1. Why Should I Care about 6 Simple Machines?
2. How Levers Work?
3. How Blocks (Pulleys) Work?
4. How a Wheel and Axle Works?
5. How an Inclined Plane (Wedge) Works?
6. How a Screw Works?
7. How Gears Work?
8. What Public Domain Documents are Available for Further Study?
9. Tricks of the Trade & Rules of Thumb for Simple Machines:
You should care because it's cool stuff that helps you understand how almost everything works on the jobsite. The text on this page is lifted from the US Navy training manuals and referenced throughout the page.
Through the ages, ships have evolved from crude rafts to the huge complex cruisers and carriers of today’s Navy. It was a long step from oars to sails, another long step from sails to steam, and another long step to today’s nuclear power. Each step in the progress of shipbuilding has involved the use of more and more machines. Today’s Navy personnel are specialists in operating and maintaining machinery. Boatswains operate winches to hoist cargo and the anchor; personnel in the engine room operate pumps, valves, generators, and other machines to produce and control the ship’s power; personnel in the weapons department operate shell hoists and rammers and elevate and train the guns and missile launchers; the cooks operate mixers and can openers; personnel in the CB ratings drive trucks and operate cranes, graders, and bulldozers. In fact, every rating in the Navy uses machinery sometime during the day’s work. Each machine used aboard ship has made the physical work load of the crew lighter; you don’t walk the capstan to raise the anchor, or heave on a line to sling cargo aboard. Machines are your friends. They have taken much of the backache and drudgery out of a sailor’s lift. Reading this book should help you recognize and understand the operation of many of the machines you see about you.
WHAT IS A MACHINE? As you look about you, you probably see half a dozen machines that you don’t recognize as such. Ordinarily you think of a machine as a complex device-a gasoline engine or a typewriter. They are machines; but so are a hammer, a screwdriver, a ship’s wheel. A machine is any device that helps you to do work. It may help by changing the amount of force or the speed of action. A claw hammer, for example, is a machine. You can use it to apply a large force for pulling out a nail; a relatively small pull on the handle produces a much greater force at the claws. We use machines to transform energy. For example, a generator transforms mechanical energy into electrical energy. We use machines to transfer energy from one place to another. For example, the connecting rods, crankshaft, drive shaft, and rear axle of an automobile transfer energy from the engine to the rear wheels. Another use of machines is to multiply force. We use a system of pulleys (a chain hoist, for example) to lift a heavy load. The pulley system enables us to raise the load by exerting a force that is smaller than the weight of the load. We must exert this force over a greater distance than the height through which the load is raised; thus, the load will move slower than the chain on which we pull. The machine enables us to gain force, but only at the expense of speed. Machines may also be used to multiply speed. The best example of this is the bicycle, by which we gain speed by exerting a greater force. Machines are also used to change the direction of a force. For example, the Signalman’s halyard enables one end of the line to exert an upward force on a signal flag while a downward force is exerted on the other end. There are only six simple machines: the lever, the block, the wheel and axle, the inclined plane, the screw, and the gear. Physicists, however, recognize only two basic principles in machines: those of the lever and the inclined plane. The wheel and axle, block and tackle, and gears may be considered levers. The wedge and the screw use the principle of the inclined plane. When you are familiar with the principles of these simple machines, you can readily understand the operation of complex machines. Complex machines are merely combinations of two or more simple machines.
THE LEVER The simplest machine, and perhaps the one with which you are most familiar, is the lever. A seesaw is a familiar example of a lever in which one weight balances the other. You will find that all levers have three basic parts: the fulcrum (F), a force or effort (E), and a resistance (R). Look at the lever in figure 1-1.
You see the pivotal point (fulcrum) (F); the effort (E), which is applied at a distance (A) from the fulcrum; and a resistance (R), which acts at a distance (a) from the fulcrum. Distances A and a are the arms of the lever.
CLASSES OF LEVERS The three classes of levers are shown in figure 1-2. The location of the fulcrum (the fixed or pivot point) in relation to the resistance (or weight) and the effort determines the lever class.
First Class In the first class (fig. 1-2, part A), the fulcrum is located between the effort and the resistance. As mentioned earlier, the seesaw is a good example of a first-class lever. The amount of weight and the distance from the fulcrum can be varied to suit the need. Notice that the sailor in figure 1-3 applies effort on the handles of the oars. An oar is another good example. The oarlock is the fulcrum, and the water is the resistance. In this case, as in figure 1-1, the force is applied on one side of the fulcrum and the resistance to be overcome is applied to the opposite side; hence, this is a first class lever. Crowbars, shears, and pliers are common examples of this class of levers.
Second Class The second class of lever (fig. 1-2, part B) has the fulcrum at one end, the effort applied at the other end, and the resistance somewhere between those points. The Figure 1-2.-Three classes of levers. Figure 1-3.-Oars are levers. wheelbarrow in figure 1-4 is a good example of a second-class lever. If you apply 50 pounds of effort to the handles of a wheelbarrow 4 feet from the fulcrum (wheel), you can lift 200 pounds of weight 1 foot from the fulcrum. If the load were placed farther away from the wheel, would it be easier or harder to lift? Levers of the first and second class are commonly used to help in overcoming big resistances with a relatively small effort.
