ВходНахал topic simple machines. Методическая разработка занятия по английскому языку на тему "Машины и работа" (3 курс)
(15 minutes)- Distribute small toy cars that have wheels joined by axles to groups of students. Kick-start a discussion with some questions about the toy car mechanics, such as: How do these toy cars move? How are the wheels on each side of the car joined to each other?
- Have a student volunteer point to the rod that holds the two wheels together. Explain that the bar that joins two wheels is called an axle .
- Tell students that they will be learning about wheels and axles.
- Hold up the doorknob, explaining that it is an everyday example of a wheel and axle.
- Challenge the students to help you identify the wheel and axle in the doorknob. Listen as different students call out their guesses.
- After some speculation, tell students that the knob that turns is the wheel. The inner rod that is attached to the knob is the axle.
- Demonstrate how the wheel and axle works by turning the knob (wheel). That turns the inner rod (axle) and moves the latch, to open the door.
Guided Practice
(15 minutes)- To consolidate student thinking, set up activity stations with play dough and a rolling pin.
- Let students practice flattening the dough with the pin.
- Guide them to express these understandings: The rolling pin is a wheel and axle. When you push on the handles (the axle) the wheel turns and flattens out the dough.
- Challenge students to think of other common machines that have one wheel like the rolling pin. Great examples include a wheelbarrow, a top, and a playground merry-go-round.
Independent working time
(15 minutes)- Pass out a copy of the Wheel and Axle worksheet to each student to complete independently.
- Walk around the classroom to offer support to students who get stuck.
Differentiation
- Enrichment: Have students who need more of a challenge read a history of other simple machines, and fill out an accompanying word search.
- Support: Put students who need more support into pairs to complete the Wheel and Axle worksheet.
Assessment
(10 minutes)- Collect the worksheets that the students have filled out, and correct them using the Wheel and Axle answer sheet.
Review and closing
(5 minutes)- In summary, remind students that the rolling pin is a wheel and axle. When you push on the handles (the axle) the wheel turns and flattens out the dough.
- Challenge students to think of other common machines that have one wheel like the rolling pin, such as a wheelbarrow, top, and merry-go-round.
- Remind your class that the wheel and axle is only one of six common simple machines that help things move. For homework or additional independent work, consider encouraging students to learn more about other kinds of simple machines.
Easier
- A simple
machine is a device that helps make work easier; a
device that makes it easier to move something. Some
simple machines are a wheel, a pulley, a lever, a
screw, and an inclined plane.
Harder
- Most
machines consist of a number of elements, such as
gears and ball bearings, that work together in a
complex way. No matter how complex a machine, it is
still based on the compounding of six types of simple
machines. The six types of machines are the lever, the
wheel and axle, the pulley, the inclined plane, the
wedge, and the screw.
Background
Information for Simple Machines
from
National Museum of Science and Technology
,
Canada
http://www.science-tech.nmstc.ca/english/schoolzone/Info_Simple_Machines.cfm
Here you can find the answers to some commonly
asked questions about simple machines.
The
Elements of Machines: Simple Machines
from
Leonardo"s Workshop
http://www.mos.org/sln/Leonardo/InventorsToolbox.html
Learn about devices that make work easier to do by
providing some tradeoff between the force applied and
the distance over which the force is applied. Also
provides a brief introduction to uses of a gear, cam,
crank and rod, chain and belt, and the ratchet.
Levers
from Beakman & Jax
http://www.beakman.com/lever/lever.html
Play with levers and find out how work from the
fulcrum to the load to the effort.
(Wait for second page to come)
Marvelous
Machines
http://www.galaxy.net:80/~k12/machines/index.shtml
This website provides a series of experiments
about simple machines: levers, wheels and inclined
planes. They were developed for third grade students.
