3045:
37:
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2275:, the machine will move backwards, with the load force doing work on the input force. So these machines can be used in either direction, with the driving force applied to either input point. For example, if the load force on a lever is high enough, the lever will move backwards, moving the input arm backwards against the input force. These are called
1887:
319:
If a simple machine does not dissipate energy through friction, wear or deformation, then energy is conserved and it is called an ideal simple machine. In this case, the power into the machine equals the power out, and the mechanical advantage can be calculated from its geometric dimensions.
3087:
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.
2329:
On 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
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107:
losses, the work done on the load is equal to the work done by the applied force. The machine can 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 applied force is called the
1880:
1084:
912:
3095:, 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.
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The most common example is a screw. In most screws, one can move the screw forward or backward by turning it, and one can move the nut along the shaft by turning it, but no amount of pushing the screw or the nut will cause either of them to
266:, as the simple machines were called, began to be studied from the standpoint of how far they could lift a load, in addition to the force they could apply, leading eventually to the new concept of mechanical work. In 1586 Flemish engineer
988:
1764:
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1398:
204:) 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
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called a hinged joint. Similarly, the flat surface of an inclined plane and wedge are examples of the kinematic pair called a sliding joint. The screw is usually identified as its own kinematic pair called a helical joint.
2185:
1553:
784:
2022:{\displaystyle \mathrm {MA} _{\text{compound}}={F_{\text{out1}} \over F_{\text{in1}}}{F_{\text{out2}} \over F_{\text{in2}}}{F_{\text{out3}} \over F_{\text{in3}}}\ldots {F_{{\text{out}}N} \over F_{{\text{in}}N}}\,}
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128:
Although they continue to be of great importance in mechanics and applied science, modern mechanics has moved beyond the view of the simple machines as the ultimate building blocks of which all
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machine. These machines can only be set in motion by a force at the input, and when the input force is removed will remain motionless, "locked" by friction at whatever position they were left.
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derived the mechanical advantage of the inclined plane, and it was included with the other simple machines. The complete dynamic theory of simple machines was worked out by
Italian scientist
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819:
561:
1700:
The mechanical advantage of a compound machine is the ratio of the output force exerted by the last machine in the series divided by the input force applied to the first machine, that is
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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
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ranging from the steam engine to robot manipulators. The bearings that form the fulcrum of a lever and that allow the wheel and axle and pulleys to rotate are examples of a
2535:
1161:
492:
379:
3098:
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
3036:
that transmit forces and movement, monitored by sensors and controllers. The components of actuators and mechanisms consist of links and joints that form kinematic chains.
519:
348:
3420:
144:, is inadequately described by these six simple categories. Various post-Renaissance authors have compiled expanded lists of "simple machines", often using terms like
2294:
However, in some machines, if the frictional forces are high enough, no amount of load force can move it backwards, even if the input force is zero. This is called a
2359:
1663:
1356:
3020:
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.
2510:
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
2123:
1495:
284:), in which he showed the underlying mathematical similarity of the machines as force amplifiers. He was the first to explain that simple machines do not create
728:
2031:
Thus, the mechanical advantage of the compound machine is equal to the product of the mechanical advantages of the series of simple machines that form it
2962:
2333:
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
389:
3886:
3913:
3859:
3114:, 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.
2907:
299:(1452–1519), but were unpublished and merely documented in his notebooks, and were based on pre-Newtonian science such as believing friction was an
3751:
1283:
125:. The mechanical advantage of a compound machine is just the product of the mechanical advantages of the simple machines of which it is composed.
3675:
2866:{\displaystyle {\begin{aligned}2W_{\text{load}}&<W_{\text{load}}+W_{\text{fric}}\\W_{\text{load}}&<W_{\text{fric}}\end{aligned}}}
1681:
formed from a set of simple machines connected in series with the output force of one providing the input force to the next. For example, a
1665:. So a machine that includes friction will not be able to move as large a load as a corresponding ideal machine using the same input force.
1481:{\displaystyle {\begin{aligned}\eta &\equiv {P_{\text{out}} \over P_{\text{in}}}\\P_{\text{out}}&=\eta P_{\text{in}}\end{aligned}}}
3498:
2726:
3945:
3778:
2118:
Similarly, the efficiency of a compound machine is also the product of the efficiencies of the series of simple machines that form it
3614:
2875:
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
2598:
1226:, the output force is less than the input, but the distance moved by the load is greater than the distance moved by the input force.
525:
596:
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121:(sometimes called "compound machines") are composed. For example, wheels, levers, and pulleys are all used in the mechanism of a
3648:
675:
323:
Although each machine works differently mechanically, the way they function is similar mathematically. In each machine, a force
1875:{\displaystyle F_{\text{out1}}=F_{\text{in2}},\;F_{\text{out2}}=F_{\text{in3}},\,\ldots \;F_{{\text{out}}K}=F_{{\text{in}}K+1}}
3075:
by attaching a link that connects the output of one crank to the input of another. Additional links can be attached to form a
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3534:
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1645:
So in non-ideal machines, the mechanical advantage is always less than the velocity ratio by the product with the efficiency
196:
in the lever. Archimedes' famous remark with regard to the lever: "Give me a place to stand on, and I will move the Earth," (
3972:
3724:
60:(also called leverage) to multiply force. Usually the term refers to the six classical simple machines that were defined by
3297:
3219:
1089:
This can be calculated from the geometry of the machine. For example, the mechanical advantage and distance ratio of the
3575:
2459:
1136:, the output force is greater than the input, the machine acts as a force amplifier, but the distance moved by the load
1079:{\displaystyle \mathrm {MA} _{\text{ideal}}={F_{\text{out}} \over F_{\text{in}}}={d_{\text{in}} \over d_{\text{out}}}\,}
907:{\displaystyle \mathrm {MA} _{\text{ideal}}={F_{\text{out}} \over F_{\text{in}}}={v_{\text{in}} \over v_{\text{out}}}\,}
4060:
3393:
3307:
2502:(ideal mechanical advantage). If both the friction and ideal mechanical advantage are high enough, it will self-lock.
3587:
3381:
3354:
791:
4504:
3440:
4442:
4269:
3049:
3386:
Proceedings of the 9th Annual
Workshop on the Design, Specification, and Verification of Interactive Systems
3326:
1635:{\displaystyle \mathrm {MA} ={F_{\text{out}} \over F_{\text{in}}}=\eta {v_{\text{in}} \over v_{\text{out}}}}
2309:
Self-locking occurs mainly in those machines with large areas of sliding contact between moving parts: the
2109:{\displaystyle \mathrm {MA} _{\text{compound}}=\mathrm {MA} _{1}\mathrm {MA} _{2}\ldots \mathrm {MA} _{N}}
1197:
1107:
1393:) is defined as the ratio of power out to the power in, and is a measure of the frictional energy losses
308:
3428:, U.S. Navy Naval Education and Training Professional Development and Technology Center, NAVEDTRA 14037.