Third Class Sometimes you will want to speed up the movement of the resistance even though you have to use a large amount of effort. Levers that help you accomplish this are in the third class of levers. As shown in figure 1-2, part C, the fulcrum is at one end of the lever, and the weight or resistance to be overcome is at the other end, with the effort applied at some point between. You can always spot the third-class levers because you will find the effort applied between the fulcrum and the resistance. Look at figure 1-5. It is easy to see that while E moved the short distance (e), the resistance (R) was moved a greater distance (r). The speed of R must have been greater than that of E, since R covered a greater distance in the same length of time. Your arm (fig. 1-6) is a third-class lever. It is this lever action that makes it possible for you to flex your arms so quickly. Your elbow is the fulcrum. Your biceps muscle, which ties onto your forearm about an inch below the elbow, applies the effort; your hand is the resistance, located about 18 inches from the fulcrum. In the split second it takes your biceps muscle to contract an inch, your hand has moved through an 18-inch arc. You know from experience that it takes a big pull at E to overcome a relatively small resistance at R. Just to experience this principle, try closing a door by pushing on it about 3 or 4 inches from the hinges (fulcrum). The moral is, you don’t use third-class levers to do heavy jobs; you use them to gain speed.
One convenience of machines is that you can determine in advance the forces required for their operation, as well as the forces they will exert. Consider for a moment the first class of levers. Suppose you have an iron bar, like the one shown in figure 1-7. This bar is 9 feet long, and you want to use it to raise a 300-pound crate off the deck while you slide a dolly under the crate; but you can exert only 100 pounds to lift the crate. So, you place the fulcrum-a wooden block-beneath one end of the bar and force that end of the bar under the crate. Then, you push down on the other end of the bar. After a few adjustments of the position of the fulcrum, you will find that your 100-pound force will just fit the crate when the fulcrum is 2 feet from the center of the crate. That leaves a 6-foot length of bar from the fulcrum to the point where you pushdown. The 6-foot portion is three times as long as the distance from the fulcrum to the center of the crate. And you lifted a load three times as great as the force you applied (3 x 100 = 300 pounds).
There is another thing about the first and second classes of levers that
you have probably noticed by now.
Since they can be used to magnify the applied force, they provide positive mechanical advantages. The third-class
lever provides what is called a fractional mechanical advantage, which is really a mechanical disadvantage—
you use more force than the force of the load you lift.
In the wheelbarrow problem, you saw that a 50-pound pull actually
overcame the 200-pound weight
Figure 1-9.-A curved lever arm. of the sand. The sailor’s effort was magnified four times, so you may say that the mechanical advantage of the
wheelbarrow is 4. Expressing the same idea in mathematical terms,
MECHANICAL ADVANTAGE = RESISTANCE/EFFORT
or, in the case of the wheelbarrow, M.A. = 200/50 = 4
This rule—mechanical advantage equals resistance (load) divided by effort —applies to all machines.
The mechanical advantage of a lever may also be found by dividing the
length of effort arm A by the length
of resistance arm a. Stated as a formula, this reads:
M.A. of a lever = Effort Arm/Resistance Arm
How does this apply to third-class levers? Your muscle pulls with a force of 1,800 pounds to lift a 100-pound projectile. So you have a mechanical advantage of 100/1800 or 1/18th, which is fractional-less than 1.
The basic machines get used every day on your jobsite. If you understand the principles, you’ll be in a better position to solve problems that develop. Think of a simple but treacherous example. A building partially collapses and traps a worker under a big chunk of concrete floor. A back hoe can’t get into the space and you have to act quickly.
The piece of floor is about 8’ x 4’ and 6” thick. You know, or should know, that concrete weighs 150 pounds per cubic foot and that 8 x 4 x .5 = 16 cf. So 16 cf x 150 lb/cf = 2,400 pounds.
To lift the concrete off the trapped worker, you’d need 12 guys each lifting 100 pounds to lift half the weight, to lift it up like you were lifting the load on a wheel barrow (which is a 2nd class lever). But you don’t have 12 guys, you’ve got two guys and some long sections of 3” sprinkler piping. You know you could use the pipe as a 1st class lever to lift the slab.
So how long a piece of pipe do you need? If you’ve only got two guys to help with the lever, and one to pull the trapped worker out, you could assume that each guy could pull down 150 pounds, so you have a force of 300 pounds to work with. If you have a pivot point 2’ from your lift point, you need at lease 8’ of pipe on the side of pivot point to lift the 1200 pound concrete and free the worker. So if you grab a 12’ section of pipe, you free the trapped worker.
If you only have one person to lift, you probably could still free the guy if you have a 20’ section of pipe. The ability to do those quick calculations, and even more importantly, to understand the basic lever principles will be useful for the rest of your life. So why not take a few minutes and learn the basics of the 6 simple machines?
