t just move, but it moves in a direction. If you are pushing beads on a wire, there is only one direction they can move, along the wire. Technically, there are two directions, back and forth along the wire. This wire, with its constrained direction of motion, can be thought of as one-dimensional, since there is just one dimension or direction of motion, along the wire. The wire itself is an axis (Fig. 2-7). When you are pushing blocks on your desk there are two parts to the direction it can move: left/right, also called the X-axis, and toward/away from you, the Y-axis. This is a two-dimensional space, and the axes are directions along the desktop (Fig. 2-8). Each axis is perpendicular to the other axes. Distance along a wire is described by a single number, the distance from the start. Distance on a desktop, however, needs two numbers to describe, the distance between two positions along the X-axis and the Y-axis (Fig. 2-9). These are considered part of one measurement, a two-dimensional vector. If this distance describes two positions of the same object, it describes the two-dimensional motion (Áx, Áy). The Greek Á, called ‘‘delta,’’ represents a change or difference in some value. Therefore Áx represents the change in position along the X-axis. Another way _ to represent a change in position is to put a single dot over the value, x. CHAPTER 2 Mechanical Forces 21 Fig. 2-8. Two-dimensional space. Fig. 2-9. Two-dimensional motion vector. Given the distance along X and the distance along Y, you can calculate the distance d between the two points. When the distance represents motion, it is a vector. When this motion is considered across a measured span of time, it defines a velocity: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d ¼ x2 þ y2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v ¼ Áx2 þ Áy2 ð2-1Þ 22 CHAPTER 2 Mechanical Forces If you can lift objects off the desk, there is a third axis that points straight up from the desk, the Z-axis (Fig. 2-10), perpendicular to both X and Y. Z adds a third number to the vector, making it a three-dimensional vector. Another word for each number, x, y, or z, in a vector is ordinate. While the motion of an object in space is a vector, the position of an object in space is called a coordinate (Fig. 2-11). A coordinate specifies the distance of an object from an arbitrary, predefined point in space called the origin. The origin is normally described as being at position x ¼ 0, y ¼ 0, z ¼ 0 or (0, 0, 0) (Fig. 2-10). All positions in space are then distances from this origin. The whole package, the three axes plus the origin and the units used to measure it, is called a coordinate system. In this case, the Cartesian coordinate system. There are other systems of position, such as the polar coordinate system, not used here. Fig. 2-10. Three-dimensional space. Fig. 2-11. Ordinates in a coordinate. CHAPTER 2 Mechanical Forces ACCELERATION: a Feet per second per second: ft/s2 Meters per second per second: m/s2 Like velocity, acceleration is a derived unit. Also like velocity, acceleration occurs in a particular direction. Acceleration is a change in velocity over time. For example, step on the gas of your car or drop a ball and its velocity increases over time. Acceleration can be in terms of meters or feet, since it relies on a distance measurement. Since acceleration is the change of velocity over time, and velocity is itself a change in position over time, acceleration is the change in position over time over time. This is why we use symbols. It is much easier to say this with the mathematical statement: a¼ d s2 ð2-2Þ 23 While velocity is easy to visualize, what exactly is a change in position over time squared? What is square time? This question doesn’t have an intuitive answer. Acceleration isn’t motion, but a change in motion. It is the result of a push against an object. Where the position of something might be described _ symbolically as x, and the change in position, or velocity, is Áx or x, the € change in velocity adds a second dot to become Á(Áx) or x. Gravity is an acceleration. The force of gravity on Earth is constantly trying to accelerate everything on Earth at a rate of 9.80665 m/s2 toward the Earth’s center. This acceleration is the gravitational acceleration constant g. What this means in practice is that if you drop something, it falls. In fact, if you ignore wind resistance by dropping something in a vacuum or by dropping a heavy, round ball, that ball will accelerate at 9.8 meters by each second, squared. At the start of the fall, it isn’t moving and at the end of the first second, it will be moving at the velocity of 9.8 m/s. The average velocity, from zero to 9.8 m/s, is actually half that amount, and the ball has only traveled 4.9 meters. But it’s still speeding up! At the end of the second second, it is traveling at 4  9.8 ¼ 32.9 m/s. The average velocity is still about half that. Each second it falls, the object gets faster and faster—until it hits ground. Then, typically, it breaks (Fig. 2-12). Starting from a dead stop, you can calculate how far the ball has fallen using this equation, where d is the distance traveled and t is the time in 24 CHAPTER 2 Mechanical Forces Fig. 2-12. Acceleration. seconds of the fall: d¼ a  t2 2 ð2-3Þ FORCE: F Pounds force: lbf Newtons: N ¼ kg  m/s2 Generally speaking, force equals mass times acceleration, F ¼ m  a. Note that this is the ‘‘mass’’ m and not the ‘‘meters’’ m. Just a few definitions into the list of physical formulas and we already find another meaning for pounds: pounds as a pushing force, the force of whacking a nail with a hammer. The pound is definitely overused and will be ignored here. From this point forward, we will abandon the Imperial units and talk only in terms of SI units. Let’s talk about Newtons, and not the figgy kind. The SI unit of force is named after Isaac Newton. Newton’s second and third laws of motion relate to the force applied to an object. Newton’s second law is: Change of motion takes place in the direction of the impressed force, and is proportional to it. CHAPTER 2 Mechanical Forces Or, when you push on something, it moves in the direction of the push. How much your push changes the object’s motion depends on how hard you push. Newton’s third law of motion is: Action and reaction are equal, and in contrary directions. 25 So when you push on an object, such as a bowling ball or marble, you feel an equal force pushing back at you from the object. A Newton is practical acceleration. Pure acceleration is a bit too abstract for solid objects. Sure, gravity can get away with accelerating everything like magic. But when you push on it, a LEGO brick moves differently than a car. To get the same velocity out of the car, you have to push it a lot harder than the plastic brick. The difference lies in the mass of the object. The more mass, the harder you have to push it to accelerate it at the same rate as the lighter object. As far as acceleration is concerned, it doesn’t matter how hard you had to push to get to a speed. But your muscles care. The Newton measures how hard and how long you have to push to get an object moving to a certain speed, or to get it to stop moving. It measures force. The other side of force is how much energy a moving ball, for example, transmits to your head when it hits you. (Kids, don’t try this at home. No, not even with your kid brother.) A sponge ball traveling at 10 meters per second won’t hurt much. A baseball, with more mass than sponge, thrown at the same speed, will hurt. A lot. It’s not just the speed and mass of the object that matters. It’s how hard your head had to push against it to accelerate it in the opposite direction and stop it. Not only that, but how quickly your head stops the ball makes a big difference. Being a bit more sensible about catching baseballs, let’s use a baseball mitt. If someone throws the ball at you and you hold your hand stiffly so it doesn’t move, the ball will stop quickly and it will hurt. If you let your hand travel with the ball a bit, cushioning the blow with the motion, it’s much less painful. In the first case, you reverse-accelerate (decelerate) the ball all at once, which requires a lot of force in a small amount of time. In the less painful catch, the same total amount of force is needed, but since it is spread out over more time there isn’t as much force during each moment. It’s like the difference between the pain of pushing the sharp end of a thumb tack into your finger and what you feel from the flat end on the finger doing the pushing. Deceleration is just acceleration, but in the opposite direction of an object’s current direction of travel. 26 CHAPTER 2 Mechanical Forces MOMENTUM: p p ¼ kg  m/s Momentum is closely related to force. Where force is tied to the acceleration of the object, momentum uses its velocity. Momentum is defined as mass times velocity, p ¼ m  v. ENERGY: E Joule: J ¼ kg  m2/s2 Finally, we have reached the last definition in this section. It’s been a thick few pages to this point, but we needed all of the above to finally be able to define energy, also known as work. The unit of energy is the Joule, which is defined as force across a distance: J¼NÂm ð2-4Þ Lifting an apple above your head is work and it adds energy into the apple. As the apple is in motion, your hand is accelerating it upward and, as the apple accelerates, it gains velocity and momentum. Once it’s above your head and gravity decelerates it to a stop against your palm, it loses its velocity and momentum. However, it has gained potential energy. When you drop the apple, all that work you put into it is undone as it regains its velocity and momentum (thanks to gravity’s acceleration) until it hits the floor. And, typically, it breaks, making a mess. Be sure to clean up after trying this one. Kinetic energy: KE KE ¼ m  v2 2 ð2-5Þ Kinetic energy is the energy stored in a moving object. Note the similarity of kinetic energy to momentum. Kinetic energy is one half of the mass times the square of the velocity. Make an object move twice as fast and it has four times the energy. This is related to the squared time factor from the acceleration that pushed it to this velocity. CHAPTER 2 Mechanical Forces Potential energy: PE Where kinetic energy is the energy of a moving object, potential energy is the energy that is hidden in the object’s situation, waiting for an opportunity to become kinetic energy. There are actually different kinds of potential energy. An object held high above the floor and against gravity has a bunch of potential kinetic energy. The amount of potential energy due to gravity is calculated as the mass of the object times the acceleration of gravity and its height above ground: PE ¼ m  g  h ð2-6Þ 27 However, there is also potential chemical and electrical energy in a battery, and a different 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. Storing Energy 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 different types of springs: long flat 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 effective at extremely small distances. Note that there are other atomic forces that push the atoms apart. 