(Comes up slowly
)
| After exploring some or all of the websites below, complete one or more of these activities: Investigate Wheels with Your Bicycle. Go to PBS Teachersource"s website and use your bicycle to learn about the wheel. Find Out How Stuff Works. Check out How Stuff Works . Look for a device that uses a simple machine as part of how it works. Create a poster showing how it works. Gear Up with a Tricycle & Bicycle. Visit PBS Teachersource"s site and follow the procedures there to learn a lot more about gears. Complete a Simple Machines WebQuest. Follow or adapt the procedures found at one of these webQuest sites: 1) Exploring Simple Machines by Paula Markowitz (Grade 4) http://www.lakelandschools.org/EDTECH/Machines/Machines.htm 2) Simple Machines http://www.eng.iastate.edu/twt/Course/packet/labs/wheels&leverLab.htm 3) Simple Machines WebQuest (Grade 4-6) http://www.plainfield.k12.in.us/hschool/webq/webq8/jjquest.htm 4) Simple Machines http://www.beth.k12.pa.us/schools/wwwclass/mcosgrove/simple.htm 5) Simple Machines Webquest http://www.jsd.k12.ak.us/ab/el/simplemachines.html Complete an Online Simple Machines Activity. Learn more about simple machines by following the directions at A Time for Simple Machines . You may also want to test your knowledge at Gadget Anatomy . Complete Some Simple Machine Experiments. Find lots of experiments at sites like Marvelous Machines and Motion, Energy and Simple Machines . |
HanicalSimple Machines and its Mechanical Advantage What are Simple Machines ? What do we mean by Mechanical Advantage? Simple Machines * creates a greater output force than the input force Therefore since work is performed by applying a force over a distance, with the use of these machines we can do more work with lesser effort than working with our bare hands. In short, they make work easier. Mechanical Advantage * The Ratio between the input force and the output force. * The measure of the force amplification achieved by using a tool, mechanical device or machine system. Anyway what is input and output force? Input refers to the force you applied while output refers to the resultant force the object has from the input force. Example: I pushed a ball with 10 N of force, it is rolling with 10 N of force. I input 10 N into it, now it is outputting 10 N. The Six Classical Simple Machines The Lever(French word that means “to raise”) * A simple machine that allows you to gain a mechanical advantage in moving an object or in applying a force to an object. It is considered a "pure" simple machine because friction is not a factor to overcome, as in other simple machines . Part | Description | Fulcrum | Is where a solid board or rod can pivot...
Simple Machines Examples With Pictures Essay
Applied Force Other First Class Lever Examples Applied Force Action Force Spring Load Force Action http://library.thinkquest.org/J002079F/lever.htm Third Class Lever Effort or Applied Force Egg ready to be launched Release hook Compressed Spring Load or Resistance Fulcrum Applied force can be in any direction http://www.usoe.k12.ut.us/curr/science/sciber00/8th/machines /sciber/lever3.htm http://www.usoe.k12.ut.us/curr/science/sciber00/8th/machines /images/tweezer.gif http://www.usoe.k12.ut.us/curr/science/sciber00/8th/machines /images/base.jpg Inclined Plane An inclined plane is a slanted surface used to raise an object. An inclined plane decreases the size of the effort force needed to move an object. However, the distance through which the effort force is applied is increased. The Big Rock rolling downhill with gravitational force IS NOT an example of an inclined plane. The inclined plane gives you mechanical advantage AGAINST gravity. Big Rock http://www.sirinet.net/~jgjohnso/simple.html An example of how an Inclined Plane can be used to raise a mass to activate another simple machine Egg ready to be launched By First Class Lever F Big Rock Force pushing (or pulling) Big Rock up the hill Inclined Plane First Class Lever Wedges Pulleys Wedges are moving inclined planes that are driven under loads to lift Pulleys use a wheel or set of wheels around which a single length (not...
Activity 1.1.2 Simple Machines Practice Problems Answer Key Essay
Activity 1.1.2 Simple Machines Practice Problems Answer Key Procedure Answer the following questions regarding simple machine systems. Each question requires proper illustration and annotation, including labeling of forces, distances, direction, and unknown values. Illustrations should consist of basic simple machine functional sketches rather than realistic pictorials. Be sure to document all solution steps and proper units. All problem calculations should assume ideal conditions and no friction loss. Simple Machines – Lever A first class lever in static equilibrium has a 50lb resistance force and 15lb effort force. The lever’s effort force is located 4 ft from the fulcrum. 1. Sketch and annotate the lever system described above. 2. What is the actual mechanical advantage of the system? Formula Substitute / Solve Final Answer AMA = 3.33 3. Using static equilibrium calculations, calculate the length from the fulcrum to the resistance force. Formula Substitute / Solve Final Answer A wheel barrow is used to lift a 200 lb load. The length from the wheel axle to the center of the load is 2 ft. The length from the wheel and axle to the effort is 5 ft. 4. Illustrate and annotate the lever system described above. 5. What is the ideal mechanical advantage of the system?...