Additional information and explanation is available in the following,
Basic Machines Training Course - US Navy ("Levers" excerpt, NAVEDTRA 14037, 1994)
Blocks or pulleys are simple machines that have many uses aboard ship, as well as onshore. Remember how your mouth hung open as you watched movers taking a piano out of a fourth story window? The guy on the end of the tackle eased the piano safely to the sidewalk with a mysterious arrangement of blocks and ropes. Or, you’ve been in the country and watched the farmer use a block and tackle to put hay in a barn. Since old Dobbin or the tractor did the hauling, there was no need for a fancy arrangement of ropes and blocks. Incidentally, you’ll often hear the rope or tackle called the fall, block and tack, or block and fall. In the Navy you’ll rig a block and tackle to make some of your work easier. Learn the names of the parts of a block. Figure 2-1 will give you a good start on this. Look at the single block and see some of the ways you can use it. If you lash a single block to a fixed object-an overhead, a yardarm, or a bulkhead-you give yourself the advantage of being able to pull from a convenient direction. For example, in figure 2-2 you haul up a flag hoist, but you really pull down. You can do this by having a single sheaved block made fast to the yardarm. This makes it possible for you to stand in a convenient place near the flag bag and do the job. Otherwise you would have to go aloft, dragging the flag hoist behind you.
With a single fixed sheave, the force of your down pull on the fall must be equal to the weight of the object hoist. You can’t use this rig to lift a heavy load or resistance with a small effort-you can change only the direction of your pull. A single fixed block is a first-class lever with equal arms. The arms (EF and FR) in figure 2-3 are equal; hence, the mechanical advantage is 1. When you pull down at A with a force of 1 pound, you raise a load of 1 pound at B. A single fixed block does not magnify force nor speed. You can, however, use a single block and fall to magnify the force you exert. Notice in figure 2-4 that the block is not fixed.
The fall is doubled as it supports the 200-pound cask. When rigged
this way, you call the single block and fall a runner. Each half of the
fall carries one-half of the total bad, or 100 pounds. Thus, with the
runner, the sailor is lifting a 200-pound cask with a 100-pound pull.
The mechanical advantage is 2. Check this by the formula:
The single movable block in this setup is a second-class lever. See figure 2-5. Your effort (E) acts upward upon the arm (EF), which is the diameter of the sheave. The resistance (R) acts downward on the arm (FR), which is the radius of the sheave. Since the diameter is twice the radius, the mechanical advantage is 2. When the effort at E moves up 2 feet, the load at R is raised only 1 foot. That’s something to remember about blocks and falls—if you are actually getting a mechanical advantage from the system. The length of rope that passes through your hands is greater than the distance that the load is raised. However, if you can lift a big load with a small effort, you don’t care how much rope you have to pull. The sailor in figure 2-4 is in an awkward position to pull. If he had another single block handy, he could use it to change the direction of the pull, as in figure 2-6. This second arrangement is known as a gun tackle. Because the second block is fixed, it merely changes the direction of pull—and the mechanical advantage of the whole system remains 2. You can arrange blocks in several ways, depending on the job to be done and the mechanical advantage you want to get.
For example, a luff tack consists of a double block and a single
block, rigged as in figure 2-7. Notice that the weight is suspended by
the three parts of rope that extend from the movable single block. Each
part of the rope carries its share of the load. If the crate weighs 600
pounds, then each of the three parts of the rope supports its share—200
pounds. If there’s a pull of 200 pounds downward on rope B, you will
have to pull downward with a force of 200 pounds on A to counterbalance
the pull on B. Neglecting the friction in the block, a pull of 200
pounds is all that is necessary to raise the crate. The mechanical
Here’s a good tip. If you count the number of parts of rope going to and from the movable block you can figure the mechanical advantage at a glance. This simple rule will help you to approximate the mechanical advantage of most tackles you see in the Navy. Many combinations of single-, double-, and triplesheave blocks are possible. Two of these combinations are shown in figure 2-8. You can secure the dead end of the fall to the movable block. The advantage is increased by 1. Notice that this is done in figure 2-7. That is a good point to remember. Remember, also, that the strength of your fall—rope—is a limiting factor in any tackle. Be sure your fall will carry the load. There is no point in rigging a 6-fold purchase that carries a 5-ton load with two triple blocks on a 3-inch manila rope attached to a winch. The winch could take it, but the rope couldn’t. Now for a review of the points you have learned about blocks, and then to some practical applications aboard ship: With a single fixed block the only advantage is the change of direction of the pull. The mechanical advantage is still 1. A single movable block gives a mechanical advantage of 2. Many combinations of single, double, and triple blocks can be rigged to give greater advantages. Remember that the number of parts of the fall going to and from the movable block tells you the approximate mechanical advantage of the tackle. If you fix the dead end of the fall to the movable block you increase the mechanical advantage by one 1.