28 CHAPTER 2 Mechanical Forces 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 ¼ Àk  l ð2-7Þ k is the spring constant, which describes how ‘‘springy’’ the spring is, and l is how far the spring has been stretched or squished (Fig. 2-13). The spring’s force pushes in the opposite direction of the force used to deform it. The spring’s stored force exactly matches the force it took to deform it. The same with a rubber band, though rubber bands are only useful in the stretch direction. In robotics, you can use the force stored in a spring or rubber band to push against the acceleration of gravity, to make it easier for the robot’s motors to lift something. Springs can also be used to hold something in position, to keep it from moving. Fig. 2-13. Spring forces. CHAPTER 2 Mechanical Forces 29 Losing Energy Energy is never really ‘‘lost,’’ it is only shuffled around into different forms. Kinetic energy is converted into potential energy, which might be stored as deformation in a spring or as a displacement against gravity. These might eventually be turned back into kinetic energy. So energy changes form, but it never goes away. So why does the brick stop moving when you push it across your desk? Where is the kinetic energy going? The energy you are adding to the brick is being lost into the desk through friction. Friction is what we call the process of transferring energy by rubbing things together. The force of friction always appears to act in the opposite direction of the kinetic energy causing the friction. Because of this, an object rubbing against another object slows down and stops. There are two kinds of friction. An object at rest on a surface has a higher friction than an object that is already moving. The stationary, or static, friction force is called stiction. When you press on the brakes in your car, the force holding the wheel to the road is this stiction. Once you start skidding, the lesser force of friction takes over. Once the wheels start to get hot and melt, it gets even more difficult. Friction can be an extremely complicated thing, especially if either of the objects being rubbed together are sticky, fuzzy, oily, or otherwise not dry and smooth. Plain vanilla friction is molecules, by way of their atomic forces, banging against each other. Let’s look down into the atoms of the object and see what this banging means to them. Everything that you come into contact with has heat. Heat is a form of energy and, in fact, it is a form of energy stored by motion. Each atom within an object is not just sitting there quietly but is vibrating madly against the springy forces that keep it from escaping. This vibration is described as the heat of the object. The faster the atoms in an object are moving, the more energy it is storing; it’s hotter. Of course, if something gets too hot, the atoms get enough energy to break their springs and they escape. At one temperature the springs are only mostly broken, so the object doesn’t hold together as firmly and its atoms are pulled down by gravity. It melts. Get it even hotter and the atoms have enough energy to jump up away from gravity’s pull and the attraction of its neighbors and the object evaporates, or becomes a gas. Of course, like almost everything else in this book, it’s a bit more complicated than that. But you get the general idea. When you hold a hot object against a cold object, the atoms in the hot object bang into the atoms in the cold object, making the slower atoms move 30 CHAPTER 2 Mechanical Forces faster and the faster atoms move slower. Some of the energy is transferred so that both objects come closer to having the same amount of energy. It is as if the heat flows from the hot object to the cold one. When you push a block across the table, the atoms in the block are banging against the atoms in the table. This takes some of the kinetic energy, which is an energy of motion on a large scale, and transfers it into the motion of the individual atoms in the table. These microscopic interactions also make the atoms in the block vibrate faster in their springy cages, so some of the block’s kinetic energy is transferred to its own atoms as heat. Both the desk and the block heat up and kinetic energy is lost. The total energy is the same, it has just changed from one form (motion) to another (heat). Even when you squeeze or stretch a spring there is friction, only this friction is inside the spring. Some of the force you apply to the spring turns into heat as the spring moves. You can feel this internal friction yourself with a coat hanger. Get a wire coat hanger that nobody will mind you breaking. Now, grab it firmly in both hands and make a sharp bend in it. Now bend it back the other way. Do this a few times quickly, and the bend will become very hot. Do it enough, and the hanger breaks. We normally want to preserve the kinetic energy of an object and keep it from being converted to heat. Motion is useful and, unless you are cooking something, heat is not. There are different ways of doing this, such as lubrication or ball-bearings. We’ll look at these friction-reducing ideas later. Summary In this chapter, we introduced a bunch of mechanical forces, their meaning, and symbols to represent them. We learned how to describe something’s position in space and its distance from another object. We learned about the energy in moving objects as well as the force and energy needed to change an object’s motion, not to mention the difference between force and energy. Finally, we took a look at storing energy in springs and how energy is lost through friction. Quiz 1. If a ball dropped on planet Earth takes a half second to hit the ground, how high was it dropped from? CHAPTER 2 Mechanical Forces Bonus: If you drop a ball from 3 meters (about 9 feet) above ground, how long does it take to hit? What does it look like if you graph the results of these tests? One graph would show how far the ball falls for a range of times. Another graph would show how long the ball takes to fall a given distance. 2. Take a half-kilogram ball (about a pound) and throw it at 10 meters per second at a wall (NOT someone’s head). Assume the wall takes 1/10 of a second to stop the ball. What is the force applied to the ball over that tenth of a second? What if the wall was really soft and took 1/4 second to stop the ball? 3. What is the kinetic energy of this half-kilogram ball moving at 10 meters per second? What if it were moving at 20 meters per second? Try graphing the kinetic energy of the ball at different velocities. 4. If you carry this poor, abused half-kilo ball to the roof of your building, which is 4 meters high, how much potential energy does it now have? What does all this have to do with robots? Lots! Say you had a 10 kg robot that was trying to climb a 10 degree hill. How much push (acceleration) does it have to have to make it to the top? If the hill is 100 meters high, how much energy was expended to get it there (think potential energy)? You don’t have enough information to answer these robot questions yet, but you will soon. 31 3 CHAPTER Simple Machines Introduction Now that you have had a chance to meet the relevant physical forces, we can start playing with them. The basic set of mechanisms for manipulating force are known as the simple machines. Variations on these simple machines are the base components used by more complicated machines. Robots, for example, are built up from many of these simple machines working together. Before looking at moving mechanisms, we look at the strength of structures that don’t move. There are two branches to mechanics. One is statics, which is the study of objects that aren’t moving. Though there are forces applied to a static object, those forces are balanced so there are no continuing changes in shape or position. The other branch is dynamics, which is the study of objects in motion. Dynamics is further divided into kinematics and kinetics. Kinematics is the study of mechanical motion without worrying about the forces behind it. The shape of the motion. Kinetics then studies the forces driving the motion. 32 Copyright © 2005 by The McGraw-Hill Companies, Inc. Click here for terms of use. CHAPTER 3 Simple Machines In this book, we are not going to be concerned with this breakdown, though most of our work is related to dynamics. After a brief introduction on how to build models that hold together instead of fall apart, we investigate some of the variations available in ramps, or inclined planes, levers, and wheels. These devices, and the others that are related to them, all provide methods of trading speed for strength. For example, how is it that one person can lift a car engine with their hands? On the one hand, we have an engine that weighs, for example, 200 kg (over 400 lb); on the other hand, an average person who is going to be able to lift a quarter of that amount, at best. The person could lift that engine, though, using simple hand-powered machines. Remember that force operates over time, and energy is the application of force across space. What we do is use a small amount of force over a long period of time and a long distance. We can add up this long, drawn-out force up and use it to lift an engine a short distance. Essentially, what the simple machines do is let us trade distance for force. This is also known as using mechanical advantage. As a side effect, we trade time for force. Moving something twice as far to get twice the force at half the distance is also going to take more time. So, read on to learn how to convert distance and time into superhuman strength. We also introduce a few more terms as we need them. 33 Structural Strength There is a whole study of the strength of materials and structures known as mechanical statics. Engineering classes spend a lot of time on this subject, since we prefer our bridges to remain standing and our buildings vertical. For our purposes, however, there is one simple principle to learn: Triangles are strong. Everything else flows from this, even if it’s not obvious. Let’s look at triangles and squares in general. Then we can look for the hidden triangles in a few structures. TRIANGLES AND SQUARES Different shapes have different strengths, just because of the shape. A shape will also have different strengths depending on how force is applied to it. 34 CHAPTER 3 Simple Machines For example, look at your basic drinking straw. If you squeeze it from end to end, pushing through the straw’s length, it’s pretty strong. But grab both ends and bend it and it folds up with no effort. For another example, look at a ruler. If you place it flat on your desk so that half sticks out over the edge, you will find that you can easily bend the ruler down. However, turn it so that the skinny edge is against the desk and you will find it much harder to bend down. In fact, it will twist before it bends. To look at the intrinsic strength of squares and triangles, we need to build each of these shapes with hinged corners (Fig. 3-1), so that the corners can bend. If you push down on a square, straight down on the top, it’s pretty strong. The force is sent down the sides and into the ground, or bottom edge. The force passing straight through the sides is called compression and the rods are very strong under compression. If the force goes to one side even a little bit, the corners bend and the shape folds up flat. It has no built-in strength in the side-to-side direction. When you push on the point of a triangle the force is passed down the center of its edges, compressing them, and into the joints at the other side. At the other side the force pushes out at the joints, which pulls on the bottom bar. This pulling force is tension, and these bars are also very strong under tension. At no time do the joints of the triangle rotate and let the shape collapse. The edge rods or pivot pins will break first. This is what I mean when I say that triangles are strong. The shape has strength built into it. Another strong shape is the circle, because force at one edge tends to be redirected around the edge into compression. You see circles in action in arches, eggs, and domes. Fig. 3-1. Strength of shapes. CHAPTER 3 Simple Machines A third force, not illustrated here, is applied by scissors to paper. This is the shear force. I mention it only to be complete. The forces, compression, tension, and shearing, all cause stress in an object. There is a lot that can be said about the static strength of structures. We looked at just two cases using a hinged link. There are other shapes, and other ways of fastening the pieces together. And then there is the math behind it all. However, we can safely ignore most of those details. 