Compound Machine
Our compound machine , consisting of mainly three different simple machines , is a crane designed to multiply your force in order to effectively and efficiently lift the four 75 kg up a steep hill. Our machine starts off with the gear train. As you rotate the handle, all the gears rotate along as well. Since we connected the rope of the pulley to our gears, it then puts the pulley system into action. We created movable pulleys throughout the arm until the tip to stabilize our rope and also give us a mechanical advantage. At the top section of our arm we created a lever to support the load. This magnifies our effort force since a combination of all the mechanical energy is being carried out. With the pulley system, connected all the way to the gear train, and the lever working all together, our mechanical advantage is increased greatly. We created a series of gear trains to not only increase our advantage of torque in the machine but also to increase the mechanical advantage rather than losing efficiency due to friction and thermal energy. Doing this, we magnified our effort force onto the load. Also, in the gears, we arranged it so that the input gear and the output gear gave us a low gear ratio and the idler gears in between. It also allows us to control the direction of our force in the machine . Since it is linked to the pulley, we can control the direction of the rope. However, it only...
Essay
SAMPLE PROBLEMS: . Simple Machines – Lever A first class lever in static equilibrium has a 50lb resistance force and 15lb effort force. The lever’s effort force is located 4 ft from the fulcrum. Sketch and annotate the lever system described above. | What is the actual mechanical advantage of the system? Formula | Substitute / Solve | Final Answer | | | AMA = 3.33 | * Using static equilibrium calculations, calculate the length from the fulcrum to the resistance force. Formula | Substitute / Solve | Final Answer | | | | A wheel barrow is used to lift a 200 lb load. The length from the wheel axle to the center of the load is 2 ft. The length from the wheel and axle to the effort is 5 ft. Illustrate and annotate the lever system described above. | What is the ideal mechanical advantage of the system? Formula | Substitute / Solve | Final Answer | | | | * Using static equilibrium calculations, calculate the effort force needed to overcome the resistance force in the system. Formula | Substitute / Solve | Final Answer | | | | A medical technician uses a pair of four inch long tweezers to remove a wood sliver from a patient. The technician is applying 1 lb of squeezing force to the tweezers. If more than 1/5 lb of force is applied to the sliver, it will break and become difficult to remove. Sketch and annotate the lever system...
Essay on Simple Machines
...Simple machines are extremely important to everyday life. They make stuff that is normally difficult a piece of cake. There are several types of simple machines . The first simple machine is a lever. A lever consists of a fulcrum, load, and effort force. A fulcrum is the support. The placing of the fulcrum changes the amount of force and distance it will take in order to move an object. The load is the applied force. The effort force is the force applied on the opposite side of the load. Levers can be placed in three classes. The 1st class levers are objects like pliers where the fulcrum is at the center of the lever. The 2nd class of levers are objects that have the fulcrum on the opposite side of the applied force like a nutcracker. The 3rd and final class is objects like crab claws. These objects of the load at one end and the fulcrum on the other. An inclined plane is another simple machine . Inclined planes are also known as ramps. Ramps make a trade off between distance and force. No matter how steep the ramp, the work is still the same. A winding road on a mountain side is a good example of a ramp. Some simple machines are modified inclined planes. The wedge is one of those machines . One or two inclined planes make up a wedge. Saws, knives,needles, and axes are made from wedges....
Simple Machines Essay
...Simple Machines Definitions: Machine - A device that makes work easier by changing the speed , direction, or amount of a force. Simple Machine - A device that performs work with only one movement. Simple machines include lever, wheel and axle, inclined plane, screw, and wedge. Ideal Mechanical Advantage (IMA)- A machine in which work in equals work out; such a machine would be frictionless and a 100% efficient IMA= De/Dr Actual Mechanical Advantage (AMA)- It is pretty much the opposite of IMA meaning it is not 100% efficient and it has friction. AMA= Fr/Fe Efficiency- The amount of work put into a machine compared to how much useful work is put out by the machine ; always between 0% and 100%. Friction- The force that resist motion between two surfaces that are touching each other. What do we use machines for? Machines are used for many things. Machines are used in everyday life just to make things easier. You use many machines in a day that you might take for granted. For example a simple ordinary broom is a machine . It is a form of a lever. Our country or world would never be this evolved if it wasn"t for machine . Almost every thing we do has a machine involved. We use machines ...