Additional information and explanation is available in the following,
Basic Machines Training Course - US Navy ("Block and Tackle" excerpt, NAVEDTRA 14037, 1994)
Have you ever tried to open a door when the knob was missing? If you have, you know that trying to twist that small four-sided shaft with your fingers is tough work. That gives you some appreciation of the advantage you get by using a knob. The doorknob is an example of a simple machine called a wheel and axle. The steering wheel on an automobile, the handle of an ice cream freezer, and a brace and bit are all examples of a simple machine. All of these devices use the wheel and axle to multiply the force you exert. If you try to turn a screw with a screwdriver and it doesn’t turn, stick a screwdriver bit in the chuck of a brace. The screw will probably go in with little difficulty. There’s something you’ll want to get straight right at the beginning. The wheel-and-axle machine consists of a wheel or crank rigidly attached to the axle, which turns with the wheel. Thus, the front wheel of an automobile is not a wheel-and-axle machine because the axle does not turn with the wheel.
How does the wheel-and-axle arrangement help to magnify the force you exert? Suppose you use a screwdriver bit in a brace to drive a stubborn screw. Look at figure 3-1, view A. You apply effort on the handle that moves in a circular path, the radius of which is 5 inches. If you apply a 10-pound force on the handle, how much force will you exert against the resistance at the screw? Assume the radius of the screwdriver blade is 1/4 inch. You are really using the brace as a second-class lever—see figure 3-1, view B. You can find the size of the resistance by using the formula:
Substituting in the formula and solving:
This means that the screwdriver blade will turn the screw with a force
of 200 pounds. The relationship between the radius of the diameters or
the circumferences of the wheel and axle tells you how much mechanical
advantage you can get. Take another situation. You raise the old oaken
bucket, figure 3-2, using a wheel-and-axle arrangement. If the distance
from the center of the axle to the handle is 8 inches and the radius of
the drum around which the rope is wound is 2 inches, then you have a
theoretical mechanical advantage of 4. That’s why these rigs were used.
MOMENT OF FORCE
In several situations you can use the wheel-and-axle to speed up motion. The rear-wheel sprocket of a bike, along with the rear wheel itself, is an example. When you are pedaling, the sprocket is attached to the wheel; so the combination is a true wheel-and-axle machine. Assume that the sprocket has a circumference of 8 inches, and the wheel circumference is 80 inches. If you turn the sprocket at a rate of one revolution per second, each sprocket tooth moves at a speed of 8 inches per second. Since the wheel makes one revolution for each revolution made by the sprocket, any point on the tire must move through a distance of 80 inches in 1 second. So, for every 8-inch movement of a point on the sprocket, you have moved a corresponding point on the wheel through 80 inches. Since a complete revolution of the sprocket and wheel requires only 1 second, the speed of a point on the circumference of the wheel is 80 inches per second, or 10 times the speed of a tooth on the sprocket. (NOTE: Both sprocket and wheel make the same number of revolutions per second, so the speed of turning for the two is the same.) Here is an idea that you will find useful in understanding the wheel and axle, as well as other machines. You probably have noticed that the force you apply to a lever starts to turn or rotate it about the fulcrum. You also know that a sheave on a fall starts to rotate the sheave of the block. Also when you turn the steering wheel of a car, it starts to rotate the steering column. Whenever you use a lever, or a wheel and axle, your effort on the lever arm or the rim of the wheel causes it to rotate about the fulcrum or the axle in one direction or another. If the rotation occurs in the same direction as the hands of a clock, we call that direction clockwise. If the rotation occurs in the opposite direction from that of the hands of a clock, we call that direction of rotation counterclockwise.
A glance at figure 3-3 will make clear the meaning of these terms. The force acting on the handle of a carpenter’s brace depends not only on the amount of that force, but also on the distance from the handle to the center of rotation. This is known as a moment of force, or a torque (pronounced tork). Moment of force and torque have the same meaning. Look at the effect of the counterclockwise movement of the capstan bar in figure 3-4. Here the amount of the effort is designated and the distance from the point where you apply the force to the center of the axle is L1 Then, E1 x L1 is the moment of force. You’ll notice that this term includes both the amount of the effort and the distance from the point of application of effort to the center of the axle. Ordinarily, you measure the distance in feet and the applied force in pounds. Therefore, you measure moments of force in footpounds (ft-lb). A moment of force is frequently called a moment. By using a longer capstan bar, the sailor in figure 3-4 can increase the effectiveness of his push without making a bigger effort. If he applied his effort closer to the head of the capstan and used the same force, the moment of force would be less.