35 HIDDEN TRIANGLES When you nail two long boards together with one nail, that nail makes a nice pivot point, allowing the two boards to rotate at that point, resisted only by friction. But what happens when you put two nails into the boards? This keeps them from rotating, so these nails should act to make the square strong. Doesn’t this break the rule of triangles? No, because that second nail defines a triangle (Fig. 3-2). When you get to the section on levers, you will see that the strength provided by that nail triangle is actually pretty small. Your house is probably made up of squares, and yet it doesn’t fall down on you. What makes a wall strong? The wall’s covering, sheetrock on the inside and plywood and decorative materials on the outside. This covering Fig. 3-2. Hidden triangle in two boards. 36 CHAPTER 3 Simple Machines Fig. 3-3. Hidden triangle in a wall. defines giant triangles in the wall. An open wall with just a diagonal brace will be almost as strong as a covered wall (Fig. 3-3). There are times when you won’t find a hidden triangle in your structure, such as in the construction in Fig. 3-4. This is when you look for levers. When you build your machines, you want to do so with a keen eye to the triangles and levers in it. Engineering statics is a complicated subject. Simplifying it down to triangles and levers, however, makes it about as simple as it can be while still being useful. Inclined Plane The inclined plane, a simple ramp, is the simplest of the simple machines. You use it when you walk up a hill. If you have a large hill in your town, think about how much easier it is to walk up a path to the top than to have to climb straight up a wall of the same height. This is the inclined plane in action. There are different ways to think about the inclined plane. We shall look at how it helps us raise objects against the acceleration of gravity first. Starting with an object on the ground, gravity is accelerating it down at the brisk rate of 9.8 m/s2. The force developed by this acceleration is directed straight down into the ground (Fig. 3-5). What happens when you put that same object on a slippery slope (Fig. 3-6)? Assuming there is no friction, it will slide down to the bottom of the ramp. While gravity is accelerating the block straight down, the ramp is in the way. CHAPTER 3 Simple Machines 37 Fig. 3-4. Hidden lever. Fig. 3-5. Gravity pushing a block down. At this point, the force from gravity is split into two parts. Each of these two parts describes a direction. The force of gravity is directed down, which makes it the force direction. This acceleration can be described by its own vector. In our simplified, twodimensional world, the X ordinate in the vector is the amount of acceleration 38 CHAPTER 3 Simple Machines Fig. 3-6. Block on a ramp. side to side. The Y ordinate is the acceleration straight down. The overall length of the vector gives the strength of the force. In this case, the gravity vector would have a length of 9.8, representing gravity’s 9.8 m/s2 acceleration. Now for the two force vectors as applied to the block on the ramp. One force vector, the perpendicular vector, points directly into the ramp’s face and creates friction. The other force vector, the parallel vector, points along the face of the ramp and is the force that moves the block down to the ground. The relative size of each force vector depends on the angle of the ramp,  (theta, sometimes shown in the capitalized form È, and which often represents an angle). The perpendicular force vector has a length of g  cos  and the parallel vector a length of g  sin . The sine function starts at zero and increases to one as the angle increases to 90 degrees. When the object is flat on the ground, the parallel force is zero. If the ramp is in fact a wall (Fig. 3-7), the parallel force is one. The cosine function is the reverse, starting at one. For a ramp at a 30 degree angle, the perpendicular acceleration is 8.43 m/s2 and the parallel acceleration is 4.9 m/s2. Most of the force is being applied to friction, but still half of it is applied to moving the block. Wait a second. Those numbers don’t add up to 9.8 m/s2! Right, because the parallel and perpendicular vectors don’t add up to the same length as the gravity vector. Instead, they are appended to each other, making half of a box around the gravity vector. If you fill in the box, as shown in the corner of Fig. 3-6, you can see the relationship. Gravity cuts the corner across the box. CHAPTER 3 Simple Machines 39 Fig. 3-7. Block on a wall. The relationship is described by the Pythagorean theorem, which states: a2 þ b2 ¼ c2 ð3-1Þ where a and b are the lengths of the parallel and perpendicular sides, and c is the hypotenuse, or long side described by gravity in our example. Other ways to show this relationship are: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c ¼ a2 þ b2 ð3-2Þ a¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c2 À b2 ð3-3Þ Note that this is the same relationship used to calculate the distance between two points, used in the section about velocity in Chapter 2, and equation (3-2) is the same as equation (2-1). Now, back to the ramp and how it changes our use of force. When you push an object across the floor, you only have to counteract its friction and momentum. Ignoring friction, we are only acting against the mass of the object. Lifting the object straight up, we act against the full force of gravity. When we push the object in the direction of the ramp, we are only pushing against the parallel force. Remember that we are ignoring friction, which is a function of the perpendicular force. For a very shallow ramp angle, there is almost no parallel force, and it is easy to push the object up the ramp against gravity. However, it doesn’t get 40 CHAPTER 3 Simple Machines very far off the ground unless we push it a long ways. Lifting straight up, all of the motion is up but it’s much harder work. This is where we are trading side-to-side motion for force. The farther we push an object to raise it a certain distance, the less force we have to use pushing it but the longer we have to push. WEDGE A wedge is essentially an inclined plane in portable form (Fig. 3-8). Instead of gravity pushing, we apply our own force. Looking at the wedge, if its sides are at 45 degrees to the towers, then for every meter we push it into the gap, it pushes outward by one meter. This just redirects the force and doesn’t make the pushing any easier. If the wedge is long and skinny, however, so that for every two meters you push it down it pushes out one meter, it has a mechanical advantage of 2. Fig. 3-8. A wedge for mechanical advantage. CHAPTER 3 Simple Machines You have to push it twice as far, but it generates twice as much force outwards. In the diagram in the corner of Fig. 3-8, you can see that the wedge is just a ramp on its side. The height of the ramp h is the width of the wedge and the length l is the length of the wedge. The mechanical advantage (MA) is defined as: MA ¼ l h ð3-4Þ 41 In terms of energy, we haven’t done anything except rearrange some terms. Remember, energy is just force in Newtons applied across distance. We have the energy we are putting into the wedge, Ein, and the energy the wedge is putting into the towers, Eout. The relationship is defined as: ðMA  Eout Þ Â m ¼ Ein  ðMA  mÞ ð3-5Þ where m is distance. On one side, the mechanical advantage adds to the output force. On the other side, we have to move the wedge that much farther. Another way to look at it is as:   F ð3-6Þ E ¼ ðm  MAÞ Â MA where E is the energy, or work being done, and m is still distance. The mechanical advantage MA just shifts the focus of our efforts from the force being applied to the distance we have to move to apply it. The wedge is a different way of looking at the inclined plane. A third look is the screw. SCREW A screw is an inclined plane wrapped around a tube. We see the screw shape in bolts, screws of course, and worm gears. The screw puts the inclined plane into a very compact form. The angle of the plane can be low and we can get a lot of force out of it. This force is applied by turning the screw, which is essentially the same thing as moving a block up the ramp or driving a wedge into a gap. Einstein said that all motion is relative, and whether the resistance (the block or tower) moves, or the inclined plane (ramp, wedge, screw) moves, the effect is the same. 42 CHAPTER 3 Simple Machines Levers A lever is another way to apply mechanical advantage. Though the lever is a more complicated machine, it can be described with simpler math than the inclined plane. LEVER MACHINE Try This: For levers, let’s build a LEGO lever machine. In the fine tradition of these types of projects, the construction steps are depicted in pictures, shown in Fig. 3-9. The last step, and an informative example showing range of motion, is in Fig. 3-10. Pushing down on the long arm of the lever creates an upward force on the short arm. While the long arm moves four times as far, the short arm creates four times the force. You can hang weights at different points on this machine to get a feel for how it works. How does it feel when you hang the weight on the long end Fig. 3-9. Building the lever. CHAPTER 3 Simple Machines 43 Fig. 3-10. LEGO lever. Fig. 3-11. First-class lever. instead of the short end? Try the weight at different positions and see how it affects the force and range of motion. A formal description of the lever is given in Fig. 3-11. This lever is known as a first-class lever. All levers have the same three pieces. The pivot in the middle is the fulcrum. The distance from the fulcrum to where the input force, or effort (E), is applied is the effort arm (dE). The distance from the fulcrum to where the force is used is the resistance arm (dR). The lever is applied against resistance 44 CHAPTER 3 Simple Machines Fig. 3-12. Second-class lever. Fig. 3-13. Third-class lever. (R). If dE is larger than dR, then your force is increased. The mechanical advantage is calculated as: MA ¼ dE dR ð3-7Þ Equation (3-7) is essentially the same as equation (3-4) for the wedge. Though we look at several different simple machines, each with their own approach to increasing force, the principles behind each one are the same. Force is force, and the rules governing force are not going to change. If we seem to be getting more force at the output of a mechanism, somewhere inside it we are spending velocity or distance to get it. A second-class lever is shown in Fig. 3-12, and a third-class lever in Fig. 3-13. These have the same pieces as a first-class lever, just in different positions. Note that the third-class lever has you pushing harder to get greater distance, backward from the first and second-class levers. Your arm is a third-class lever with your elbow at