Simple Machine A machine with few Essay
... Simple Machine : A machine with few or no moving parts. Simple machines make work easier. Examples: Screw, Wheel and Axle, Wedge, Pulley, Inclined Plane, Lever Compound Machine : Two or more simple machines working together to make work easier. Examples: Wheelbarrow, Can Opener, Bicycle Inclined plane: A sloping surface, such as a ramp. Makes lifting heavy loads easier. The trade-off is that an object must be moved a longer distance than if it was lifted straight up, but less force is needed. Examples: Staircase, Ramp Lever: A straight rod or board that pivots on a point known as a fulcrum. Pushing down on one end of a lever results in the upward motion of the opposite end of the fulcrum. Examples: Door on Hinges, Seesaw, Hammer, Bottle Opener Pulley: A wheel that usually has a groove around the outside edge for a rope or belt. Pulling down on the rope can lift an object attached to the rope. Work is made easier because pulling down on the rope is made easier due to gravity. Examples: Flag Pole, Crane, Mini-Blinds Screw: An inclined plane wrapped around a shaft or cylinder. This inclined plane allows the screw to move itself or to move an object or material surrounding it when rotated. Examples: Bolt, Spiral Staircase Wedge: Two inclined planes joined back to back. Wedges are used to split things....
The wheel and axle , the inclined plane , the wedge , the , and the screw . Several of these simple machines are related to each other. But, each has a specific purpose in the world of doing work.
There are special tools for measuring the force necessary to move an object. These are known as force meters. They use a spring and a hook to determine how much pull is required to slide an object up an inclined plane. Really very simple to use.
Compound Machines
Simple machines can be combined together to form compound machines. Many of our everyday tools and the objects we use are really compound machine . Scissors are a good example. The edge of the blades are wedges. But the blades are combined with a lever to make the two blades come together to cut.
A lawnmower combines wedges (the blades) with a wheel and axle that spins the blades in a circle. But there is even more. The engine probably works in combination of several simple machines and the handle that you use to push the lawnmower around the yard is a form of a lever. So even something complicated can be broken down into the simplest of machines.
Take a look around you — can you figure out what simple machines make up a can opener, the hand cranked pencil sharpener, the ice dispenser in the refrigerator or the stapler? Just be careful, though. In our modern times, many things rely on electronics and light waves to function and are not made of simple machines. But even then, you may be surprised. The turntable in your microwave oven is a wheel and axle. The lid to the laptop is connected to the pad by a hinge or lever.
Simple machines may be simple — but they are simply everywhere.
A Word or Two About Rube
Rube Goldberg was a famous cartoonist who lived between 1883 and 1970. His life was spent creating art and sculptures, but his most famous work was for his "inventions." These inventions were a series of simple machines put together in a complex fashion to accomplish something very simple, but it took many steps to get there. Contests have been run for many years since Mr. Goldberg first created his unique ideas. In the contests people try to come up with new ways to turn on a light, or start a toaster using these combinations of the simple machines to wow judges and audiences for their unique way of doing these simple tasks.
Rube Goldberg machines are fun to watch and to build. Visit this site for some fun — see if you can identify each of the simple machines as they work together in this animation of a Rube Goldberg gadget designed to get this guy out of bed in the morning. Click .
For more information about Rube Goldberg"s life and his art, click .
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Transcription
You"re watching FreeSchool! Hi everyone! Today we"re going to talk about simple machines. A simple machine is a device that makes work easier by magnifying or changing the direction of a force. That means that simple machines allow someone to do the same work with less effort! Simple machines have been known since prehistoric times and were used to help build the amazing structures left behind by ancient cultures. The Greek philosopher Archimedes identified three simple machines more than 2,000 years ago: the lever, the pulley, and the screw. He discovered that a lever would create a mechanical advantage, which means that using a lever would allow a person to move something that would normally be too heavy for them to shift. Archimedes said that with a long enough lever and a place to rest it, a person could move the world. Over the next few centuries more simple machines were recognized but it was less than 450 years ago that the last of the simple machines, the inclined plane, was identified. There are six types of simple machines: the Lever, the Wheel and Axle, the Pulley, the Inclined plane, the Wedge, and the Screw. Pulleys and Wheel and Axles are both a type of Lever. Wedges and Screws are both types of Inclined Planes. Each type of Simple Machine has a specific purpose and way they help do work. When speaking of simple machines, "work" means using energy to move an object across a distance. The further you have to move the object, the more energy it takes to move it. Let"s see how each type of simple machine helps do work. A LEVER is a tool like a bar or rod that sits and turns on a fixed support called a fulcrum. When you use a lever, you apply a small force