You know that the sailor in figure 3-4 would land flat on his face if the anchor hawser snapped. As long as nothing breaks, he must continue to push on the capstan bar. He is working against a clockwise moment of force that is equal in magnitude, but opposite in direction, to his counterclockwise moment of force. The resisting moment, like the effort moment, depends on two factors. In the case of resisting moment, these factors are the force (R2) with which the anchor pulls on the hawser and the distance (L2) from the center of the capstan to its rim. The existence of this resisting force would be clear if the sailor let go of the capstan bar. The weight of the anchor pulling on the capstan would cause the whole works to spin rapidly in a clockwise direction—and good-bye anchor! The principle involved here is that whenever the counterclockwise and the clockwise moments of force are in balance, the machine either moves at a steady speed or remains at rest. This idea of the balance of moments of force can be summed up by the expression CLOCKWISE COUNTER = CLOCKWISE MOMENTS MOMENTS. Since a moment of force is the product of the amount of the force times the distance the force acts from the center of rotation, this expression of equality may be written:
Put this formula to work on a capstan problem. You grip a single capstan bar 5 feet from the center of a capstan head with a radius of 1 foot. You have to lift a 1/2-ton anchor. How big of a push does the sailor have to exert? First, write down the formula:
Consider now the sad case of Slim and Sam, as illustrated in figure 3-5. Slim has suggested that they carry the 300-pound crate slung on a handy 10-foot pole. He was smart enough to slide the load up 3 feet from Sam’s shoulder. Here’s how they made out. Use Slim’s shoulder as a fulcrum (F1). Look at the clockwise movement caused by the 300-pound load. That load is 5 feet away from Slim’s shoulder. If R1 is the load, and L1 the distance from Slim’s shoulder to the load, the clockwise (MA) moment is:
With Slim’s shoulder still acting as the fulcrum, the resistance of Sam’s effort causes a counterclockwise moment (MB)acting against the load moment. This counterclockwise moment is equal to Sam’s effort (E2) times the distance (L3) from his shoulder to the fulcrum (F1) at Slim’s shoulder. Since L2 = 8 ft, the formula is:
There is no rotation, so the clockwise moment and the counterclockwise
moment are equal. MA = (MB) Hence:
So poor Sam is carrying 187.5 pounds of the 330-pound load. What is Slim carrying? The difference between 300 and 187.5 = 112.5 pounds, of course! You can check your answer by the following procedure. This time, use Sam’s shoulder as the fulcrum (F2). The counterclockwise moment (MC) is equal to the 300-pound load (R1) times the distance (L2 = 3 feet) from Sam’s shoulder. MC 300 x 3 = 900 foot-pounds. The clockwise moment (MD) is the result of Slim’s lift (E1) acting at a distance (L3) from the fulcrum. L3 = 8 feet. Again, since counterclockwise moment equals clockwise moment, you have: 900 = E1 x 8, and
Slim, the smart sailor, has to lift only 112.5 pounds. There’s a sailor who really puts his knowledge to work.
Take a look at figure 3-6. It’s another capstanturning situation. To increase an effective effort, place a second capstan bar opposite the first and another sailor can apply a force on the second bar. The two sailors in figure 3-6 will apparently be pushing in opposite directions. Since they are on opposite sides of the axle, they are actually causing rotation in the same direction. If the two sailors are pushing with equal force, the moment of force is twice as great as if only one sailor were pushing. This arrangement is known technically as a couple. You will see that the couple is a special example of the wheel and axle. The moment of force is equal to the product of the total distance (Ln) between the two points and the force (E1) applied by one sailor. The equation for the couple may be written:
Additional information and explanation is available in the following,
Basic Machines Training Course - US Navy ("Wheel and Axle" excerpt, NAVEDTRA 14037, 1994)
You have probably watched a driver load barrels on a truck. He backs the truck up to the curb. The driver then places a long double plank or ramp from the sidewalk to the tailgate, and then rolls the barrel up the ramp. A 32-gallon barrel may weigh close to 300 pounds when full, and it would be a job to lift one up into the truck. Actually, the driver is using a simple machine called the inclined plane. You have seen the inclined plane used in many situations. Cattle ramps, a mountain highway and the gangplank are familiar examples. The inclined plane permits you to overcome a large resistance, by applying a small force through a longer distance when raising the load. Look at figure 4-1.
Here you see the driver easing the 300-pound barrel up to the bed of the truck, 3 feet above the sidewalk. He is using a plank 9 feet long. If he didn’t use the ramp at all, he’d have to apply 300-pound force straight up through the 3-foot distance. With the ramp, he can apply his effort over the entire 9 feet of the plank as he rolls the barrel to a height of 3 feet. It looks as if he could use a force only three-ninths of 300, or 100 pounds, to do the job. And that is actually the situation.
Here’s the formula:
In which L = length of the ramp, measured along the slope, 1 = height of the ramp, R = weight of the object to be raised, or lowered, E = force required to raise or lower the object. Now apply the formula this problem: In this case, L = 9ft, 1 = 3 ft, and R = 300 lb. By substituting these values in the formula, you get:
Since the ramp is three times as long as its height, the mechanical advantage is three. You find the theoretical mechanical advantage by dividing the total distance of the effort you exert by the vertical distance the load is raised or lowered. THE WEDGE The wedge is a special application of the inclined plane. You have probably used wedges. Abe Lincoln used a wedge to help him split logs into rails for fences. The blades of knives, axes, hatchets, and chisels act as wedges when they are forced into apiece of wood. The wedge is two inclined planes set base-to-base. By driving the wedge full-length into the material to cut or split, you force the material apart a distance equal to the width of the broad end of the wedge. See figure 4-2. Long, slim wedges give high mechanical advantage. For example, the wedge of figure 4-2 has a mechanical advantage of six. The greatest value of the wedge is that you can use it in situations in which other simple machines won’t work. Imagine the trouble you’d have trying to pull a log apart with a system of pulleys.