4223:
4200:
2443:{\displaystyle \eta \equiv {\frac {F_{\text{out}}/F_{\text{in}}}{d_{\text{in}}/d_{\text{out}}}}<0.5}
2220:
1361:
1253:
300:
2249:
568:
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2567:
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236:
88:
2513:
1139:
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357:
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1250:
All real machines have friction, which causes some of the input power to be dissipated as heat. If
497:
326:
117:
Simple machines can be regarded as the elementary "building blocks" of which all more complicated
3162:
3033:
2453:
243:, and describes their fabrication and uses. However the Greeks' understanding was limited to the
28:
4100:
4053:
2310:
2199:
1231:
644:. Similarly the power input from the applied force is equal to the velocity of the input point
464:
189:
140:
texts. The great variety and sophistication of modern machine linkages, which arose during the
93:
3524:
4447:
3999:
2334:
1336:
141:
24:
3246:
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3127:
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1341:
456:
382:
248:
193:
185:
129:
110:
57:
3576:"Evolution of design, use, and strength calculations of screw threads and threaded joints"
8:
3123:
3122:
The design of mechanisms to perform required movement and force transmission is known as
983:{\displaystyle {v_{\text{out}} \over v_{\text{in}}}={d_{\text{out}} \over d_{\text{in}}}}
209:
1759:{\displaystyle \mathrm {MA} _{\text{compound}}={F_{{\text{out}}N} \over F_{\text{in1}}}}
4133:
4029:
3474:
3060:
304:
3478:
3044:
4467:
4046:
4005:
3978:
3951:
3919:
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3865:
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3814:
3784:
3757:
3730:
3681:
3654:
3620:
3583:
3530:
3504:
3389:
3360:
3303:
3225:
3193:
2203:
296:
3072:
1239:
467:, in an ideal simple machine, the power output (rate of energy output) at any time
4483:
4452:
4350:
4213:
4025:
3152:
3131:
3107:
3103:
3076:
3056:
2207:
448:
351:
271:
165:
156:
to distinguish them from the classical simple machines above. By the late 1800s,
100:
20:
920:
is also equal to the ratio of the distances covered in any given period of time
19:
This article is about the concept in physics. For independent record label, see
4312:
4153:
4138:
4110:
4085:
3099:
3092:
3064:
2314:
1694:
252:
205:
197:
169:
157:
137:
83:
73:
208:) and were able to calculate their (ideal) mechanical advantage. For example,
4498:
4462:
4307:
4302:
4241:
4175:
2180:{\displaystyle \eta _{\text{compound}}=\eta _{1}\eta _{2}\ldots \;\eta _{N}.}
1685:
consists of a lever (the vise's handle) in series with a screw, and a simple
992:
Therefore, the mechanical advantage of an ideal machine is also equal to the
133:
3126:. This is a collection of geometric techniques for the mechanical design of
1548:{\displaystyle F_{\text{out}}v_{\text{out}}=\eta F_{\text{in}}v_{\text{in}}}
4297:
4208:
4143:
4128:
267:
3616:
Groundbreaking
Experiments, Inventions, and Discoveries of the Middle Ages
3382:"Foundations of cognitive support: Toward abstract patterns of usefulness"
1234:, which uses rotational motion, the input force should be replaced by the
4457:
4373:
4365:
4287:
4231:
4190:
779:{\displaystyle F_{\text{out}}v_{\text{out}}=F_{\text{in}}v_{\text{in}}\,}
259:
61:
3700:
This fundamental insight was the subject of
Galileo Galilei's 1600 work
3461:
The kinematics of machinery (translated and annotated by A.B.W. Kennedy)
36:
4416:
4378:
4292:
4264:
3157:
3135:
3111:
2452:
Whether a machine is self-locking depends on both the friction forces (
2211:
1686:
181:
1490:
As above, the power is equal to the product of force and velocity, so
56:. In general, they can be defined as the simplest mechanisms that use
4393:
3580:
HMM2004 International
Symposium on History of Machines and Mechanisms
2337:
force from the wood walls will cause it to pop back out of the block.
2194:
1094:
3809:
Uicker, John J. Jr.; Pennock, Gordon R.; Shigley, Joseph E. (2003),
3480:
Reuleaux
Collection of Mechanisms and Machines at Cornell University
3190:
Mechanical sciences: engineering mechanics and strength of materials
16:
Mechanical device that changes the direction or magnitude of a force
4398:
4388:
4317:
4170:
3438:
3167:
3029:
3011:{\displaystyle W_{\text{2,1}}=W_{\text{load}}-W_{\text{fric}}<0}
1768:
Because the output force of each machine is the input of the next,
452:
292:
228:
180:
The idea of a simple machine originated with the Greek philosopher
104:
3321:
3319:
431:{\displaystyle \mathrm {MA} ={F_{\text{out}} \over F_{\text{in}}}}
4408:
4327:
4279:
4069:
451:
than they receive from the input force. A simple machine with no
440:
that can be calculated from the machine's geometry and friction.
244:
122:
118:
49:
247:
of simple machines (the balance of forces), and did not include
4345:
4185:
4095:
3573:
3316:
1235:
444:
285:
232:
78:
2950:{\displaystyle W_{\text{load}}=W_{\text{2,1}}+W_{\text{fric}}}
2641:{\displaystyle W_{\text{1,2}}=W_{\text{load}}+W_{\text{fric}}}
4437:
4432:
4383:
4120:
4090:
2341:
A machine will be self-locking if and only if its efficiency
2246:
on the machine is high enough in relation to the input force
1090:
996:, the ratio of input distance moved to output distance moved
637:{\displaystyle P_{\text{out}}=F_{\text{out}}v_{\text{out}}\,}
251:, the tradeoff between force and distance, or the concept of
240:
224:
68:
53:
3170:, the only elementary machine discovered in the 20th century
1326:{\displaystyle P_{\text{in}}=P_{\text{out}}+P_{\text{fric}}}
4340:
4335:
4180:
4157:
4038:
2713:{\displaystyle \eta =W_{\text{load}}/W_{\text{1,2}}<0.5}
2202:'s self-locking property is the reason for its wide use in
1690:
1682:
1278:
is the power lost to friction, from conservation of energy
3432:
1100:
The mechanical advantage can be greater or less than one:
716:{\displaystyle P_{\text{in}}=F_{\text{in}}v_{\text{in}}\!}
160:
had identified hundreds of machine elements, calling them
3028:
Machines are studied as mechanical systems consisting of
3188:
Paul, Akshoy; Roy, Pijush; Mukherjee, Sanchayan (2005),
2537:
is equal to the sum of the work done on the load force
223:
lists five mechanisms that can "set a load in motion":
3646:
3181:
3091:
However, a more successful strategy was identified by
3813:(third ed.), New York: Oxford University Press,
2965:
2910:
2881:
2780:
2729:
2672:
2601:
2570:
2543:
2516:
2462:
2369:
2347:
2252:
2223:
2126:
2039:
1890:
1774:
1708:
1651:
1566:
1498:
1401:
1364:
1344:
1286:
1256:
1200:
1169:
1142:
1110:
1005:
928:
833:
794:
731:
678:
650:
599:
571:
528:
500:
473:
392:
360:
329:
4004:. New Delhi: PHI Learning Private Ltd. p. 202.
3808:
3650:
Wheels, clocks, and rockets: a history of technology
3574:
Strizhak, Viktor; Igor Penkov; Toivo Pappel (2004).