one end, your wrist at the other, and the muscle attached in between. Pulleys A pulley is essentially a wheel. Where a wheel wears a skirt of rubber so it has a lot of friction, the pulley has a groove for a rope around its edge. Pulleys are designed so they don’t add much friction to the machine they are a part of. Methods for removing friction are explored in a later chapter. CHAPTER 3 Simple Machines 45 Fig. 3-14. Pulley. A pulley provides an easy way to change the direction of motion, as shown in Fig. 3-14. When you pull down on the rope, the force is used to lift an object. The pulley itself is fixed into position so that it can rotate but not travel. PULLEY MACHINE Try This: Building a pulley machine starts out the same as for the lever machine, as shown in Fig. 3-15. Instead of a pivot for the lever, however, we put in an anchor to tie our string to. We don’t use this anchor yet. The pulley itself snaps onto the other side of the tower, as shown in Fig. 3-16. You can experiment with this pulley, though its operation is fairly obvious. The fun begins when we begin to make pulleys behave like levers, to amplify our strength. To double our strength, we need to find a way to pull twice as much rope while making the weight rise the same distance. This could look like Fig. 3-17. The new pulley is not fixed into position, but travels with the 46 CHAPTER 3 Simple Machines Fig. 3-15. LEGO pulleys. Fig. 3-16. Single pulley. CHAPTER 3 Simple Machines 47 Fig. 3-17. Double pulley. weight. The weight helps to keep this pulley on its rope. The end of the rope is anchored somewhere near the fixed pulley. When you pull down on the rope you have a two-to-one mechanical advantage. The mechanical advantage is the number of times the rope goes between pulleys, or the pulleys and the anchor point (not counting the rope you are pulling). In this case, we have two passes. Your pull on the rope must be divided between these two sections, doubling your force and halving the weight’s travel distance per pull. You can build a weight for the LEGO pulley as shown in Fig. 3-18. The wheels on the little cart provide some heft. To get an even better feel for the action you can replace them with metal washers or some other heavy thing. Tie a length of string to the anchor bar (it may be easier to do this if you remove it first). Run it straight down and under the lower pulley. Run the string back up and over the top pulley. When you pull the string down, the weight will rise up. You can add another pass to the system, giving you a mechanical advantage of three (Fig. 3-19). To test this, you need to add another pulley to your machine. 48 CHAPTER 3 Simple Machines Fig. 3-18. LEGO weight. Note that our load cart has the two pulleys on the same shaft. Putting pulleys together like this makes a pulley block, and it’s an easy way to stack pulleys to get greater mechanical advantage. If you added more loops, you would add pulleys to the top of the machine, too. With each loop you reverse the direction that you need to pull to raise the weight. It’s normal to have an even number of loops and pulleys so you pull down to raise the weight up. This combination of pulley blocks and rope is known as a block and tackle, where the block is the set of pulleys and the tackle is the rope. CHAPTER 3 Simple Machines 49 Fig. 3-19. Triple pulley. Wheels and Torque  ¼ kg  m2 =s2 We already mentioned that a pulley is a form of wheel. Left to itself, a wheel’s job is to roll. The wheel is a great invention that we use to reduce the friction of moving objects. It’s much easier to roll a car on its wheels than to drag it on its frame. Not all wheels simply roll. Some wheels push. And, of course, the ground pushes against them. What do these forces look like (Fig. 3-20)? Where the rubber meets the road, a powered wheel pushes against the ground. This force moves the wheel, and whatever it is attached to, forward. Or, in some cases, the wheel could be fixed and the ‘‘ground’’ could be forced to move— it’s all relative. The distance from the center of the wheel to the edge is called its radius, represented by the symbol r. 50 CHAPTER 3 Simple Machines Fig. 3-20. Wheel. If you draw a line from the center of the wheel to the ground, it looks a lot like a first- or second-class lever. The catch is that the point of effort on a powered wheel is at the same spot as the fulcrum, or pivot point. This gives an effort arm of zero, and yet the wheel moves. If we try to spin the wheel from its edge, the point of resistance is at the center. A zero resistance arm is even harder to solve for in our mechanical advantage equations. So how do we deal with this impossibility? We add a new force. The force of a wheel turning around a single point is called torque, and is usually represented by the Greek letter  (tau). The raw calculation of torque was given at the head of this section,  ¼ kg  m2/s2, which is the same relationship that defines energy in Joules. In other terms, it is  ¼ m  (kg  m2/s2), also known as  ¼ m  F. The m is for the radius of the wheel in meters, and F is the force applied at the edge of the wheel. The same equations work if the wheel isn’t round but is in fact a lever attached to a shaft. The wheel is a continuous, rotating lever. If you push on the edge of a wheel with a force F, the torque you create depends on the radius of the wheel:  ¼FÂm ð3-8Þ If the wheel is being powered with a given input torque , the push at the edge of the wheel is:  ð3-9Þ F¼ m where m is still the radius in meters. CHAPTER 3 Simple Machines 51 Gears and Sprockets A gear is a wheel with teeth in it so it won’t slip as it rubs against another gear. Two or more gears connected together make a gear train. Gears may also push against a toothed bar, called a rack, making a rack and pinion. The gear is called a pinion in this application (Fig. 3-21). Two gears in a train convert torque from one shaft to force where the gears meet, and back to torque in the other shaft. This makes the gear train a rotary lever, with its mechanical advantage calculated from the radius of the gears. Any number of gears can be paired together like this, in many clever arrangements. Some of these are explored in Chapter 9. When you select gears and calculate the mechanical advantage of a gear train, you don’t use the gear radius, you use the tooth count. The number of teeth on a gear is directly related to its radius by way of the circumference. The circumference of a circle, including gears, is: c¼2ÂÂr ð3-10Þ The Greek symbol  (pi) is a ‘‘magic number’’ that represents the ratio of a circle’s circumference to its diameter. Pi has a value of about 3.14, though the numbers after the decimal point never come to an end. The diameter of a circle is simply the distance all the way across, or twice the radius. Fig. 3-21. Gears and sprocket. 52 CHAPTER 3 Simple Machines The mechanical advantage generated by two gears is the ratio of the number of teeth on the output gear A to the teeth on the input gear B: MA ¼ A : B MA ¼ A B ð3-11Þ Since the number of teeth is directly related to the gear’s circumference, MA ¼ Cout Cin ð3-12Þ If you stretch the circumference of the gear out flat, you have a rack. While it is flat, it is easy to see that the number of teeth you can fit onto the circumference depends on the width of the teeth and the distance between the teeth. The size of the teeth is called the pitch of the gear. The larger the teeth, the stronger they will be but the less you can fit onto the gear. The pitch on two meshed gears must be the same. The shape of a gear’s teeth is specially designed to give the gear a smoothly adjusting contact between the meshed teeth at all times. Many gears can be squeezed into a small space, often with two gears sharing a single shaft. These gears can change huge amounts of distance, in terms of the rotation of the input gear, into huge amounts of torque on the output gear. A sprocket is a gear designed to mesh with the links of a chain instead of with another gear. The chain travels through space and meshes with a different sprocket. Sprockets and chains are one method of sending force a long way away. They are commonly used on bicycles. Sometimes a pair of pulleys are used like sprockets, with a tightly-fitting rubber belt stretched between them instead of a chain. These are easy to make and are used on power tools and other equipment to transmit force. Pulleys and belts are quieter than chains, though they can slip. Sometimes you want things to be able to slip, so if the machine gets stuck force is lost in the slipping instead of breaking your machine. Inside your car you can see a pulley and belt arrangement. The pulley and belt both have large, square teeth. These prevent the belt from slipping, so you get many of the best features of chains and toothless belts. These toothed belts are often called timing belts, while the toothless ones are v-belts, since they tend to have sloping edges giving them a ‘‘V’’ shape. CHAPTER 3 Simple Machines 53 Summary In this chapter we looked at many ways to make yourself stronger. The simple machines let you turn a long, easy push or pull into a short, yet powerful, force that can lift or move an object. All of the simple machines are based on this principle of mechanical advantage. The simplest machine is just a hill, or inclined plane. A portable inclined plane is a wedge. A spinning wedge is a screw. A different approach to mechanical advantage is given by the lever and by pulleys. Wheels, we learned, are like rotating levers and have their own force, torque, assigned to them. Gears and sprockets are toothed wheels that can be combined in large numbers to give a lot of mechanical advantage in a small space. Quiz 1. If you wanted to study the forces acting on your robot when it is standing still, what would you study? How about when it is in motion? 2. What force is involved when you cut a sheet of paper with scissors? When you crush a grape? When you break a string? 3. Remember that robot trying to climb a 10 degree hill? As it is being pushed up the hill, how hard is gravity pulling against the push? 4. What kind of lever is your knee a fulcrum of ? Your ankle? 5. You have a gear with twenty-five teeth, each of which takes 1/8 of an inch (eight teeth per inch). How big is your gear? If you mesh it with a gear that has a 4.97 inch diameter, what is the mechanical advantage? 4 CHAPTER Electricity Introduction The study of electricity and electronics is the study of the electron and proton, the fields surrounding them, and how we affect their behavior. The electron and proton are both charged particles, since they carry an electric charge. The electron is the key player in most electronics studies, since in metals it is the electron that moves around. A charged particle at rest has an electrical field around it, radiating into space. A charged particle in motion generates a magnetic field. These fields are normally studied together as the electromagnetic field, since they are parts of the same thing. Electronics are the nervous system of the robot, replacing the mechanical gears and cams of the automata with wire and whizzing electrons. This chapter introduces you to the electrical and magnetic forces that are used in electronics. We’ll try to keep it short and painless. 