APPLICATIONS AFLOAT AND ASHORE
A common use of the inclined plane in the Navy is the gangplank. Going aboard the ship by gangplank illustrated in figure 4-3, is easier than climbing a sea ladder. You appreciate the mechanical advantage of the gangplank even more when you have to carry your seabag or a case of sodas aboard. Remember that hatch dog in figure 1-10? The use of the dog to secure a door takes advantage of the lever principle. If you look sharply, you can see that the dog seats itself on a steel wedge welded to the door. As the dog slides upward along this wedge, it forces the door tightly shut. This is an inclined plane, with its length about eight times its thickness. That means you get a theoretical mechanical advantage of eight. In chapter 1, you figured that you got a mechanical advantage of four from the lever action of the dog. The overall mechanical advantage is 8 x 4, or 32, neglecting friction. Not bad for such a simple gadget, is it? Push down with 50 pounds heave on the handle and you squeeze the door shut with a force of 1,600 pounds on that dog. You’ll find the damage-control parties using wedges by the dozen to shore up bulkheads and decks. A few sledgehammer blows on a wedge will quickly and firmly tighten up the shoring. Chipping scale or paint off steel is a tough job. How-ever, you can make the job easier with a compressed-air chisel. The wedge-shaped cutting edge of the chisel gets in under the scale or the paint and exerts a large amount of pressure to lift the scale or paint layer. The chisel bit is another application of the inclined plane.
The inclined plane is a simple machine that lets you raise or lower heavy objects by applying a small force over a long distance. You find the theoretical mechanical advantage of the inclined plane by dividing the length of the ramp by the perpendicular height of the load that is raised or lowered. The actual mechanical advantage is equal to the weight of the resistance or load, divided by the force that must be used to move the load up the ramp. The wedge is two inclined planes set base-to-base. It finds its greatest use in cutting or splitting materials.
The screw is a simple machine that has many uses. The vise on a workbench makes use of the mechanical advantage (M.A.) of the screw. You get the same advantage using glued screw clamps to hold pieces of furniture together, a jack to lift an automobile, or a food processor to grind meat. A screw is a modification of the inclined plane. Cut a sheet of paper in the shape of a right triangle and you have an inclined plane. Wind this paper around a pencil, as in figure 5-1, and you can see that the screw is actually an inclined plane wrapped around a cylinder. As you turn the pencil, the paper is wound up so that its hypotenuse forms a spiral thread. The pitch of the screw and paper is the distance between identical points on the same threads measured along the length of the screw.
To understand how the screw works, look at figure 5-2. Here you see the type of jack screw used to raise a house or apiece of heavy machinery. Notice that the jack has a lever handle; the length of the handle is equal to r.
If you pull the lever handle around one turn, its outer end has described a circle. The circumference of this circle is equal to . (Remember that equals 3.14, or 22/7). That is the distance you must apply the effort of the lever arm. At the same time, the screw has made one revolution, raising its height to equal its pitch (p). You might say that one full thread has come up out of the base. At any rate, the load has risen a distance p. Remember that the theoretical mechanical advantage (T.M.A.) is equal to the distance through which you apply the effort or pull, divided by the distance and resistance the load is moved. Assuming a 2-foot, or 24-inch, length for the lever arm and a 1/4-inch pitch for the thread, you can find the theoretical mechanical advantage by the formula:
A 50-pound pull on the handle would result in a theoretical lift of 50 x 602 or about 30,000 pounds—15 tons for 50 pounds. However, jacks have considerable friction loss. The threads are cut so that the force used to overcome friction is greater than the force used to do useful work. If the threads were not cut this way and no friction were present, the weight of the load would cause the jack to spin right back down to the bottom as soon as you released the handle.
In using the jack you exerted your effort through a distance of or 150 inches, to raise the screw 1/4 inch. It takes a lot of circular motion to get a small amount of straight line motion from the head of the jack. You will use this point to your advantage in the micrometer; it’s a useful device for making accurate small measurements—measurements of a few thousandths of an inch. In figure 5-3, you see a cutaway view of a micrometer.
The thimble turns freely on the sleeve, rigidly attached to the micrometer frame. The spindle attaches to the thimble and is fitted with screw threads that move the spindle and thimble to the right or left in the sleeve when you rotate the thimble. These screw threads are cut 40 threads to the inch. Hence, one turn of the thimble moves the spindle and thimble 1/40 of inch. This represents one of the smallest divisions on the micrometer. Four of these small divisions make 4/40 of an inch, or 1/10 inch. Thus, the distance from 0 to 1 or 1 to 2 on the sleeve represents 1/10, or 0.1, inch. To allow even finer measurements, the thimble is divided into 25 equal parts. It is laid out by graduation marks around its rim, as shown in figure 5-4. If you turn the thimble through 25 of these equal parts, you have made one complete revolution of the screw. This represents a lengthwise movement of 1/40 of an inch. If you turn the thimble one of these units on its scale, you have moved the spindle a distance of 1/25 of 1/40 inch, or 1/1000 of an inch—0.001 inch. The micrometer in figure 5-4 reads 0.503 inch, that is the true diameter of the half-inch drill-bit shank measured. This tells you that the diameter of this bit is 0.003 inch greater than its nominal diameter of 1/2 inch—0.5000 inch. Because you can make accurate measurements with this instrument, it is vital in every machine shop.