3500:
An introduction to the
History of Project Management
2760:{\displaystyle 2W_{\text{load}}<W_{\text{1,2}}\,}
3299:
Academic Press
Dictionary of Science and Technology
1163:is less than the distance moved by the input force
350:is applied to the device at one point, and it does
99:A simple machine uses a single applied force to do
3673:
3653:. US: W. W. Norton & Company. pp. 85–87.
3248:Physics for Technical Students: Mechanics and Heat
3071:Two levers, or cranks, are combined into a planar
3010:
2949:
2894:
2865:
2759:
2712:
2640:
2583:
2556:
2529:
2495:{\displaystyle d_{\textrm {in}}/d_{\textrm {out}}}
2494:
2442:
2353:
2267:
2238:
2179:
2108:
2021:
1874:
1758:
1657:
1634:
1547:
1480:
1385:
1350:
1325:
1270:
1218:
1183:
1155:
1128:
1078:
982:
906:
813:
778:
715:
664:
636:
585:
555:
513:
486:
430:
373:
342:
132:are composed, which arose in the Renaissance as a
3884:
3503:, Delft: Eburon Academic Publishers, p. 42,
825:, the ratio of input velocity to output velocity
712:
565:The power output equals the velocity of the load
552:
4496:
3997:
3187:
788:So the mechanical advantage of an ideal machine
3277:. Vol. 3. John Donaldson. 1773. p. 44
3473:
3359:. US: Courier Dover Publications. p. 98.
3302:. Gulf Professional Publishing. p. 1993.
814:{\displaystyle \mathrm {MA} _{\text{ideal}}\,}
556:{\displaystyle P_{\text{out}}=P_{\text{in}}\!}
4054:
3804:
3802:
3800:
3701:
3263:
3082:
1882:, this mechanical advantage is also given by
275:
164:. Modern machine theory analyzes machines as
52:that changes the direction or magnitude of a
3749:
3718:
3716:
3452:
3439:U.S. Navy Bureau of Naval Personnel (1971),
3414:
3412:
3224:, New York: Barnes & Noble, p. 88,
3213:
3211:
3209:
2456:) between its parts, and the distance ratio
2287:machines, and the backward motion is called
3970:
3857:
3835:Kinematics and Dynamics of Planar Machinery
3522:
3379:
3331:, University of Virginia Physics Department
3055:Simple machines are elementary examples of
2217:In many simple machines, if the load force
443:Simple machines do not contain a source of
184:around the 3rd century BC, who studied the
4061:
4047:
4028:, New York: McGraw-Hill, online link from
3939:
3937:
3935:
3885:Goyal, M. C.; Raghuvanshee, G. S. (2011).
3797:
2163:
1832:
1801:
1245:
27:. For broader coverage of this topic, see
4024:Hartenberg, R.S. & J. Denavit (1964)
3998:Goyal, M. C.; Raghuvanshi, G. S. (2009).
3722:
3713:
3647:Stephen, Donald; Lowell Cardwell (2001).
3409:
3206:
2756:
2018:
1828:
1267:
1215:
1180:
1125:
1075:
903:
810:
775:
661:
633:
582:
3726:A Complete Course in Certificate Physics
3608:
3606:
3458:
3244:
3048:Illustration of a four-bar linkage from
3043:
3023:
2193:
2189:
35:
3932:
3743:
3640:
3492:
3490:
3348:
3346:
3238:
3192:, Prentice Hall of India, p. 215,
314:
168:composed of elementary linkages called
23:. For the Internet forum software, see
4497:
3943:
3911:
3905:
3878:
3776:
3770:
3467:
3418:
3295:
3217:
3117:
103:against a single load force. Ignoring
4042:
3991:
3612:
3603:
3529:. Thompson Brooks/Cole. p. 123.
3352:
3289:
3245:Anderson, William Ballantyne (1914).
307:(1699) and were further developed by
3851:
3832:
3783:. Firewall Media. pp. 378–380.
3750:Simmons, Ron; Cindy, Barden (2008).
3523:Ostdiek, Vern; Bord, Donald (2005).
3496:
3487:
3343:
3251:. New York: McGraw Hill. p. 112
2592:
1668:
1219:{\displaystyle \mathrm {MA} <1\,}
1129:{\displaystyle \mathrm {MA} >1\,}
188:simple machines: lever, pulley, and
3964:
3729:. India: Pitambar. pp. 28–30.
3039:
13:
3977:. Universities Press. p. 82.
3864:. Universities Press. p. 80.
3674:Armstrong-Hélouvry, Brian (1991).
3356:A History of Mechanical Inventions
2096:
2093:
2078:
2075:
2063:
2060:
2045:
2042:
1896:
1893:
1714:
1711:
1571:
1568:
1205:
1202:
1115:
1112:
1011:
1008:
839:
836:
800:
797:
397:
394:
14:
4521:
3811:Theory of Machines and Mechanisms
3677:Control of machines with friction
3380:Wallenstein, Andrew (June 2002).
2239:{\displaystyle F_{\textrm {out}}}
1386:{\displaystyle 0<\eta \ <1}
1271:{\displaystyle P_{\text{fric}}\,}
303:fluid. They were rediscovered by
202:δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω
192:. He discovered the principle of
40:The six classical simple machines
3582:. Kluwer Academic. p. 245.
3442:Basic machines and how they work
2268:{\displaystyle F_{\textrm {in}}}
672:multiplied by the applied force
586:{\displaystyle v_{\text{out}}\,}
4026:Kinematic synthesis of linkages
4018:
3950:. Firewall Media. p. 382.
3918:. Nelson Thornes. p. 110.
3826:
3694:
3667:
3567:
3550:
3516:
3463:, New York: reprinted by Dover.
3296:Morris, Christopher G. (1992).
2895:{\displaystyle W_{\text{fric}}}
2771:
2664:If the efficiency is below 50%
2654:
2584:{\displaystyle W_{\text{fric}}}
2557:{\displaystyle W_{\text{load}}}
1184:{\displaystyle d_{\text{in}}\,}
665:{\displaystyle v_{\text{in}}\,}
295:in machines were discovered by
3971:Rao, S.; Durgaiah, R. (2005).
3858:Rao, S.; Durgaiah, R. (2005).
3373:
3079:or in series to form a robot.
2564:and the work lost to friction
2530:{\displaystyle W_{\text{1,2}}}
2454:coefficient of static friction
1156:{\displaystyle d_{\text{out}}}
487:{\displaystyle P_{\text{out}}}
374:{\displaystyle F_{\text{out}}}
1:
3891:. PHI Learning. p. 212.
3753:Discover! Work & Machines
3353:Usher, Abbott Payson (1988).
3174:
3050:Kinematics of Machinery, 1876
1093:is equal to the ratio of its
593:multiplied by the load force
514:{\displaystyle P_{\text{in}}}
343:{\displaystyle F_{\text{in}}}
291:The classic rules of sliding
213:
4068:
3756:. US: Milliken. p. 29.
494:is equal to the power input
7:
4224:Internal combustion engines
4201:External combustion engines
3153:Cam and follower mechanisms
3141:
3132:cam and follower mechanisms
309:Charles-Augustin de Coulomb
10:
4526:
3619:. Greenwood. p. 163.
3419:Prater, Edward L. (1994),
3083:Classification of machines
1238:, and the velocity by the
175:
18:
4476:
4425:
4407:
4364:
4326:
4278:
4255:
4222:
4199:
4152:
4119:
4078:Classical simple machines
4076:
3723:Bhatnagar, V. P. (1996).