over a long distance, and the lever converts it to a larger force over a shorter distance. Some examples of levers are seesaws, crowbars, and tweezers. A Wheel and Axle is easy to recognize. It consists of a wheel with a rod in the middle. You probably already know that it"s easier to move something heavy if you can put it in something with wheels, but you might not know why. For one thing, using wheels reduces the friction - or resistance between surfaces - between the load and the ground. Secondly, much like the lever, a smaller force applied to the rim of the wheel is converted to a larger force traveling a smaller distance at the axle. Wheel and axles are used for machines such as cars, bicycles, and scooters, but they are also used in other ways, like doorknobs and pencil sharpeners. A Pulley is a machine that uses a wheel with a rope wrapped around it. The wheel often has a groove in it, which the rope fits into. One end of the rope goes around the load, and the other end is where you apply the force. Pulleys can be used to move loads or change the direction of the force you are using, and help make work easier by allowing you to spread a weaker force out along a longer path to accomplish a job. By linking multiple pulleys together, you can do the same job with even less force, because you are applying the force along a much longer distance. Pulleys may be used to raise and lower flags, blinds, or sails, and are used to help raise and lower elevators. An Inclined Plane is a flat surface with one end higher than the other. Inclined planes allow loads to slide up to a higher level instead of being lifted, which allows the work to be accomplished with a smaller force spread over a longer distance. You may recognize an inclined plane as the simple machine used in ramps and slides. A Wedge is simply two inclined planes placed back to back. It is used to push two objects apart. A smaller force applied to the back of the wedge is converted to a greater force in a small area at the tip of the wedge. Examples of wedges are axes, knives, and chisels. A Screw is basically an inclined plane wrapped around a pole. Screws can be used to hold things together or to lift things. Just like the inclined plane, the longer the path the force takes, the less force is required to do the work. Screws with more threads take less force to do a job since the force has to travel a longer distance. Examples of screws are screws, nuts, bolts, jar lids, and lightbulbs. These six simple machines can be combined to form compound or complex machines, and are considered by some to be the foundation of all machinery. For example, a wheelbarrow is made of levers combined with a wheel and axle. A pair of scissors is another complex machine: the two blades are wedges, but they are connected by a lever that allows them to come together and cut. We use simple machines to help us do work every day. Every time you open a door or a bottle, cut up your food, or even just climb stairs, you are using simple machines. Take a look and see if you can identify the simple machines around you and figure out how they make it easier to do work.
Contents
History
The idea of a simple machine originated with the Greek philosopher Archimedes around the 3rd century BC, who studied the Archimedean simple machines: lever, pulley, and screw . He discovered the principle of mechanical advantage in the lever. Archimedes" famous remark with regard to the lever: "Give me a place to stand on, and I will move the Earth." (Greek : δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω ) expresses his realization that there was no limit to the amount of force amplification that could be achieved by using mechanical advantage. Later Greek philosophers defined the classic five simple machines (excluding the inclined plane) and were able to roughly calculate their mechanical advantage. For example, Heron of Alexandria (ca. 10–75 AD) in his work Mechanics lists five mechanisms that can "set a load in motion"; lever , windlass , pulley , wedge , and screw , and describes their fabrication and uses. However the Greeks" understanding was limited to the statics of simple machines; the balance of forces, and did not include dynamics ; the tradeoff between force and distance, or the concept of work .
Frictionless analysis
Although each machine works differently mechanically, the way they function is similar mathematically. In each machine, a force F in {\displaystyle F_{\text{in}}\,} is applied to the device at one point, and it does work moving a load, F out {\displaystyle F_{\text{out}}\,} at another point. Although some machines only change the direction of the force, such as a stationary pulley, most machines multiply the magnitude of the force by a factor, the mechanical advantage
M A = F out / F in {\displaystyle \mathrm {MA} =F_{\text{out}}/F_{\text{in}}\,}that can be calculated from the machine"s geometry and friction.
The mechanical advantage can be greater or less than one:
- The most common example is a screw. In most screws, applying torque to the shaft can cause it to turn, moving the shaft linearly to do work against a load, but no amount of axial load force against the shaft will cause it to turn backwards.
- In an inclined plane, a load can be pulled up the plane by a sideways input force, but if the plane is not too steep and there is enough friction between load and plane, when the input force is removed the load will remain motionless and will not slide down the plane, regardless of its weight.
- A wedge can be driven into a block of wood by force on the end, such as from hitting it with a sledge hammer, forcing the sides apart, but no amount of compression force from the wood walls will cause it to pop back out of the block.