54 Copyright © 2005 by The McGraw-Hill Companies, Inc. Click here for terms of use. CHAPTER 4 Electricity 55 Pieces of Matter Everything is composed of atoms, which are little specks of matter. Atoms are themselves composed of a heavy core of neutrons and protons surrounded by a whirling cloud of lightweight electrons. And that is all a lie. In the early days, mankind looked around and saw that the world was made up of hundreds, thousands!, of things. Rock and sand and water and mildew and hair and skin and bugs and teeth and metal and wood and bark and leaves and fire—so many things! And of course, we gave everything names and thought up stories as to why these things were here and what they were for. At some point, philosophers and magicians and alchemists got to thinking about these things. What is wood made out of? What if we took a piece of wood and chopped it into smaller and smaller pieces until we had the smallest possible piece of wood? Is that piece still wood? What does it mean to be ‘‘wood’’? At a later point in time, European alchemists would have said that the smallest pieces of everything were composed of the four elements Earth, Air, Fire, and Water. From China, the answer was more likely to be the five elements Water, Fire, Metal, Earth, and Wood. A more detailed response says that the fundamental piece is the atom, which is simply Greek for ‘‘can’t be cut,’’ and that there are a bunch of different types of atoms. These atoms can be assembled into molecules, which in turn are the building blocks of our daily ‘‘stuff.’’ Chemistry comes to the front line now and defines the behavior of the various atoms and molecules. We ultimately identified 116 atomic elements and organized them in the periodic table of elements according to their weights and behaviors. Briefly, in 1999, Berkeley Lab scientists thought they had found element number 118, but later retracted this claim. Elements 113, 115, and 117 are implied by the table but at this time remain undiscovered. At the atomic level, all matter is built up out of these elements and their variations. Life was good. We had atoms and we had mysterious ‘‘forces’’ like gravity and electromagnetism to keep things in place. Looking deeper, we were able to pry the atom apart into three pieces. Almost all of the atom’s mass came from the heavy particles called neutrons and protons. Neutrons are neutral, in that they do not have any electromagnetic charge. Protons, however, have a positive charge. The neutrons and protons are bound together in the center, or nucleus, of the atom. Whizzing around this nucleus is an array of lightweight electrons. One electron has a negative charge equal to one proton, but it takes about 56 CHAPTER 4 Electricity 1,800 electrons to make up the mass of a single proton. Early models of electrons showed them in orbits like planets, though later models assign the electrons to mathematical clouds of probability around the nucleus. The negative charge of the electron is strongly attracted to the positive charge of the proton. Electrons, however, repel other electrons and protons repel other protons. The protons are kept in the nucleus by even stronger forces, but these stronger forces don’t leak out so we can ignore them from here on. There were still questions. There always are. What keeps the electron from collapsing into the nucleus? How do the charges really work? As we dig deeper, our simple atomic model turns into the complex quantum model with its dozens of flavors of quarks and leptons with their colors and flavors and favorite movies. And the harder we dig trying to make sense of gravity and electromagnetism, the farther the answer slips away. Now we are looking at elevendimensional universes composed of ethereal strings. Or maybe it’s something else now. We keep looking. I suspect that, once all is said and done, it will become simple again. But for now, if you want to understand how matter works on a basic level, you must be prepared to have your mind bent. We, however, are just trying to build robots. So we work with the lie, the convenient simplification. The atomic model of electrons, protons, and neutrons as held together by gravity and electromagnetism. Electrons in Metal All metals behave more or less the same when it comes to electricity, so let’s look at copper as an example. A single copper atom has 29 electrons in four orbital shells. The outside shell carries one lonely electron. When you stick a bunch of copper atoms together, you get a useful metallic copper. This can be pulled into wires, rolled into sheets, cast into shapes, and so forth. That lone electron in the outer shell isn’t tied particularly tightly to the copper atom. When the copper atoms get together for a party in your wires, the outer electron just floats around in the metal. It always stays near somebody’s nucleus, to cancel out the proton charge, but it doesn’t really care whose nucleus. The loose electrons become the electron sea, unbound and easily shifted around in the metal. All metals have this electron sea. Materials with loosely CHAPTER 4 Electricity bound electrons are conductors. This doesn’t mean, however, that you can pick up a wire and just shake the electrons off of it. The protons still keep their grip! Most atoms are more jealous than metals and keep a tight grip on all of their electrons. When electrons can’t move easily through a material, that material is an insulator. This is another reason why electrons don’t jump off their wire. Where would they go? Attach themselves to another element, like the oxygen or nitrogen in the air? These elements don’t want another electron, they have plenty already. So the electrons stay in place. They are insulated, blocked, prevented from moving off the metal. In the real world most materials are not made from one pure element, and most elements are not perfect conductors or perfect insulators. Because of this variety, we can create a wide range of electron behaviors. 57 Electromagnetic Field The electron has a negative charge and the proton has a positive charge. These charges affect the space around them, not unlike gravity, creating an electric field, also known as an E-field. Electrons and protons, together, are known as charged particles. When you put a bunch of mass together in one place, you get a noticeable gravitational field. When you place an object on a tall hill in the presence of gravity, that field pulls it down to the bottom of the hill. When you take two large balls of mass, such as planets, they create such a large distortion that they are attracted toward each other across a huge expanse of space. Both gravity and the electromagnetic forces reach out forever. The catch is, they get weaker with the square of the distance. At one ‘‘step’’ from the source, they have a strength of 1. Double that distance and they are 1/4 as strong, to 1/9, 1/16, and so on. We deal with gravity every day and have a good sense of how it controls our lives. One aspect of gravity we don’t notice is how quickly it ‘‘moves.’’ When you wiggle a planet—okay, if you could wiggle a planet—the effect of this movement is that its gravitational field travels, or propagates, at the speed of light. So if the Earth was suddenly shifted a few thousands miles to the left, the moon wouldn’t notice until the change in the gravity field reached it. Electric fields also propagate at the speed of light. Gravity only attracts, while electric fields can attract or repel. It is as if the negative charge is a deep hole in the fabric of space and the positive charge is a tall hill. Hills push away from other hills, and holes push away other holes. 58 CHAPTER 4 Electricity But hills and holes draw towards each other and cancel out, making space smooth again. The electric field is different from gravity in another important way. It is much stronger, about 1036 times stronger. That’s a 1 with 36 zeros after it, which is a really big number. Two grains of sand held close together have no noticeable gravitational attraction. If, however, the gravitational field was as strong as the electrical field, they would slam together with a force of over three tons. The electric field is strong. A modest collection of electrons or protons, without their balancing partners, can create a huge electrical field. When you rub a balloon with a piece of fur, you create a modest electric charge on the balloon. Yet the electric field has enough strength to make your hairs stand on end from inches away. When a charged particle is accelerated it creates a magnetic field, also known as a B-field. Both the electric field and the magnetic field are vector fields. A vector field has not only a strength but a direction. The electric field around an electron, for example, pulls protons toward the electron and pushes other electrons away. The magnetic field created by a moving charge curls around the direction of motion. It is perpendicular to the direction of motion, but its idea of ‘‘perpendicular’’ is to wrap itself around the wire (Fig. 4-1). Note that a proton moving in the same direction as an electron will create a magnetic field of an opposite polarity. A magnetic field that is changing in intensity generates an electric field. A changing electric field in turn generates a magnetic field. In fact, the total amount of field is constant, just rotating between magnetic and electric Fig. 4-1. Magnetic field from electron motion. CHAPTER 4 Electricity forms. These two fields are so closely related that we talk about them as a single electromagnetic field. When you accelerate a charged particle, a self-sustaining electromagnetic wave radiates out away from the motion. If you move the charged particle back and forth, you get a stream of these waves. Depending on how fast you move the charge, these waves could be radio waves, microwaves, and so forth. If you move a wire through a magnetic field, or move a magnet past a wire, the moving magnetic field accelerates the charged particles in the wire. Even if the magnetic field is just getting stronger or weaker, it accelerates the electrons. This is how radios work. On one side, the transmitter is moving electrons to send electromagnetic waves out into space. Somewhere else, these waves cross the wire antenna of a receiver and make its electrons move. It is interesting to note that if you move the electrons in a wire to create a magnetic field, and then stop moving the electrons, the field goes away. While the field is collapsing, it is actually in motion and tries to push the electrons back in the direction they came from. There is another piece to the electromagnetic puzzle, and this is the motion of the wire in relation to the magnetic field. If you hold a wire steady and move the magnetic field past the wire, the electrons are given a boost. This is how generators work. Looking at this from the other direction, if you move the wire’s electrons in the presence of a magnetic field, it generates a mechanical force between the electrons and the field. This is how motors work. All three forces work at right angles to each other—the magnetic field vector B, the direction of the electrons moving in the wire I, and the force vector F pushing the wire. These are shown in Fig. 4-2. If you reverse any one of the vectors, one of the others must change to match. For example, keeping the B field constant and reversing I will cause F to reverse. 