3613:Krebs, Robert E. (2004).
3388:. Springer. p. 136.
447:, so they cannot do more
201:
3680:. Springer. p. 10.
2505:
1689:consists of a number of
4463:Check weighing machines
3275:Encyclopædia Britannica
3163:Mechanism (engineering)
3059:that are used to model
1697:) connected in series.
1246:Friction and efficiency
29:Mechanism (engineering)
4505:Mechanical engineering
3944:Gujral, I. S. (2005).
3777:Gujral, I. S. (2005).
3702:
3459:Reuleaux, F. (1963) ,
3218:Asimov, Isaac (1988),
3052:
3012:
2959:So the output work is
2951:
2896:
2867:
2761:
2714:
2642:
2585:
2558:
2531:
2496:
2444:
2355:
2269:
2240:
2214:
2181:
2110:
2023:
1876:
1760:
1659:
1636:
1549:
1482:
1387:
1352:
1327:
1272:
1220:
1185:
1157:
1130:
1080:
984:
908:
815:
780:
717:
666:
638:
587:
557:
515:
488:
465:conservation of energy
432:
375:
344:
276:
41:
4448:Seed-counting machine
4001:Engineering Mechanics
3974:Engineering Mechanics
3947:Engineering Mechanics
3912:Avison, John (2014).
3888:Engineering Mechanics
3861:Engineering Mechanics
3833:Paul, Burton (1979).
3780:Engineering Mechanics
3483:, Cornell University.
3448:, Dover Publications.
3221:Understanding Physics
3158:Gears and gear trains
3136:gears and gear trains
3047:
3024:Modern machine theory
3013:
2952:
2897:
2868:
2762:
2715:
2643:
2586:
2559:
2532:
2497:
2445:
2356:
2354:{\displaystyle \eta }
2270:
2241:
2197:
2190:Self-locking machines
2182:
2111:
2024:
1877:
1761:
1660:
1658:{\displaystyle \eta }
1637:
1550:
1483:
1388:
1353:
1351:{\displaystyle \eta }
1337:mechanical efficiency
1328:
1273:
1242:the shaft is turned.
1221:
1186:
1158:
1131:
1081:
985:
909:
816:
781:
718:
667:
639:
588:
558:
516:
489:
433:
376:
345:
288:, only transform it.
142:Industrial Revolution
39:
25:Simple Machines Forum
4247:Nutating disc engine
4237:Reciprocating engine
3915:The World of Physics
3558:Pappus of Alexandria
3526:Inquiry into Physics
3497:Chiu, Y. C. (2010),
3148:Linkage (mechanical)
2963:
2908:
2879:
2778:
2727:
2670:
2599:
2568:
2541:
2514:
2460:
2367:
2345:
2250:
2221:
2124:
2037:
1888:
1772:
1706:
1649:
1564:
1496:
1399:
1362:
1358:of a machine (where
1342:
1284:
1254:
1198:
1167:
1140:
1108:
1003:
926:
831:
792:
729:
676:
648:
597:
569:
526:
498:
471:
390:
383:mechanical advantage
358:
327:
315:Ideal simple machine
262:the dynamics of the
219:–75 AD) in his work
194:mechanical advantage
111:mechanical advantage
58:mechanical advantage
3124:kinematic synthesis
3118:Kinematic synthesis
210:Heron of Alexandria
4270:Peaucellier-Lipkin
4030:Cornell University
3475:Cornell University
3061:mechanical systems
3053:
3008:
2947:
2892:
2863:
2861:
2757:
2710:
2638:
2581:
2554:
2527:
2492:
2440:
2351:
2265:
2236:
2215:
2204:threaded fasteners
2177:
2106:
2019:
1872:
1756:
1655:
1632:
1545:
1478:
1476:
1383:
1348:
1323:
1268:
1216:
1181:
1153:
1126:
1076:
980:
904:
811:
776:
713:
662:
634:
583:
553:
511:
484:
428:
371:
340:
305:Guillaume Amontons
42:
4492:
4491:
4468:Riveting machines
4166:Archimedes' screw
4011:978-81-203-3789-3
3984:978-81-7371-543-3
3957:978-81-7008-636-9
3925:978-0-17-438733-6
3898:978-81-203-4327-6
3871:978-81-7371-543-3
3844:978-0-13-516062-6
3837:. Prentice Hall.
3820:978-0-19-515598-3
3790:978-81-7008-636-9
3763:978-1-4291-0947-5
3736:978-81-209-0868-0
3687:978-0-7923-9133-3
3660:978-0-393-32175-3
3626:978-0-313-32433-8
3536:978-0-534-49168-0
3510:978-90-5972-437-2
3366:978-0-486-25593-4
3328:Compound machines
3231:978-0-88029-251-1
3199:978-81-203-2611-8
2999:
2986:
2973:
2944:
2931:
2918:
2889:
2856:
2839:
2825:
2812:
2795:
2753:
2740:
2701:
2686:
2662:
2661:
2635:
2622:
2609:
2578:
2551:
2524:
2488:
2471:
2432:
2428:
2413:
2401:
2386:
2261:
2232:
2134:
2052:
2016:
2009:
1994:
1979:
1976:
1966:
1955:
1952:
1942:
1931:
1928:
1918:
1903:
1859:
1841:
1822:
1809:
1795:
1782:
1754:
1751:
1737:
1721:
1669:Compound machines
1630:
1627:
1617:
1600:
1597:
1587:
1542:
1532:
1516:
1506:
1471:
1451:
1438:
1435:
1425:
1376:
1320:
1307:
1294:
1264:
1177:
1150:
1073:
1070:
1060:
1046:
1043:
1033:
1018:
978:
975:
965:
951:
948:
938:
901:
898:
888:
874:
871:
861:
846:
807:
772:
762:
749:
739:
709:
699:
686:
658:
630:
620:
607:
579:
549:
536:
508:
481:
426:
423:
413:
368:
337:
297:Leonardo da Vinci
264:mechanical powers
150:compound machines
136:amplification of
50:mechanical device
4517:
4171:Eductor-jet pump
4063:
4056:
4049:
4040:
4039:
4033:
4022:
4016:
4015:
3995:
3989:
3988:
3968:
3962:
3961:
3941:
3930:
3929:
3909:
3903:
3902:
3882:
3876:
3875:
3855:
3849:
3848:
3830:
3824:
3823:
3806:
3795:
3794:
3774:
3768:
3767:
3747:
3741:
3740:
3720:
3711:
3705:
3698:
3692:
3691:
3671:
3665:
3664:
3644:
3638:
3637:
3635:
3633:
3610:
3601:
3600:
3598:
3596:
3571:
3565:
3554:
3548:
3547:
3545:
3543:
3520:
3514:
3513:
3494:
3485:
3484:
3471:
3465:
3464:
3456:
3450:
3449:
3447:
3436:
3430:
3429:
3427:
3416:
3407:
3406:
3404:
3402:
3377:
3371:
3370:
3350:
3341:
3340:
3338:
3336:
3323:
3314:
3313:
3293:
3287:
3286:
3284:
3282:
3267:
3261:
3260:
3258:
3256:
3242:
3236:
3235:
3215:
3204:
3203:
3185:
3073:four-bar linkage
3057:kinematic chains
3040:Kinematic chains
3017:
3015:
3014:
3009:
3001:
3000:
2997:
2988:
2987:
2984:
2975:
2974:
2971:
2956:
2954:
2953:
2948:
2946:
2945:
2942:
2933:
2932:
2929:
2920:
2919:
2916:
2901:
2899:
2898:
2893:
2891:
2890:
2887:
2872:
2870:
2869:
2864:
2862:
2858:
2857:
2854:
2841:
2840:
2837:
2827:
2826:
2823:
2814:
2813:
2810:
2797:
2796:
2793:
2766:
2764:
2763:
2758:
2755:
2754:
2751:
2742:
2741:
2738:
2721:
2719:
2717:
2716:
2711:
2703:
2702:
2699:
2693:
2688:
2687:
2684:
2656:
2647:
2645:
2644:
2639:
2637:
2636:
2633:
2624:
2623:
2620:
2611:
2610:
2607:
2593:
2590:
2588:
2587:
2582:
2580:
2579:
2576:
2563:
2561:
2560:
2555:
2553:
2552:
2549:
2536:
2534:
2533:
2528:
2526:
2525:
2522:
2501:
2499:
2498:
2493:
2491:
2490:
2489:
2486:
2479:
2474:
2473:
2472:
2469:
2449:
2447:
2446:
2441:
2433:
2431:
2430:
2429:
2426:
2420:
2415:
2414:
2411:
2404:
2403:
2402:
2399:
2393:
2388:
2387:
2384:
2377:
2360:
2358:
2357:
2352:
2274:
2272:
2271:
2266:
2264:
2263:
2262:
2259:
2245:
2243:
2242:
2237:
2235:
2234:
2233:
2230:
2186:
2184:
2183:
2178:
2173:
2172:
2159:
2158:
2149:
2148:
2136:
2135:
2132:
2115:
2113:
2112:
2107:
2105:
2104:
2099:
2087:
2086:
2081:
2072:
2071:
2066:
2054:
2053:
2050:
2048:
2028:
2026:
2025:
2020:
2017:
2015:
2014:
2010:
2007:
2000:
1999:
1995:
1992:
1985:
1980:
1978:
1977:
1974:
1968:
1967:
1964:
1958:
1956:
1954:
1953:
1950:
1944:
1943:
1940:
1934:
1932:
1930:
1929:
1926:
1920:
1919:
1916:
1910:
1905:
1904:
1901:
1899:
1881:
1879:
1878:
1873:
1871:
1870:
1860:
1857:
1847:
1846:
1842:
1839:
1824:
1823:
1820:
1811:
1810:
1807:
1797:
1796:
1793:
1784:
1783:
1780:
1765:
1763:
1762:
1757:
1755:
1753:
1752:
1749:
1743:
1742:
1738:
1735:
1728:
1723:
1722:
1719:
1717:
1695:wheels and axles
1675:compound machine
1664:
1662:
1661:
1656:
1641:
1639:
1638:
1633:
1631:
1629:
1628:
1625:
1619:
1618:
1615:
1609:
1601:
1599:
1598:
1595:
1589:
1588:
1585:
1579:
1574:
1554:
1552:
1551:
1546:
1544:
1543:
1540:
1534:
1533:
1530:
1518:
1517:
1514:
1508:
1507:
1504:
1487:
1485:
1484:
1479:
1477:
1473:
1472:
1469:
1453:
1452:
1449:
1439:
1437:
1436:
1433:
1427:
1426:
1423:
1417:
1392:
1390:
1389:
1384:
1374:
1357:
1355:
1354:
1349:
1332:
1330:
1329:
1324:
1322:
1321:
1318:
1309:
1308:
1305:
1296:
1295:
1292:
1277:
1275:
1274:
1269:
1266:
1265:
1262:
1240:angular velocity
1225:
1223:
1222:
1217:
1208:
1190:
1188:
1187:
1182:
1179:
1178:
1175:
1162:
1160:
1159:
1154:
1152:
1151:
1148:
1135:
1133:
1132:
1127:
1118:
1085:
1083:
1082:
1077:
1074:
1072:
1071:
1068:
1062:
1061:
1058:
1052:
1047:
1045:
1044:
1041:
1035:
1034:
1031:
1025:
1020:
1019:
1016:
1014:
989:
987:
986:
981:
979:
977:
976:
973:
967:
966:
963:
957:
952:
950:
949:
946:
940:
939:
936:
930:
913:
911:
910:
905:
902:
900:
899:
896:
890:
889:
886:
880:
875:
873:
872:
869:
863:
862:
859:
853:
848:
847:
844:
842:
821:is equal to the
820:
818:
817:
812:
809:
808:
805:
803:
785:
783:
782:
777:
774:
773:
770:
764:
763:
760:
751:
750:
747:
741:
740:
737:
722:
720:
719:
714:
711:
710:
707:
701:
700:
697:
688:
687:
684:
671:
669:
668:
663:
660:
659:
656:
643:
641:
640:
635:
632:
631:
628:
622:
621:
618:
609:
608:
605:
592:
590:
589:
584:
581:
580:
577:
562:
560:
559:
554:
551:
550:
547:
538:
537:
534:
520:
518:
517:
512:
510:
509:
506:
493:
491:
490:
485:
483:
482:
479:
437:
435:
434:
429:
427:
425:
424:
421:
415:
414:
411:
405:
400:
380:
378:
377:
372:
370:
369:
366:
349:
347:
346:
341:
339:
338:
335:
279:
218:
215:
203:
166:kinematic chains
154:machine elements
4525:
4524:
4520:
4519:
4518:
4516:
4515:
4514:
4510:Simple machines
4495:
4494:
4493:
4488:
4484:Spring (device)
4472:
4453:Vending machine
4421:
4403:
4360:
4322:
4274:
4251:
4218:
4214:Stirling engine
4195:
4148:
4115:
4072:
4067:
4037:
4036:
4023:
4019:
4012:
3996:
3992:
3985:
3969:
3965:
3958:
3942:
3933:
3926:
3910:
3906:
3899:
3883:
3879:
3872:
3856:
3852:
3845:
3831:
3827:
3821:
3807:
3798:
3791:
3775:
3771:
3764:
3748:
3744:
3737:
3721:
3714:
3699:
3695:
3688:
3672:
3668:
3661:
3645:
3641:
3631:
3629:
3627:
3611:
3604:
3594:
3592:
3590:
3572:
3568:
3555:
3551:
3541:
3539:
3537:
3521:
3517:
3511:
3495:
3488:
3472:
3468:
3457:
3453:
3445:
3437:
3433:
3425:
3417:
3410:
3400:
3398:
3396:
3378:
3374:
3367:
3351:
3344:
3334:
3332:
3325:
3324:
3317:
3310:
3294:
3290:
3280:
3278:
3269:
3268:
3264:
3254:
3252:
3243:
3239:
3232:
3216:
3207:
3200:
3186:
3182:
3177:
3144:
3120:
3085:
3077:six-bar linkage
3042:
3026:
2996:
2992:
2983:
2979:
2970:
2966:
2964:
2961:
2960:
2941:
2937:
2928:
2924:
2915:
2911:
2909:
2906:
2905:
2886:
2882:
2880:
2877:
2876:
2860:
2859:
2853:
2849:
2842:
2836:
2832:
2829:
2828:
2822:
2818:
2809:
2805:
2798:
2792:
2788:
2781:
2779:
2776:
2775:
2750:
2746:
2737:
2733:
2728:
2725:
2724:
2698:
2694:
2689:
2683:
2679:
2671:
2668:
2667:
2665:
2632:
2628:
2619:
2615:
2606:
2602:
2600:
2597:
2596:
2575:
2571:
2569:
2566:
2565:
2548:
2544:
2542:
2539:
2538:
2521:
2517:
2515:
2512:
2511:
2508:
2485:
2484:
2480:
2475:
2468:
2467:
2463:
2461:
2458:
2457:
2425:
2421:
2416:
2410:
2406:
2405:
2398:
2394:
2389:
2383:
2379:
2378:
2376:
2368:
2365:
2364:
2346:
2343:
2342:
2304:non-overhauling
2258:
2257:
2253:
2251:
2248:
2247:
2229:
2228:
2224:
2222:
2219:
2218:
2192:
2168:
2164:
2154:
2150:
2144:
2140:
2131:
2127:
2125:
2122:
2121:
2100:
2092:
2091:
2082:
2074:
2073:
2067:
2059:
2058:
2049:
2041:
2040:
2038:
2035:
2034:
2006:
2005:
2001:
1991:
1990:
1986:
1984:
1973:
1969:
1963:
1959:
1957:
1949:
1945:
1939:
1935:
1933:
1925:
1921:
1915:
1911:
1909:
1900:
1892:
1891:
1889:
1886:
1885:
1856:
1855:
1851:
1838:
1837:
1833:
1819:
1815:
1806:
1802:
1792:
1788:
1779:
1775:
1773:
1770:
1769:
1748:
1744:
1734:
1733:
1729:
1727:
1718:
1710:
1709:
1707:
1704:
1703:
1671:
1650:
1647:
1646:
1643:
1624:
1620:
1614:
1610:
1608:
1594:
1590:
1584:
1580:
1578:
1567:
1565:
1562:
1561:
1539:
1535:
1529:
1525:
1513:
1509:
1503:
1499:
1497:
1494:
1493:
1475:
1474:
1468:
1464:
1454:
1448:
1444:
1441:
1440:
1432:
1428:
1422:
1418:
1416:
1409:
1402:
1400:
1397:
1396:
1363:
1360:
1359:
1343:
1340:
1339:
1317:
1313:
1304:
1300:
1291:
1287:
1285:
1282:
1281:
1261:
1257:
1255:
1252:
1251:
1248:
1201:
1199:
1196:
1195:
1174:
1170:
1168:
1165:
1164:
1147:
1143:
1141:
1138:
1137:
1111:
1109:
1106:
1105:
1087:
1067:
1063:
1057:
1053:
1051:
1040:
1036:
1030:
1026:
1024:
1015:
1007:
1006:
1004:
1001:
1000:
972:
968:
962:
958:
956:
945:
941:
935:
931:
929:
927:
924:
923:
895:
891:
885:
881:
879:
868:
864:
858:
854:
852:
843:
835:
834:
832:
829:
828:
804:
796:
795:
793:
790:
789:
769:
765:
759:
755:
746:
742:
736:
732:
730:
727:
726:
706:
702:
696:
692:
683:
679:
677:
674:
673:
655:
651:
649:
646:
645:
627:
623:
617:
613:
604:
600:
598:
595:
594:
576:
572:
570:
567:
566:
546:
542:
533:
529:
527:
524:
523:
505:
501:
499:
496:
495:
478:
474:
472:
469:
468:
420:
416:
410:
406:
404:
393:
391:
388:
387:
365:
361:
359:
356:
355:
334:
330:
328:
325:
324:
317:
272:Galileo Galilei
216:
178:
170:kinematic pairs
162:simple machines
32:
21:Simple Machines
17:
12:
11:
5:
4523:
4513:
4512:
4507:
4490:
4489:
4487:
4486:
4480:
4478:
4474:
4473:
4471:
4470:
4465:
4460:
4455:
4450:
4445:
4440:
4435:
4429:
4427:
4423:
4422:
4420:
4419:
4413:
4411:
4405:
4404:
4402:
4401:
4396:
4391:
4386:
4381:
4376:
4370:
4368:
4362:
4361:
4359:
4358:
4353:
4348:
4343:
4338:
4332:
4330:
4324:
4323:
4321:
4320:
4315:
4313:Wind generator
4310:
4305:
4300:
4295:
4290:
4284:
4282:
4276:
4275:
4273:
4272:
4267:
4261:
4259:
4253:
4252:
4250:
4249:
4244:
4239:
4234:
4228:
4226:
4220:
4219:
4217:
4216:
4211:
4205:
4203:
4197:
4196:
4194:
4193:
4188:
4183:
4178:
4173:
4168:
4162:
4160:
4150:
4149:
4147:
4146:
4141:
4139:Pendulum clock
4136:
4131:
4125:
4123:
4117:
4116:
4114:
4113:
4111:Wheel and axle
4108:
4103:
4098:
4093:
4088:
4086:Inclined plane
4082:
4080:
4074:
4073:
4066:
4065:
4058:
4051:
4043:
4035:
4034:
4017:
4010:
3990:
3983:
3963:
3956:
3931:
3924:
3904:
3897:
3877:
3870:
3850:
3843:
3825:
3819:
3796:
3789:
3769:
3762:
3742:
3735:
3712:
3693:
3686:
3666:
3659:
3639:
3625:
3602:
3588:
3566:
3549:
3535:
3515:
3509:
3486:
3466:
3451:
3431:
3422:Basic machines
3408:
3395:978-3540002666
3394:
3372:
3365:
3342:
3315:
3309:978-0122004001
3308:
3288:
3262:
3237:
3230:
3205:
3198:
3179:
3178:
3176:
3173:
3172:
3171:
3165:
3160:
3155:
3150:
3143:
3140:
3119:
3116:
3100:revolute joint
3093:Franz Reuleaux
3084:
3081:
3065:kinematic pair
3041:
3038:
3025:
3022:
3007:
3004:
2995:
2991:
2982:
2978:
2969:
2940:
2936:
2927:
2923:
2914:
2885:
2852:
2848:
2845:
2843:
2835:
2831:
2830:
2821:
2817:
2808:
2804:
2801:
2799:
2791:
2787:
2784:
2783:
2749:
2745:
2736:
2732:
2709:
2706:
2697:
2692:
2682:
2678:
2675:
2660:
2659:
2650:
2648:
2631:
2627:
2618:
2614:
2605:
2574:
2547:
2520:
2507:
2504:
2483:
2478:
2466:
2439:
2436:
2424:
2419:
2409:
2397:
2392:
2382:
2375:
2372:
2361:is below 50%:
2350:
2339:
2338:
2331:
2327:
2315:inclined plane
2256:
2227:
2191:
2188:
2176:
2171:
2167:
2162:
2157:
2153:
2147:
2143:
2139:
2130:
2103:
2098:
2095:
2090:
2085:
2080:
2077:
2070:
2065:
2062:
2057:
2047:
2044:
2013:
2004:
1998:
1989:
1983:
1972:
1962:
1948:
1938:
1924:
1914:
1908:
1898:
1895:
1869:
1866:
1863:
1854:
1850:
1845:
1836:
1831:
1827:
1818:
1814:
1805:
1800:
1791:
1787:
1778:
1747:
1741:
1732:
1726:
1716:
1713:
1670:
1667:
1654:
1623:
1613:
1607:
1604:
1593:
1583:
1577:
1573:
1570:
1559:
1538:
1528:
1524:
1521:
1512:
1502:
1467:
1463:
1460:
1457:
1455:
1447:
1443:
1442:
1431:
1421:
1415:
1412:
1410:
1408:
1405:
1404:
1382:
1379:
1373:
1370:
1367:
1347:
1316:
1312:
1303:
1299:
1290:
1260:
1247:
1244:
1228:
1227:
1214:
1211:
1207:
1204:
1192:
1173:
1146:
1124:
1121:
1117:
1114:
1066:
1056:
1050:
1039:
1029:
1023:
1013:
1010:
998:
994:distance ratio
971:
961:
955:
944:
934:
918:velocity ratio
894:
884:
878:
867:
857:
851:
841:
838:
823:velocity ratio
802:
799:
768:
758:
754:
745:
735:
705:
695:
691:
682:
654:
626:
616:
612:
603:
575:
545:
541:
532:
504:
477:
419:
409:
403:
399:
396:
364:
354:moving a load
333:
316:
313:
206:inclined plane
177:
174:
158:Franz Reuleaux
146:basic machines
97:
96:
91:
86:
84:Inclined plane
81:
76:
74:Wheel and axle
71:
46:simple machine
15:
9:
6:
4:
3:
2:
4522:
4511:
4508:
4506:
4503:
4502:
4500:
4485:
4482:
4481:
4479:
4475:
4469:
4466:
4464:
4461:
4459:
4456:
4454:
4451:
4449:
4446:
4444:
4441:
4439:
4436:
4434:
4431:
4430:
4428:
4426:Miscellaneous
4424:
4418:
4415:
4414:
4412:
4410:
4406:
4400:
4397:
4395:
4392:
4390:
4387:
4385:
4382:
4380:
4377:
4375:
4372:
4371:
4369:
4367:
4363:
4357:
4354:
4352:
4349:
4347:
4344:
4342:
4339:
4337:
4334:
4333:
4331:
4329:
4325:
4319:
4316:
4314:
4311:
4309:
4308:Water turbine
4306:
4304:
4303:Steam turbine
4301:
4299:
4296:
4294:
4291:
4289:
4286:
4285:
4283:
4281:
4277:
4271:
4268:
4266:
4263:
4262:
4260:
4258:
4254:
4248:
4245:
4243:
4242:Rotary engine
4240:
4238:
4235:
4233:
4230:
4229:
4227:
4225:
4221:
4215:
4212:
4210:
4207:
4206:
4204:
4202:
4198:
4192:
4189:
4187:
4184:
4182:
4179:
4177:
4176:Hydraulic ram
4174:
4172:
4169:
4167:
4164:
4163:
4161:
4159:
4155:
4151:
4145:
4142:
4140:
4137:
4135:
4132:
4130:
4127:
4126:
4124:
4122:
4118:
4112:
4109:
4107:
4104:
4102:
4099:
4097:
4094:
4092:
4089:
4087:
4084:
4083:
4081:
4079:
4075:
4071:
4064:
4059:
4057:
4052:
4050:
4045:
4044:
4041:
4031:
4027:
4021:
4013:
4007:
4003:
4002:
3994:
3986:
3980:
3976:
3975:
3967:
3959:
3953:
3949:
3948:
3940:
3938:
3936:
3927:
3921:
3917:
3916:
3908:
3900:
3894:
3890:
3889:
3881:
3873:
3867:
3863:
3862:
3854:
3846:
3840:
3836:
3829:
3822:
3816:
3812:
3805:
3803:
3801:
3792:
3786:
3782:
3781:
3773:
3765:
3759:
3755:
3754:
3746:
3738:
3732:
3728:
3727:
3719:
3717:
3709:
3704:
3703:Le Meccaniche
3697:
3689:
3683:
3679:
3678:
3670:
3662:
3656:
3652:
3651:
3643:
3628:
3622:
3618:
3617:
3609:
3607:
3591:
3589:1-4020-2203-4
3585:
3581:
3577:
3570:
3563:
3559:
3553:
3538:
3532:
3528:
3527:
3519:
3512:
3506:
3502:
3501:
3493:
3491:
3482:
3481:
3476:
3470:
3462:
3455:
3444:
3443:
3435:
3424:
3423:
3415:
3413:
3397:
3391:
3387:
3383:
3376:
3368:
3362:
3358:
3357:
3349:
3347:
3330:
3329:
3322:
3320:
3311:
3305:
3301:
3300:
3292:
3276:
3272:
3266:
3250:
3249:
3241:
3233:
3227:
3223:
3222:
3214:
3212:
3210:
3201:
3195:
3191:
3184:
3180:
3169:
3166:
3164:
3161:
3159:
3156:
3154:
3151:
3149:
3146:
3145:
3139:
3137:
3133:
3129:
3125:
3115:
3113:
3109:
3105:
3104:sliding joint
3101:
3096:
3094:
3089:
3080:
3078:
3074:
3069:
3066:
3062:
3058:
3051:
3046:
3037:
3035:
3031:
3021:
3018:
3005:
3002:
2993:
2989:
2980:
2976:
2967:
2957:
2938:
2934:
2925:
2921:
2912:
2903:
2883:
2873:
2850:
2846:
2844:
2833:
2819:
2815:
2806:
2802:
2800:
2789:
2785:
2774:
2773:
2767:
2747:
2743:
2734:
2730:
2722:
2707:
2704:
2695:
2690:
2680:
2676:
2673:
2658:
2651:
2649:
2629:
2625:
2616:
2612:
2603:
2595:
2594:
2591:
2572:
2545:
2518:
2503:
2481:
2476:
2464:
2455:
2450:
2437:
2434:
2422:
2417:
2407:
2395:
2390:
2380:
2373:
2370:
2362:
2348:
2336:
2332:
2328:
2324:
2323:
2322:
2320:
2316:
2312:
2307:
2305:
2301:
2300:nonreversible
2297:
2292:
2290:
2286:
2282:
2278:
2254:
2225:
2213:
2209:
2205:
2201:
2196:
2187:
2174:
2169:
2165:
2160:
2155:
2151:
2145:
2141:
2137:
2128:
2119:
2116:
2101:
2088:
2083:
2068:
2055:
2032:
2029:
2011:
2002:
1996:
1987:
1981:
1970:
1960:
1946:
1936:
1922:
1912:
1906:
1883:
1867:
1864:
1861:
1852:
1848:
1843:
1834:
1829:
1825:
1816:
1812:
1803:
1798:
1789:
1785:
1776:
1766:
1745:
1739:
1730:
1724:
1701:
1698:
1696:
1692:
1688:
1684:
1680:
1676:
1666:
1652:
1642:
1621:
1611:
1605:
1602:
1591:
1581:
1575:
1558:
1555:
1536:
1526:
1522:
1519:
1510:
1500:
1491:
1488:
1465:
1461:
1458:
1456:
1445:
1429:
1419:
1413:
1411:
1406:
1394:
1380:
1377:
1371:
1368:
1365:
1345:
1338:
1333:
1314:
1310:
1301:
1297:
1288:
1279:
1258:
1243:
1241:
1237:
1233:
1212:
1209:
1193:
1171:
1144:
1122:
1119:
1103:
1102:
1101:
1098:
1096:
1092:
1086:
1064:
1054:
1048:
1037:
1027:
1021:
997:
995:
990:
969:
959:
953:
942:
932:
921:
919:
914:
892:
882:
876:
865:
855:
849:
826:
824:
786:
766:
756:
752:
743:
733:
724:
723:. Therefore,
703:
693:
689:
680:
652:
624:
614:
610:
601:
573:
563:
543:
539:
530:
521:
502:
475:
466:
462:
461:ideal machine
459:is called an
458:
454:
450:
446:
441:
438:
417:
407:
401:
385:
384:
362:
353:
331:
321:
312:
310:
306:
302:
298:
294:
289:
287:
283:
278:
277:Le Meccaniche
273:
269:
265:
261:
256:
254:
250:
246:
242:
238:
234:
230:
226:
222:
211:
207:
199:
195:
191:
187:
183:
173:
171:
167:
163:
159:
155:
