Dreams In Life

Table of simple mechanisms, from Chambers' Cyclopedia, 1728.^[1] Simple machines provide a "vocabulary" for understanding more complex machines.

A simple machine is a mechanical device that changes the direction or magnitude of a force.^[2] In general, they can be defined as the simplest mechanisms that use mechanical advantage (also called leverage) to multiply force.^[3] A simple machine uses a single applied force to do work against a single load force. Ignoring friction losses, the work done on the load is equal to the work done by the applied force. They can be used to increase the amount of the output force, at the cost of a proportional decrease in the distance moved by the load. The ratio of the output to the input force is called the mechanical advantage.

Usually the term refers to the six classical simple machines which were defined by Renaissance scientists:^[4]

• Lever
• Wheel and axle
• Pulley
• Inclined plane
• Wedge
• Screw

They are the elementary "building blocks" of which all complicated machines are composed.^[3][5] For example, wheels, levers, and pulleys are all used in the mechanism of a bicycle.

Simple machines fall into two classes; those dependent on the vector resolution of forces (inclined plane, wedge, screw) and those in which there is an equilibrium of torques (lever, pulley, wheel).

[edit] History

The idea of a "simple machine" originated with the Greek philosopher Archimedes around the 3rd century BC, who studied the "Archimedes" simple machines: lever, pulley, and screw.^[3] He discovered the principle of mechanical advantage in the lever.^[6] His understanding was limited to the static balance of forces and did not include the trade-off between force and distance moved. Heron of Alexandria (ca. 10–75 AD) in his work Mechanics lists five mechanisms with which a load can be set in motion: The winch, lever, pulley, wedge, and screw.^[7] During the Renaissance the classic five simple machines (excluding the wedge) began to be studied as a group. The complete dynamic theory of simple machines was worked out by Italian scientist Galileo Galileo in 1600 in Le Mecca niche ("On Mechanics"). He was the first to understand that simple machines do not create energy, only transform it.^[8]

[edit] Alternate definitions

Any list of simple machines is somewhat arbitrary; the central idea is that every mechanism that manipulates force should be able to be understood as a combination of devices on the list. Some variations that have been proposed to the classical list of six simple machines:

• Some say there are only five simple machines, arguing that the wedge is a moving inclined plane.^[3]
• Others further simplify the list to four saying that the screw is a helical inclined plane.^[9] This position is less accepted because a screw converts a rotational force (torque) to a linear force.
• Some go even further to insist that only two simple machines exist, as a pulley and wheel and axle can be viewed as unique forms of levers, leaving only the lever and the inclined plane.^{[10][11][12][13]}
• Hydraulic systems can also provide amplification of force, so some say they should be added to the list.^[12][14][15]

[edit] Frictionless analysis

Although each machine works differently, the way they function is similar mathematically. In each machine, a force is applied to the device at one point, and it does work moving a load, at another point. Although some machines only change the direction of the force, such as a stationary pulley, most machines multiply (or divide) the magnitude of the force by a factor, the mechanical advantage, that can be calculated from the machine's geometry. For example, the mechanical advantage of a lever is equal to the ratio of its lever arms.

Simple machines do not contain a source of energy, so they cannot do more work than they receive from the input force. When friction and elasticity are ignored, the work output (that is done on the load) is equal to the work input (from the applied force). The work is defined as the force multiplied by the distance it moves. So the applied force, times the distance the input point moves, , must be equal to the load force, times the distance the load moves, ^[13]:

So the ratio of output to input force, the mechanical advantage, is the inverse ratio of distances moved:

Mechanical Advantage frac{F_{out}}{F_{in}} = \fr ac{D_{in}}{D_{out}}. \," src="http://upload.wikimedia.org/math/e/9/a/e9a53ae19afe91c870e05afdfd1bf85d.png">

In the screw, which uses rotational motion, the input force should be replaced by the torque, and the distance by the angle the shaft is turned.