59 Units UNIT PREFIXES In mechanics, we worked with a limited scale of values. In electronics, however, we shall be working with both very large and very small values. The SI measurement system defines prefixes to scale values up and down in steps. See Table 4-1 for a list of these prefix modifiers. For example, 1,000 meters is a kilometer, or 1 km. 1/1000 of a meter is a millimeter, or 1 mm. 60 CHAPTER 4 Electricity Fig. 4-2. Magnetic field, electron motion, and force vector. SI prefixes Prefix T G M K m m n p Scale 1,000,000,000,000 1,000,000,000 1,000,000 1,000 0.001 0.000,001 0.000,000,001 0.000,000,000,001 1012 109 106 103 10À3 10À6 10À9 10À12 Table 4-1 Name tera giga mega kilo milli micro nano pico ELECTRICAL CHARGE Coulomb: C The Coulomb is a measurement of electrical charge. One coulomb is equal to the charge of 6.24  1018 electrons, which is a lot of electrons. CHAPTER 4 Electricity CURRENT: I Coulombs per second: I ¼ C/s The flow of charge past a point in an electrical circuit is known as current and is represented by the symbol I. The ampere or amp, symbol A, is the unit that current is measured in. One amp of current is one coulomb of charge passing by a point in one second. If you watch your circuit for one second and 6.24  1018 electrons march by, that’s one amp. I’ve used the word circuit twice now. Electricity is useful when it is moving from one point to another, doing work as it goes. The path that electricity takes is called a circuit. A nonelectrical definition of ‘‘circuit’’ is that of a path going in a circle, such as a race track. Since it’s not feasible to count the individual electrons flowing in a circuit, we usually measure the amp by other means. The amp can be measured because of the electromagnetic fields generated by electrical current. We measure this field and, from this, get a measurement of current. While the coulomb is a fundamental value, the measurement of the coulomb is based on the measurement of the amp. Note that, in electronics, the electrons move from the negative terminal in a battery or generator to the positive terminal. This is electron current. In many discussions of electronic circuits, the convention is to imagine that the current flows from the positive terminal to the negative, opposite of what actually happens. This conventional current is based on the history of Benjamin Franklin’s observations of electricity. As more of the true details of electricity were discovered, the convention of current flowing from positive to negative remained. This doesn’t actually affect anything. If the protons really were flowing from the positive terminal of the battery to the negative, their effect would be exactly what we see for the electron flow we do have. The magnetic fields are the same and the mechanical forces applied to the wire are the same. When we reverse the motion of a charged particle, all of the vector fields associated with it reverse as well. When we reverse the polarity of a charge particle, this reverses the polarity of the fields. If you reverse both the direction and the polarity, the associated fields remain unchanged. So electrons flowing in one direction have the exact same effect as protons moving in the opposite direction. 61 62 CHAPTER 4 Electricity CHARGE DIFFERENCE Volt: V Voltage may be represented by the symbol V or E. In this book we use V exclusively. Voltage does not exist at a single point in a circuit, but is a measurement of the difference in electric potential between two points. Remember the potential energy we discussed in Chapter 2? The potential energy of an object was defined in relation to its height above ground level. Voltage measurements have the same need for a ‘‘ground’’ or reference point to measure from. Voltage is based on electrical charge. Say you have a battery or generator that is pumping electrons into one end of a wire. Electrons find each other repulsive, so they try to stay as far away from each other as they can. But what if the wire doesn’t connect to the other side of the battery, so the electrons in the wire have no place to escape to? They crowd closer together, but they don’t enjoy it. The tighter they squeeze, the more they push against each other. Like springs, they are storing energy as they are squeezed. This creates a charge imbalance, where part of the circuit has an unusual quantity of electrons. In turn, the force created by this imbalance is known as the electromotive force (EMF). Voltage is the measurement of the difference in pressure from one point in a circuit to another. If the whole circuit is at the same pressure, the voltage will be zero even if it holds a hefty electric charge. Water provides a popular analogy for electricity. The water molecules are like the electrons, so a gallon of water is like a coulomb of electricity. Water pipes are like wires, and the flow of water stands in for electric current. Voltage is represented by water pressure. Gravity is usually used for the electric fields. The water analogy gives us illustrations like Fig. 4-3, where two tanks have different water levels and the pressure of water trying to flow from the left tank to the right tank is the voltage between the tanks. If the valve were opened, the current would be the flow through the valve. Fig. 4-3. Water analogy. CHAPTER 4 Electricity ELECTRICAL ENERGY Joule: J ¼ V  C The unit of energy, the familiar joule, is also used for electrical energy. The joule provides a crossover point between mechanical and electrical measurements. One joule is the energy needed to move one coulomb of charge up one volt of electrical potential. It is also defined as the amount of work performed by a current of one amp acting against a resistance of one ohm for one second. Resistance is discussed in the next chapter. 63 POWER: P Watt: W ¼ V  I Work or power is represented by the Watt, which is a function of voltage and current. The watt could also be considered joules per second, W ¼ J/s. Batteries and Generators This discussion of electricity has focused on the flow (current) and pressure (voltage) of the electric charges. The question is then, how do we create this voltage? With electron pumps. The electricity that comes out of the walls in your house is pumped there by giant generators. These generators use magnets to push the electrons around. Batteries do the same thing but on a smaller scale and without magnets. Inside the battery is a chemical paste that acts as a pump. As the chemical reaction inside the battery goes forwards, it charges its terminals. Batteries are like chemical springs unwinding, converting chemical potential energy into electrical energy. When you recharge a battery, you are rewinding this chemical spring. Inside a battery, a chemical redox (reduction/oxidation) reaction occurs at two electrodes, or conductive posts, which are separated by a conductive fluid or paste, the electrolyte. The reduction reaction occurs at the cathode, which is the positive electrode. The oxidation reaction occurs at the anode, which is the negative electrode. 64 CHAPTER 4 Electricity As the battery discharges, powering your circuit, the anode oxidizes (picks up oxygen) and creates a surplus of electrons. These electrons then flow through your circuit (the load) and reenter the battery at the cathode. They can get back in through the cathode because it is performing the reduction reaction (losing oxygen), which combines the electrons with the cathode. The electrolyte that bathes both the anode and cathode finishes this electron loop, allowing the electrons to hitch a ride to the anode for another trip through the oxidation reaction. Note that batteries don’t create electrons; they just provide a way to move them around. Of course it’s far more complicated than that. It’s not just electrons, the negatively charged particles, that move. Protons also flow in the electrolyte, and the chemical reactions are fairly complicated. Electrons flow from the anode to the cathode in the metal wires of an electrical circuit. In the electrolyte of a battery there is a flow, in opposite directions, of both positively and negatively charged atoms, or ions. The ion flow inside the electrolyte must exactly match the electron flow outside the battery through the load. In fact, the internal resistance of the battery to the ionic flow is an important factor in how much energy the battery can provide at a given time. The terms ‘‘anode’’ and ‘‘cathode’’ can be confusing, because they seem to mean different things when applied to batteries versus other components. The cathode is the negative side of a two-wire component such as a resistor, but it is the positive terminal of the battery. Both definitions are correct. The anode is, formally, the terminal or electrode where electrons leave a system. In a current source like a battery or generator the anode is the negative terminal because electrons are being pushed out from it. But in an energy-consuming component it is the positive terminal, since the electrons are being pulled out of the component by the positive charge on that side. Conversely, the cathode is positive on a battery yet negative on a passive component. When electrons leave a battery they enter a component—so the anode (electron source) of the battery is connected to the cathode (electron sink) of a component. SPEED OF ELECTRICITY Electric charges move very slowly through your wires, slow like the minute hand on a clock is slow. And yet, when you turn on a light switch, the power reaches the bulb at, roughly, the speed of light. CHAPTER 4 Electricity The electrons in your wire don’t move fast, but they move together. Here is another electrical analogy, the clothesline. Take two pulleys and anchor them on two different sides of your yard. Wrap a rope into a circle, through these pulleys. When you pull the rope on one side of the yard, the pulley on the other side feels the force ‘‘instantly.’’ The rope itself is moving slowly, but the power is transmitted by the rope quickly. 65 Summary This chapter covered a lot of territory, nothing less than the structure of everything in the universe! We looked the closest at the electron and the electric and magnetic fields associated with it. Because of the special relationship between magnetism and electric charges, we can use magnets to pump electricity. Using these same fields in the other direction, we can use electricity to push against the magnets. Quiz 1. What is the difference between a conductor and an insulator? 2. What is electricity? 3. How do the magnetic field and the electric field interact? How does this relate to the way radios work? Electric generators? Electric motors? 4. What is a circuit? I’m not going to ask you to define amps (coulombs of charge moving past a point per second) or voltage (charge difference) because, frankly, you can look up the formulas. It is more important to have an understanding of what electricity does before you get buried in the math describing it. Of course, in later quizzes I may not be so easy on you, so keep an eye on those equations. 5 CHAPTER Starting with Electronics Introduction Enough with the theory! The terms and definitions and forces are important, since they give us the language and concepts we need to do our work, but learning the nature of the joule isn’t where the fun is. This chapter is where we start to put theory into practice. First, of course, there is a bit more theory to learn. To describe electronic circuits, we draw them using circuit diagrams, or schematics, so you need to learn how to read those. Then there are a few practical details of where to get electronic components and how to wire them together. 66 Copyright © 2005 by The McGraw-Hill Companies, Inc. Click here for terms of use. CHAPTER 5 Starting with Electronics Then we get to play with that most basic of all components, the resistor. Even though a resistor doesn’t ‘‘do’’ anything, except perhaps turn electricity into heat, it has several subtle uses. It also provides illustrations for some of the forces we talked about in Chapter 4. 