151:
147:
143:
139:
138:ancient Greek
135:
131:
126:
124:
120:
115:
113:
112:
106:
102:
95:
92:
90:
87:
85:
82:
80:
77:
75:
72:
70:
67:
66:
65:
63:
59:
55:
51:
47:
38:
34:
30:
26:
22:
4443:Agricultural
4298:Quasiturbine
4209:Steam engine
4144:Quartz clock
4129:Atomic clock
4077:
4020:
4000:
3993:
3973:
3966:
3946:
3914:
3907:
3887:
3880:
3860:
3853:
3834:
3828:
3810:
3779:
3772:
3752:
3745:
3725:
3708:On Mechanics
3707:
3696:
3676:
3669:
3649:
3642:
3630:. Retrieved
3615:
3593:. Retrieved
3579:
3569:
3561:
3552:
3540:. Retrieved
3525:
3518:
3499:
3479:
3469:
3460:
3454:
3441:
3434:
3421:
3399:. Retrieved
3385:
3375:
3355:
3333:, retrieved
3327:
3298:
3291:
3279:. Retrieved
3274:
3265:
3253:. Retrieved
3247:
3240:
3220:
3189:
3183:
3121:
3097:
3090:
3086:
3070:
3054:
3027:
3019:
2958:
2904:
2902:is the same
2874:
2770:
2768:
2723:
2663:
2652:
2509:
2451:
2363:
2340:
2308:
2303:
2299:
2296:self-locking
2295:
2293:
2288:
2284:
2280:
2276:
2216:
2120:
2117:
2033:
2030:
1884:
1767:
1702:
1699:
1674:
1672:
1644:
1560:
1556:
1492:
1489:
1395:
1334:
1280:
1249:
1229:
1099:
1088:
999:
993:
991:
922:
917:
915:
827:
822:
787:
725:
564:
522:
460:
442:
439:
386:
322:
318:
290:
282:On Mechanics
281:
268:Simon Stevin
263:
257:
220:
179:
161:
153:
149:
145:
134:neoclassical
127:
116:
109:
98:
64:scientists:
45:
43:
33:
4458:Wind tunnel
4374:Vacuum tube
4366:Electronics
4288:Gas turbine
4232:Gas turbine
4191:Vacuum pump
4154:Compressors
4134:Chronometer
3564:, Book VIII
3271:"Mechanics"
2335:compression
2289:overhauling
2285:overhauling
2281:non-locking
2212:wood screws
1557:Therefore,
274:in 1600 in
260:Renaissance
258:During the
186:Archimedean
62:Renaissance
4499:Categories
4417:Automobile
4379:Transistor
4293:Jet engine
4265:Pantograph
3556:Quoted by
3175:References
3112:gear joint
3034:mechanisms
2277:reversible
1687:gear train
1683:bench vise
1095:lever arms
457:elasticity
182:Archimedes
4394:Capacitor
4356:Propeller
3108:cam joint
3030:actuators
2990:−
2674:η
2374:≡
2371:η
2349:η
2166:η
2161:…
2152:η
2142:η
2129:η
2089:…
1982:…
1830:…
1653:η
1606:η
1523:η
1462:η
1414:≡
1407:η
1372:η
1346:η
463:. Due to
221:Mechanics
217: 10
4409:Vehicles
4399:Inductor
4389:Resistor
4328:Aerofoil
4318:Windmill
4257:Linkages
4070:Machines
3562:Synagoge
3335:June 11,
3281:April 5,
3168:Rolamite
3142:See also
3128:linkages
2133:compound
2051:compound
1902:compound
1720:compound
453:friction
311:(1785).
301:ethereal
293:friction
249:dynamics
229:windlass
130:machines
119:machines
105:friction
4477:Springs
4280:Turbine
3632:May 21,
3595:May 21,
3542:May 22,
3401:May 21,
3255:May 11,
2330:weight.
1679:machine
1230:In the
245:statics
176:History
123:bicycle
4346:Rudder
4186:Trompe
4121:Clocks
4096:Pulley
4008:
3981:
3954:
3922:
3895:
3868:
3841:
3817:
3787:
3760:
3733:
3684:
3657:
3623:
3586:
3533:
3507:
3392:
3363:
3306:
3228:
3196:
2317:, and
1375:
1236:torque
445:energy
286:energy
239:, and
233:pulley
79:Pulley
4438:Robot
4433:Mecha
4384:Diode
4158:pumps
4106:Wedge
4101:Screw
4091:Lever
3446:(PDF)
3426:(PDF)
2772:Eq. 1
2769:From
2655:Eq. 1
2506:Proof
2326:turn.
2319:wedge
2311:screw
2302:, or
2208:bolts
2206:like
2200:screw
1691:gears
1677:is a
1232:screw
1091:lever
1017:ideal
845:ideal
806:ideal
241:screw
237:wedge
225:lever
198:Greek
190:screw
152:, or
94:Screw
89:Wedge
69:Lever
54:force
48:is a
4351:Flap
4341:Wing
4336:Sail
4181:Pump
4156:and
4006:ISBN
3979:ISBN
3952:ISBN
3920:ISBN
3893:ISBN
3866:ISBN
3839:ISBN
3815:ISBN
3785:ISBN
3758:ISBN
3731:ISBN
3682:ISBN
3655:ISBN
3634:2008
3621:ISBN
3597:2008
3584:ISBN
3544:2008
3531:ISBN
3505:ISBN
3403:2008
3390:ISBN
3361:ISBN
3337:2010
3304:ISBN
3283:2020
3257:2008
3226:ISBN
3194:ISBN
3134:and
3110:and
3032:and
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2985:load
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2811:load
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1210:<
1120:>
916:The
449:work
352:work
253:work
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2930:2,1
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2708:0.5
2700:1,2
2608:1,2
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2487:out
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2427:out
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1993:out
1975:in3
1951:in2
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1736:out
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1586:out
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535:out
480:out
455:or
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367:out
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2102:N
2097:A
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2056:=
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1937:F
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1844:K
1835:F
1826:,
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