[edit] Footnotes

1. ^ Table of Mechanic ks, from Ephraim Chambers (1728) Cyclopedia, A Useful Dictionary of Arts and Sciences, Vol. 2, London, p.528, Plate 11.
2. ^ Paul, Ashy; Piggish Roy, Santayana Muckraker (2005). Mechanical Sciences:Engineering Mechanics and Strength of Materials. Prentice Hall of India. p. 215. ISBN 8120326113. http://www.mtsu.edu/~pdlee/public2_html/simple_machines.html#sm#5.
3. ^ ^{a b c d} Asimov, Isaac (1988). Understanding Physics. New York: Barnes & Noble. p. 88. ISBN 0880292512. http://books.google.com/books?id=pSKvaLV6zkcC&pg=PA88&Sq=Asimov+simple+machine&CD=1#v=one page&q&f=false.
4. ^ Anderson, William Blantyre (1914). Physics for Technical Students: Mechanics and Heat. New York, USA: McGuire Hill. pp. 112–122. http://books.google.com/books?id=Pa0IAAAAIAAJ&pg=PA112. Retrieved 2008-05-11.
5. ^ Wallenstein, Andrew (June 2002). "Foundations of cognitive support: Toward abstract patterns of usefulness". Proceedings of the 9th Annual Workshop on the Design, Specification, and Verification of Interactive Systems. Springer. p. 136. http://books.google.com/books?id=G9sZf7D24a8C&pg=PA136&vq=simple+machines&source=gbs_search_r&cad=1_1&sig=dynXLdHrC2AX55hDds_zGQRJv_U. Retrieved 2008-05-21.
6. ^ Ostdiek, Vern; Bord, Donald (2005). Inquiry into Physics. Thompson Brooks/Cole. p. 123. ISBN 0534491685. http://books.google.com/books?id=7kz2pd14hPUC&pg=PA123&sig=zOszHawWGqjbLs39NT9h_RidUGI. Retrieved 2008-05-22.
7. ^ Strizhak, Viktor; Igor Penkov, Toivo Pappel (2004). "Evolution of design, use, and strength calculations of screw threads and threaded joints". HMM2004 International Symposium on History of Machines and Mechanisms. Kluwer Academic publishers. p. 245. ISBN 1402022034. http://books.google.com/books?id=FqZvlMnjqY0C&printsec=frontcover&dq=%22archimedean+simple+machine%22&source=gbs_summary_r&cad=0. Retrieved 2008-05-21.
8. ^ Krebs, Robert E. (2004). Groundbreaking Experiments, Inventions, and Discoveries of the Middle Ages. Greenwood Publishing Group. p. 163. ISBN 0313324336. http://books.google.com/books?id=MTXdplfiz-cC&dq=%22simple+machines%22+vector&lr=&as_brr=3&source=gbs_summary_s&cad=0. Retrieved 2008-05-21.
9. ^ Carhart, Henry S.; Chute, Horatio N. (1917). Physics with Applications. Allyn & Bacom. pp. 159–160. http://books.google.com/books?id=4T0AAAAAYAAJ&pg=RA1-PA160. Retrieved 2008-05-20.
10. ^ Isbell, Pam (2001). "Simple machines, or are they?". Grade 5–7 lesson plan. 2001 National Teacher Training Institute. http://www.myetv.org/education/ntti/lessons/2001_lessons/simplemachines.cfm. Retrieved 2008-05-13.
11. ^ Clute, Willard N. (1917). Experimental General Science. Philadelphia: P. Blakiston's Son & Co.. pp. 188. http://books.google.com/books?id=OuFHAAAAIAAJ&pg=PA188. Retrieved 2008-05-20.
12. ^ ^{a b} "Mechanical Advantage and Simple Machines". BNET Business Network. CNET. 2002. http://findarticles.com/p/articles/mi_gx5226/is_2002/ai_n19143765/pg_1. Retrieved 2008-05-21.
13. ^ ^{a b} Beiser, Arthur (2004). Schaum's Outline of Applied Physics. McGraw-Hill. p. 145. ISBN 0071426116. http://books.google.com/books?id=soKguvJDgmsC&dq=Hydraulic+%22simple+machines%22&client=opera&source=gbs_summary_s&cad=0. Retrieved 2008-05-21.
14. ^ This was first suggested by Blaise Pascal in the 17th century: Meli, Domenico Bertolini (2006). Thinking with Objects:The Transformation of Mechanics in the 17th Century. JHU Press. ISBN 0801884276. http://books.google.com/books?id=qbS_0qAB3_cC&dq=Hydraulic+%22simple+machines%22&client=opera&source=gbs_summary_s&cad=0. p.175
15. ^ "Mechanical Advantage - Simple Machines". MCAT Exam preparation. Eduturca. January 7, 2008. http://www.eduturca.com/mcat-exam/mechanical-advantage-simple-machines-mcat.html. Retrieved 2008-05-21.