67 Electronic Circuits SCHEMATIC A schematic is a diagram that represents, in abstract lines and squiggles, an electronic circuit. It is almost like a road map, but even more abstract since a road map shows where things are positioned in space relative to each other and a schematic does not. The schematic only shows how the components, or parts in an electronic circuit, are connected to each other. An example of a schematic for a simple circuit is shown in Fig. 5-1. There are several features in this figure that are common to all schematics. The little pads on the left labeled ‘‘þ5’’ and ‘‘Gnd’’ are plugs to the outside world. External to this circuit we expect there to be a 5-volt power supply. Electricity is always measured with respect to a ground state. It’s handy to label which wires we expect to be at zero volts, or ground. The inverted pyramid in the bottom-left corner is one of several symbols that mean ‘‘ground.’’ One version of ground has only one horizontal line instead of a pyramid of them. Note that ground is our source of electrons. The lines in the schematic are the wires that connect everything together. A round dot at a junction of lines means that these wires are connected. Sometimes you have to draw wires in the schematic so they cross each other Fig. 5-1. Schematic. 68 CHAPTER 5 Starting with Electronics without connecting. Crossed lines will not have a dot, or may even have a little arch in them so that they obviously cross. Each component in a schematic has its own symbol. Note that European and American schematics tend to use different symbols. We focus on the American symbols. The symbol above the label ‘‘LED1’’ is for a light-emitting diode. Component labels tend to follow a simple convention. LEDs are ‘‘LED,’’ resistors are named ‘‘R,’’ capacitors ‘‘C,’’ switches ‘‘S,’’ and so forth. The number after the name is just a counter, 1, 2, 3, to keep the various parts separate. Schematics usually come accompanied by a parts list that gives values for all of the names. The values may also be printed on the schematic, like the 330-ohm resistor on the right. Switches and relays, which are just electrically triggered switches, are normally drawn in their unactuated or default position. As we introduce various components in the projects, we shall show their schematic symbol and name, as well as what they look like physically. PRINTED CIRCUIT BOARD If a circuit is going to be of any use, the lines and components in the schematic need to be translated into physical reality. Most electronic circuits that you find in the wild are assembled on printed circuit boards (PCBs), or just circuit boards. The circuit board for our schematic is shown in Fig. 5-2. Most PCBs are created photographically. The special fiber board begins its life covered on one or both sides with copper. A photoresist mask is applied to this and then a picture of the circuit is projected onto it. Most of the mask is then washed off, leaving mask over just the traces. A strong acid is used to dissolve the rest of the copper off of the board. When that is done, holes can be drilled for the components and the board is done. The traces on the board are wires. Flat wires, but still the same thing as the wires you are used to. The pads are round or oval areas where components are inserted into the board and soldered into place. The process of soldering is described later. Cheap circuit boards have copper on just one side, or maybe on both sides, but no copper in the holes. Better circuit boards have plated holes, where copper is plated into the holes on the board. This copper plating connects to the solder pad and makes it easier to solder components into the board. CHAPTER 5 Starting with Electronics 69 Fig. 5-2. Circuit board. Plated holes are also stronger and the pads are less likely to ‘‘lift’’ off the board. The copper is held onto the board with glue, but too much heat during soldering can melt the glue and cause the pad and traces to lose their grip on the board. If there is copper on both sides of the board, plated holes also do a good job of connecting the pads on the top and bottom sides of the board. There may even be plated holes in the board that aren’t for components, used to connect traces between the front and back. These are called vias. Some circuit boards have more than two layers of copper. These multilayer boards are like several two-layer circuit boards glued, or laminated, together. In these cases the vias are critical for connections between one layer and the next. While a professional circuit board is created using computer-aided design (CAD) software, you can also make them by hand using either a chemical photoresist or stick-on resist pads and traces. I don’t personally recommend these kits, since good results can be hard to achieve and the chemicals are particularly nasty. To do your own professional schematic layout and circuit board design, I recommend the freeware version of Eagle, from CADSoft. For not too much money, you can even find companies that specialize in creating prototype circuit boards. My favorite prototype board manufacturer is Alberta Printed Circuits in Canada, but there are others listed later which also do good work. 70 CHAPTER 5 Starting with Electronics Circuit Assembly PROTOTYPING BOARDS When you are experimenting with a new circuit, you normally want to put it together in a temporary fashion to test it. Test versions of a circuit are prototypes, and prototyping boards, often called breadboards, make it easy to quickly wire a circuit. An example breadboard is shown in Fig. 5-3. Once a circuit has been tested, you may want to make a permanent version using either a generic or custom circuit board. Each hole in the breadboard is a socket that you plug wires or components into. The holes are connected together in a standard pattern, as shown in Fig. 5-4. The long bus or rail, a series of connected holes on the outside edges of the breadboard, is normally wired to the power supply. I usually take a red and black permanent marker and draw lines along these holes, to identify which strip is which. Black is the color traditionally used to represent ground and Fig. 5-3. Prototyping breadboard. Fig. 5-4. Breadboard circuit layout. CHAPTER 5 Starting with Electronics 71 Fig. 5-5. Breadboarded circuit. red is positive voltage. On a long breadboard like this one, the power rails tend to be split in the middle. I’ll also usually take short wires and connect them together into one long bus. Our previous circuit, plugged into the breadboard, might look like Fig. 5-5. Breadboards come in many different sizes, though the internal wiring is usually pretty standard. The 64-unit long board shown here is a common size. Other breadboards may come with interlocking wedges along the sides so you can connect several boards together into one unit. You can also find prototyping stations that come with multiple breadboards plus built-in power supplies and other attachments. These cost more, but can make the task of prototyping easier. You can buy circuit boards that are laid out like the breadboards. These let you solder your components and jumper wires into place permanently. You can often take a design straight from the breadboard onto the matching circuit board. DEAD BUG AND WIRE WRAPPING There is one inelegant method of assembling components that is often referred to as the dead bug technique. It is called this because it is normally used with integrated circuits, which look like futuristic bugs. Dead bug assembly is where you solder the wires and components together without any type of printed circuit board, prototyping board, or other 72 CHAPTER 5 Starting with Electronics structural support. The circuit simply hangs together in space, waiting to get bumped and shorted out. Wire wrapping replaces soldering with tightly wrapped wires. Though a popular prototyping method, I’ve never enjoyed the process so can’t recommend it. SOLDERING Most of the work in this book is done on breadboards, so soldering is a useful skill to have. Soldering is the process of joining two wires together, or a wire to a circuit board, by melting a soft metal, solder, into the junction. Equipment Solder (Fig. 5-6) is a soft metal wire made from a mix of tin (symbol Sn) and lead (symbol Pb), usually about 60% tin and 40% lead. My solder is marked SN63PB37, indicating the popular mixture of 63% tin and 37% lead by weight. This solder melts at the low temperature, for metals, of 1908C (3748F). Since there is lead in solder, it is a somewhat hazardous material. You don’t want to eat lead or rub it in your eyes, so wash your hands after handling solder. When metals get hot they react to the oxygen in the air more than they would normally. This creates an oxidized layer on the metal that interferes with the solder sticking. It also insulates the metal from what we are trying to solder it to. Fig. 5-6. Solder. CHAPTER 5 Starting with Electronics To prevent oxidation, as well as to clean off existing oxidation, you use solder with a flux. In plumbing and other large-scale soldering projects this flux is an acid paste. Never use acid flux in electronics! It will damage your circuit. Electronic flux is usually a rosin paste, based on pine-tree sap. For convenience, most electronic solders are formed as hollow tubes with a rosin flux core. Sometimes you want lots of extra flux, so you can buy rosin flux in liquid form, thinned with alcohol. Solder is heated with a soldering iron, such as my old workhorse shown in Fig. 5-7. A basic soldering iron is a cool handle with a hot tip, plus some kind of stand to keep it from burning your desk. A better soldering iron includes temperature controls and a place for your sponge. All irons feature replaceable tips, since these wear out over time. Since you have a choice of tip, use a small pointy tip. While you can get large tips, flat screwdriver-shaped tips, and so on, these are clumsy for most electronics work. It is important to keep your tip clean. This is what the sponge is for. Never use sandpaper or other abrasive materials to clean your tip, since these will damage its protective plating. When your soldering iron is hot, you clean it by wiping the tip on a damp sponge. Once you wipe off as much crud as you can that way, cover the hot 73 Fig. 5-7. Soldering iron. 74 CHAPTER 5 Starting with Electronics Fig. 5-8. Third hand. tip with solder. The rosin flux will help clean the tip further, and the coating of solder keeps the tip from oxidizing again. This process of cleaning and coating the tip of your soldering iron is called tinning. You may need to tin and wipe the tip several times before it becomes clean. You can tell when the tip is properly tinned when it shines a bright silver, rather than a dull gray. The wire or component leads also need to be clean. If they are dull and dirty, you can scrape them clean with a sharp blade (which will soon be made dull) or sandpaper. Dirt, oil, or oxidations keep you from getting a good solder joint. So keep everything clean. You can tin the ends of your wires, and this can make a big difference in how easy they are to solder. Note, however, that tinned stranded wire is hard to bend, so you want to shape it first. When soldering wires, it can be handy to have a third hand (Fig. 5-8) to hold the components. Your other two hands are holding the iron and the solder, respectively. Hobby stores and many electronics suppliers provide various clamps and clips designed to act as a third hand. Some of these are