A machine will be self-locking if and only if its efficiency η is below 50%:
η ≡ F o u t / F i n d i n / d o u t < 0.50 {\displaystyle \eta \equiv {\frac {F_{out}/F_{in}}{d_{in}/d_{out}}}<0.50\,}Whether a machine is self-locking depends on both the friction forces (coefficient of static friction) between its parts, and the distance ratio d in /d out (ideal mechanical advantage). If both the friction and ideal mechanical advantage are high enough, it will self-lock.
Proof
When a machine moves in the forward direction from point 1 to point 2, with the input force doing work on a load force, from conservation of energy the input work W 1,2 {\displaystyle W_{\text{1,2}}\,} is equal to the sum of the work done on the load force W load {\displaystyle W_{\text{load}}\,} and the work lost to friction
W 1,2 = W load + W fric (1) {\displaystyle W_{\text{1,2}}=W_{\text{load}}+W_{\text{fric}}\qquad \qquad (1)\,}If the efficiency is below 50% η = W load / W 1,2 < 1 / 2 {\displaystyle \eta =W_{\text{load}}/W_{\text{1,2}}<1/2\,}
2 W load < W 1,2 {\displaystyle 2W_{\text{load}}When the machine moves backward from point 2 to point 1 with the load force doing work on the input force, the work lost to friction W fric {\displaystyle W_{\text{fric}}\,} is the same
W load = W 2,1 + W fric {\displaystyle W_{\text{load}}=W_{\text{2,1}}+W_{\text{fric}}\,}So the output work is
W 2,1 = W load − W fric < 0 {\displaystyle W_{\text{2,1}}=W_{\text{load}}-W_{\text{fric}}<0\,}Thus the machine self-locks, because the work dissipated in friction is greater than the work done by the load force moving it backwards even with no input force
Modern machine theory
Kinematic chains
Classification of machines
The identification of simple machines arises from a desire for a systematic method to invent new machines. Therefore, an important concern is how simple machines are combined to make more complex machines. One approach is to attach simple machines in series to obtain compound machines.
However, a more successful strategy was identified by Franz Reuleaux , who collected and studied over 800 elementary machines. He realized that a lever, pulley, and wheel and axle are in essence the same device: a body rotating about a hinge. Similarly, an inclined plane, wedge, and screw are a block sliding on a flat surface.
This realization shows that it is the joints, or the connections that provide movement, that are the primary elements of a machine. Starting with four types of joints, the revolute joint , sliding joint , cam joint and gear joint , and related connections such as cables and belts, it is possible to understand a machine as an assembly of solid parts that connect these joints.
See also
References
- Chambers, Ephraim (1728), "Table of Mechanicks", Cyclopædia, A Useful Dictionary of Arts and Sciences , London, England, Volume 2, p. 528, Plate 11 .
- Paul, Akshoy; Roy, Pijush; Mukherjee, Sanchayan (2005), Mechanical sciences: engineering mechanics and strength of materials , Prentice Hall of India, p. 215, ISBN .
- ^ Asimov, Isaac (1988), Understanding Physics , New York, New York, USA: Barnes & Noble, p. 88, ISBN .
- Anderson, William Ballantyne (1914). Physics for Technical Students: Mechanics and Heat . New York, USA: McGraw Hill. pp. 112–122. Retrieved 2008-05-11 .
- ^ Compound machines , University of Virginia Physics Department, retrieved 2010-06-11 .
- ^ Usher, Abbott Payson (1988). A History of Mechanical Inventions . USA: Courier Dover Publications. p. 98. ISBN .
- Wallenstein, Andrew (June 2002). . Proceedings of the 9th Annual Workshop on the Design, Specification, and Verification of Interactive Systems . Springer. p. 136. Retrieved 2008-05-21 .
- ^ Prater, Edward L. (1994), Basic machines (PDF) , U.S. Navy Naval Education and Training Professional Development and Technology Center, NAVEDTRA 14037.
- U.S. Navy Bureau of Naval Personnel (1971), Basic machines and how they work (PDF) , Dover Publications.
- Reuleaux, F. (1963) , The kinematics of machinery (translated and annotated by A.B.W. Kennedy) , New York, New York, USA: reprinted by Dover.
- Cornell University , Reuleaux Collection of Mechanisms and Machines at Cornell University , Cornell University.
- ^ Chiu, Y. C. (2010), An introduction to the History of Project Management , Delft: Eburon Academic Publishers, p. 42,