APPLICATIONS AFLOAT AND ASHORE
It’s a tough job to pull a rope or cable tight enough to get all the slack out of it. However, you can do it by using a turnbuckle. The turnbuckle (fig, 5-5) is an application of the screw. If you turn it in one direction, it takes up the slack in a cable. Turning it the other way allows slack in the cable. Notice that one bolt of the turnbuckle has left-hand threads and the other bolt has right-hand threads. Thus, when you turn the turnbuckle to tighten the line, both bolts tighten up. If both bolts were right-hand threadstandard thread-one would tighten while the other one loosened an equal amount. That would result in no change in cable slack. Most turnbuckles have the screw threads cut to provide a large amount of frictional resistance to keep the turnbuckle from unwinding under load. In some cases, the turnbuckle has a locknut on each of the screws to prevent slipping. You’ll find turnbuckles used in a hundred different ways afloat and ashore. Ever wrestled with a length of wire rope? Obstinate and unwieldy, wasn’t it? Riggers have dreamed up tools to help subdue wire rope. One of these tools-the rigger’s vise-is shown in figure 5-6. This rigger’s vise uses the mechanical advantage of the screw to hold the wire rope in place. The crew splices a thimble-a reinforced loop—onto the end of the cable. Rotating the handle causes the jaw on that screw to move in or out along its grooves. This machine is a modification of the vise on a workbench. Notice the right-hand and left-hand screws on the left-hand clamp. Figure 5-7 shows you another use of the screw. Suppose you want to stop a winch with its load suspended in mid-air.
To do this, you need a brake. The brakes on most anchor or cargo winches consist of a metal band that encircles the brake drum. The two ends of the band fasten to nuts connected by a screw attached to a handwheel. As you turn the handwheel, the screw pulls the lower end of the band (A) up toward its upper end (B). The huge mechanical advantage of the screw puts the squeeze on the drum, and all rotation of the drum stops. One type of steering gear used on many small ships and as a spare steering system on some larger ships is the screw gear. Figure 5-8 shows you that the wheel turns a long threaded shaft. Half the threads— those nearer the wheel end of this shaft-are right-hand threads. The other half of the threads-those farther from the wheel—are left-hand threads. Nut A has a right-hand thread, and nut B has a left-hand thread. Notice that two steering arms connect the crosshead to the nuts; the crosshead turns the rudder. If you stand in front of the wheel and turn it in a clockwise direction— to your right—arm A moves forward and arm B moves backward. That turns the rudder counterclockwise, so the ship swings in the direction you turn the wheel. This steering mechanism has a great mechanical advantage. Figure 5-9 shows you another practical use of the screw. The quadrant davit makes it possible for two men to put a large lifeboat over the side with little effort. The operating handle attaches to a threaded screw that passes through a traveling nut. Cranking the operating handle in a counterclockwise direction (as you face outboard), the nut travels outward along the screw. The traveling nut fastens to the davit arm by a swivel. The davit arm and the boat swing outboard as a result of the outward movement of the screw. The thread on that screw is the self-locking type; if you let go of the handle, the nut remains locked in position.
You have learned the following basic information about the screw from this chapter; now notice the different ways the Navy uses this simple machine: The screw is a modification of the inclined plane— modified to give you a high mechanical advantage. The theoretical mechanical advantage of the screw can be found by the formula:
As in all machines, the actual mechanical advantage equals the resistance divided by the effort. In many applications of the screw, you make use of the large amount of friction that is commonly present in this simple machine. By using the screw, you reduce large amounts of circular motion to very small amounts of straight-line motion.
Did you ever take a clock apart to see what made it tick? Of course you came out with some parts left over when you got it back together again. And they probably included a few gear wheels. We use gears in many machines. Frequently the gears are hidden from view in a protective case filled with grease or oil, and you may not see them. An eggbeater gives you a simple demonstration of the three jobs that gears do. They can change the direction of motion, increase or decrease the speed of the applied motion, and magnify or reduce the force that you apply. Gears also give you a positive drive. There can be, and usually is, creep or slip in a belt drive. However, gear teeth are always in mesh, so there can be no creep and slip. Follow the directional changes in figure 6-1.