specially designed to hold circuit boards. Wire-to-wire connection Try This: There are times when you need to solder two wires together. This section goes over the soldering process. First a word about wires. There are two basic types of wire, solid and stranded. Solid wire is just that, a single solid wire, usually inside some type CHAPTER 5 Starting with Electronics of plastic insulation. The is your standard ‘‘jumper wire’’ used to connect components on breadboards and circuit boards. When you work with solid wire you need to be careful not to nick it, or it is likely to break at that point. Stranded wire comes in many varieties and forms, but has the common trait of being made up of many little wires twisted or braided into a larger wire. Stranded wire doesn’t work well for board-to-board connections, since the little strands tend to get rowdy and provide short circuits. If you have a job where the wire might bend during use, such as attaching a sensor or control, or are carrying a signal a long way from the circuit, you need to use stranded wire. A short circuit is where you create an accidental connection where you don’t want one. It creates a shortcut through your circuit, and is almost always going to prevent the circuit from working correctly. Stranded wire holds up to being bent and flexed a lot better than solid wire. So, solid wire for nonmoving jobs, stranded wire for things that flex. The first step in using wire is to cut it to length. The second step is to strip the ends so a short section of bare wire is exposed (Fig. 5-9). Solder is not very strong, so you need to make a mechanical connection between your wires. I like to use round-nosed pliers to make a loop in the end of the wire (Fig. 5-10), though you can use any type of small plier to bend the wire. While the loop-to-loop connection works well for component leads, you can also twist the ends of wires together to make a splice. There are many different ways to connect wires together, so feel free to experiment to get the best connection for your projects. Holding the wire in a third hand, or placing it on a heatproof surface, you want to touch the end of your soldering iron to the junction of the two wires. You need to heat both wires to the solder’s melting temperature to get a good joint. I prefer to have my soldering iron heavily tinned, so there is actually a tiny drop of solder on the tip. This gives a better path for the heat to flow from the iron to the wire than a bare tip. Once the wires are hot, touch the solder to 75 Fig. 5-9. Stripped wire. 76 CHAPTER 5 Starting with Electronics Fig. 5-10. Bend wire. Fig. 5-11. Solder wire. them until the solder melts into a small, shiny blob. Be careful not to move the wires while the solder is cooling, or it can make a poor connection. Also be sure you aren’t applying the solder to the soldering iron. The melted metal flows to where the heat is, and if you touch it to the hottest part, the iron, it won’t flow around the wires where you want it. See Fig. 5-11. CHAPTER 5 Starting with Electronics Wire to board Soldering a wire or component to a circuit board is easier than wire-to-wire. The process is essentially the same as wire-to-wire soldering, only you insert your wire into a hole in the circuit board to start. You can bend the wire or component lead a little bit so it doesn’t fall out when you turn the board over to solder it. Figure 5-12 shows the component in the circuit board with the wires poking out through the back of the board. The soldering iron is heating the wire and the pad together. Once you have soldered the wire to the pad, you will have a shiny cone that flows around the entire pad and up the wire. A ‘‘blobby’’ junction needs to be reheated, taking care to heat both the wire and the pad. If the holes in your board are not plated through, it can be difficult to get a good solder junction. You may need to put in extra solder to bridge the gap from the pad to the wire. Be careful, though, since too much solder can create a solder bridge to another pad and create a short circuit. Once soldered into place, trim the wires down to the top of the solder cone (Fig. 5-13) and turn the board over to admire your work (Fig. 5-14). I can almost never get my parts to sit flat on the board, but minor aesthetic details like that don’t matter. As long as the solder joint is good, the part isn’t too high off the board, and you didn’t create a short, it’s good. If the 77 Fig. 5-12. Soldering to board. 78 CHAPTER 5 Starting with Electronics Fig. 5-13. Trim wires. Fig. 5-14. Resistor on board. part is too far off the board, it could bend over and short against a neighboring part. Desoldering Since nobody is perfect, you may have to remove the solder from a joint. There are different ways to do this. One way is with desoldering braid, which is a type of stranded wire. You lay the braid over the soldered joint and heat it with the soldering iron. Once the solder flows into the braid you can remove it, the iron, and the solder from the joint. CHAPTER 5 Starting with Electronics You can also get different types of ‘‘solder suckers.’’ These can be small squeeze bulbs or spring-action devices that provide a quick inhalation. The idea is to heat up the solder so it is liquid and then suck it into the device. These actually work, and high-end soldering stations include a small vacuumpump desoldering nozzle. Either way, you may need to heat up the wire and pad again to be able to pull the wire out of its hole, since there will still be a small amount of solder ‘‘gluing’’ it together. As with all things, soldering and desoldering are skills that will get better as you practice. In fact, you may want to practice now, before you need to solder something you care about. 79 SUPPLIERS To work with electronics, you need to find a source for parts. Radio Shack has a fair selection of parts, and they should have everything that we use in this book. For many people, they are the most convenient source of parts. Fry’s Electronics, when you have one in your neighborhood, is also a good source of parts. Most larger towns also have some kind of electronic supply store that supports the local electronics repair and hobbyist communities. You can find these using your local Yellow Pages. Almost everyone has access to mail order suppliers. Table 5-1 lists a number of the more common mail order electronics suppliers. If you want to branch out into circuit board design, Table 5-2 lists a few manufacturers of prototype boards. Note that CadSoft doesn’t make circuit boards, but has a freeware software package you can use to design them. Table 5-1 Electronics suppliers http://www.allcorp.com/ All Electronics Digi-Key Corporation http://www.digikey.com/ Fry’s Electronics Jameco Electronics JDR Microdevices Mouser Radio Shack http://www.outpost.com/ http://www.jameco.com/ http://www.jdr.com/ http://www.mouser.com/ http://www.radioshack.com/ 80 CHAPTER 5 Starting with Electronics Table 5-2 Prototype circuit board manufacturers http://www.apcircuits.com/ http://www.cadsoft.de/ http://www.expresspcb.com/ AP Circuits CadSoft ExpressPCB PCB Express http://www.pcbexpress.com/ Resistors RESISTOR Everything acts as a resistor to some extent. However, there is also a specific electronic component called the resistor that provides a calibrated resistance. Resistance is measured in ohms, and the ohm is represented by the Greek letter  (omega). Resistance is the measure of a material’s opposition to the movement of electrical charge. As you are trying to pump electrons through a circuit, the resistance of the circuit is fighting back, keeping the electrons from moving as easily as they might. Everything has some resistance, even the wire and copper traces in a circuit board that you use to connect components together. While many resistors are made from a carbon film, like a conductive paint, highly accurate resistors are made from fine wire. Usually, though, the resistance in your wire is too small to make any difference for low-power circuits. One of the byproducts of resistance is heat. The harder you push electrons through a resistor, the more heat is created. The energy you are using to push electrons through the resistor doesn’t make it all the way through, since the resistor is opposing that force. The result, then, is heat. Using the clothesline analogy again, as you are pulling on the clothesline, someone in the middle is pinching the rope with their fingers. This slows down the rope, or at least makes it harder to pull, at the expense of making their fingers hot. Looking at Fig. 5-15, you can see the schematic symbol for the resistor is a jagged line. The resistor itself is a cylindrical blob on a wire, with three or four stripes. The stripes will normally be closer to one end of the resistor than the other. To read the stripes, orient the resistor so the stripes are on the left. Note that resistors don’t care which direction you plug them into circuit. We put the stripes on the left for easy reading. CHAPTER 5 Starting with Electronics 81 Fig. 5-15. Resistor. The first and second stripes are color codes for different digits. Black is 0, Brown is 1, and so forth. All of the colors and their meanings are listed in Table 5-3. The third stripe is a multiplier, and it determines how many zeros you add after the first two digits. A resistor marked Black, Brown, Black has a value of 1 . Black, Brown, Brown adds a zero, so the value is 10 , and so forth. The reverse is also true. When you see a resistor valued at 4.7K on a schematic, you want a resistor whose first two stripes are Yellow and Violet. Since ‘‘K’’ means 1,000, the full value is 4,700. Since we need to add two zeros, the third stripe is Red. The fourth and last stripe is an optional tolerance indicator. No device is perfect, so this stripe indicates how imperfect the resistor is. If there is no fourth band, the resistor’s actual value is plus or minus 20%, or somewhere between (R  0.80) and (R  1.20). Better resistors have tighter tolerances, as indicated in Table 5-3. In addition to the resistance value, resistors also have a power rating. The power rating determines how much power, in the form of heat, the resistor can handle. Most circuits use 1/8 or 1/4 watt resistors. When a larger resistor is needed, the power rating is usually specified in the parts list. OHM’S LAW The unit of resistance, the ohm, is named after the German physicist Georg Ohm. His work had a strong influence on our understanding of electricity and resistance. The relationship of resistance to current and voltage is known as Ohm’s Law in his honor. Ohm’s Law states: V¼IÂR ð5-1Þ Equation (5-1) states that when a current encounters friction in the form of resistance, a voltage appears across the resistor. Remember that voltage is like a pressure difference between two points in the circuit. When the 82 CHAPTER 5 Starting with Electronics Table 5-3 Color Black Brown Red Orange Yellow Green Blue Violet Gray White Resistor color code Digit 0 1 2 3 4 5 6 7 8 9 Multiplier 1 10 100 1,000 10,000 100,000 1,000,000 10,000,000 100,000,000 not used Tolerance (no stripe) Silver Gold Brown Æ 20% Æ 10% Æ 5% Æ 1% electrons meet resistance, they don’t flow as easily through it. This creates a reduced electrical ‘‘pressure’’ downstream from the resistor. The more resistance given to a current, the higher the voltage difference. The traditional description of Ohm’s Law is that a potential difference of 1 volt will push a current of 1 amp through 1 ohm of resistance.

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