The crank handle turns in the direction shown by the arrow—clockwise—when viewed from the right. The 32 teeth on the large vertical wheel (A) mesh with the 8 teeth on the right-hand horizontal wheel (B), which rotates as shown by the arrow. Notice that as B turns in a clockwise direction, its teeth mesh with those of wheel C and cause wheel C to revolve in the opposite direction. The rotation of the crank handle has been transmitted by gears to the beater blades, which also rotate. Now figure out how the gears change the speed of motion. There are 32 teeth on gear A and 8 teeth on gear B. However, the gears mesh, so that one complete revolution of A results in four complete revolutions of gear B. And since gears B and C have the same number of teeth, one revolution of B results in one revolution of C. Thus, the blades revolve four times as fast as the crank handle. In chapter 1 you learned that third-class levers increase speed at the expense of force. The same happens with the eggbeater. The magnitude of force changes. The force required to turn the handle is greater than the force applied to the frosting by the blades. This results in a mechanical advantage of less than one.
TYPES OF GEARS
When two shafts are not lying in the same straight line, but are parallel, you can transmit motion from one to the other by spur gears. This setup is shown in figure 6-2. Spur gears are wheels with mating teeth cut in their surfaces so that one can turn the other without slippage. When the mating teeth are cut so that they are parallel to the axis of rotation, as shown in figure 6-2, the gears are called straight spur gears. When two gears of unequal size are meshed together, the smaller of the two is usually called a pinion. By unequal size, we mean an unequal number of teeth causing one gear to be a larger diameter than the other. The teeth, themselves, must be of the same size to mesh properly. The most commonly used gears are the straight spur gears. Often you’ll run across another type of spur gear called the helical spur gear. In helical gears the teeth are cut slantwise across the working face of the gear. One end of the tooth, therefore, lies ahead of the other. Thus, each tooth has a leading end and a trailing end. Figure 6-3, view A, shows you the construction of these gears. In the straight spur gears, the whole width of the teeth comes in contact at the same time. However, with helical (spiral) gears, contact between two teeth starts first at the leading ends and moves progressively across the gear faces until the trailing ends are in contact. This kind of meshing action keeps the gears in constant contact with one another. Therefore, less lost motion and smoother, quieter action is possible.
One disadvantage of this helical spur gear is the tendency of each gear to thrust or push axially on its shaft. It is necessary to put a special thrust bearing at the end of the shaft to counteract this thrust. You do not need thrust bearings if you use herringbone gears like those shown in figure 6-4. Since the teeth on each half of the gear are cut in opposite directions, each half of the gear develops a thrust that counterbalances the other half. You’ll find herringbone gears used mostly on heavy machinery. Figure 6-3, views B, C, and D, also shows you three other gear arrangements in common use. The internal gear in figure 6-3, view B, has teeth on the inside of a ring, pointing inward toward the axis of rotation. An internal gear is meshed with an external gear, or pinion, whose center is offset from the center of the internal gear. Either the internal or pinion gear can be the driver gear, and the gear ratio is calculated the same as for other gears—by counting teeth. You only need a portion of a gear where the motion of the pinion is limited. You use the sector gear shown in figure 6-3, view C, to save space and material. The rack and pinion in figure 6-3, view D, are both spur gears. The rack is a piece cut from a gear with an extremely large radius. The rack-and-pinion arrangement is useful in changing rotary motion into linear motion.
THE BEVEL GEAR
So far most of the gears you’ve learned about transmit motion between parallel shafts. However, when shafts are not parallel (at an angle), we use another type of gear called the bevel gear. This type of gear can connect shafts lying at any given angle because you can bevel them to suit the angle. Figure 6-5, view A, shows a special case of the bevel gear-the miter gear. You use the miter gears to connect shafts having a 90-degree angle; that means the gear faces are beveled at a 45-degree angle. You can see in figure 6-5, view B, how bevel gears are designed to join shafts at any angle. Gears cut at any angle other than 45 degrees are bevel gears. The gears shown in figure 6-5 are straight bevel gears, because the whole width of each tooth comes in contact with the mating tooth at the same time. However, you’ll run across spiral bevel gears with teeth cut to have advanced and trailing ends. Figure 6-6 shows you what spiral bevel gears look like. They have the same advantage as other spiral (helical) gears—less lost motion and smoother, quieter operation.
THE WORM AND WORM WHEEL
Figure 6-7.—Worm gears. Worm and worm-wheel combinations, like those in figure 6-7, have many uses and advantages. However, it’s better to understand their operating theory before learning of their uses and advantages. Figure 6-7, view A, shows the action of a single-thread worm. For each revolution of the worm, the worm wheel turns one tooth. Thus, if the worm wheel has 25 teeth, the gear ratio is 25:1.
Figure 6-7, view B, shows a double-thread worm. For each revolution of the worm in this case, the worm wheel turns two teeth. That makes the gear ratio 25:2 if the worm wheel has 25 teeth. A triple-thread worm would turn the worm wheel three teeth per revolution of the worm. A worm gear is a combination of a screw and a spur gear. You can obtain remarkable mechanical advantages with this arrangement. You can design worm drives so that only the worm is the driver-the spur cannot drive the worm. On a hoist, for example, you can raise or lower the load by pulling on the chain that turns the worm. If you let go of the chain, the load cannot drive the spur gear; therefore, it lets the load drop to the deck. This is a nonreversing worm drive.
Additional information and explanation is available in the 178 page US Navy training manual Basic Machines Training Course, also known as NAVEDTRA 14037 February 1994.