25:
1428:
184:
352:), then the lever amplifies the input force. If the distance from the fulcrum to the input force is less than from the fulcrum to the output force, then the lever reduces the input force. To Archimedes, who recognized the profound implications and practicalities of the law of the lever, has been attributed the famous claim, "Give me a place to stand and with a lever I will move the whole world."
180:
gearset). In such a gearset, gears having smaller radii and less inherent mechanical advantage are used. In order to make use of non-collapsed mechanical advantage, it is necessary to use a 'true length' rotary lever. See, also, the incorporation of mechanical advantage into the design of certain types of electric motors; one design is an 'outrunner'.
128:
1682:
1673:
is an assembly of a rope and pulleys that is used to lift loads. A number of pulleys are assembled together to form the blocks, one that is fixed and one that moves with the load. The rope is threaded through the pulleys to provide mechanical advantage that amplifies that force applied to the rope.
1436:
Consider the 18-speed bicycle with 7 in (radius) cranks and 26 in (diameter) wheels. If the sprockets at the crank and at the rear drive wheel are the same size, then the ratio of the output force on the tire to the input force on the pedal can be calculated from the law of the lever to be
1418:
Chains and belts dissipate power through friction, stretch and wear, which means the power output is actually less than the power input, which means the mechanical advantage of the real system will be less than that calculated for an ideal mechanism. A chain or belt drive can lose as much as 5% of
1677:
In order to determine the mechanical advantage of a block and tackle system consider the simple case of a gun tackle, which has a single mounted, or fixed, pulley and a single movable pulley. The rope is threaded around the fixed block and falls down to the moving block where it is threaded around
179:
In modern times, this kind of rotary leverage is widely used; see a (rotary) 2nd-class lever; see gears, pulleys or friction drive, used in a mechanical power transmission scheme. It is common for mechanical advantage to be manipulated in a 'collapsed' form, via the use of more than one gear (a
610:
Gear teeth are designed so that the number of teeth on a gear is proportional to the radius of its pitch circle, and so that the pitch circles of meshing gears roll on each other without slipping. The speed ratio for a pair of meshing gears can be computed from ratio of the radii of the pitch
1431:
Mechanical advantage in different gears of a bicycle. Typical forces applied to the bicycle pedal and to the ground are shown, as are corresponding distances moved by the pedal and rotated by the wheel. Note that even in low gear the MA of a bicycle is less than
2489:, is the mechanical advantage of a device with the assumption that its components do not flex, there is no friction, and there is no wear. It is calculated using the physical dimensions of the device and defines the maximum performance the device can achieve.
2725:
2468:
of force out. In an actual system, the force out would be less than 600 pounds due to friction in the pulleys. The second ratio also yields a MA of 6 in the ideal case but a smaller value in the practical scenario; it does not properly account for
194:
into and out of the lever is the same, so must come out the same when calculations are being done. Power is the product of force and velocity, so forces applied to points farther from the pivot must be less than when applied to points closer in.
1656:
The ratio of the force driving the bicycle to the force on the pedal, which is the total mechanical advantage of the bicycle, is the product of the speed ratio (or teeth ratio of output sprocket/input sprocket) and the crank-wheel lever ratio.
1516:
Now, assume that the front sprockets have a choice of 28 and 52 teeth, and that the rear sprockets have a choice of 16 and 32 teeth. Using different combinations, we can compute the following speed ratios between the front and rear sprockets
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Mechanical advantage that is computed using the assumption that no power is lost through deflection, friction and wear of a machine is the maximum performance that can be achieved. For this reason, it is often called the
176:. Where a lever rotates continuously, it functions as a rotary 2nd-class lever. The motion of the lever's end-point describes a fixed orbit, where mechanical energy can be exchanged. (see a hand-crank as an example.)
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Notice that in every case the force on the pedals is greater than the force driving the bicycle forward (in the illustration above, the corresponding backward-directed reaction force on the ground is indicated).
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2730:
The speed ratio of a machine can be calculated from its physical dimensions. The assumption of constant power thus allows use of the speed ratio to determine the maximum value for the mechanical advantage.
2872:
2743:(AMA) is the mechanical advantage determined by physical measurement of the input and output forces. Actual mechanical advantage takes into account energy loss due to deflection, friction, and wear.
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The assumptions of an ideal machine are equivalent to the requirement that the machine does not store or dissipate energy; the power into the machine thus equals the power out. Therefore, the power
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1864:
172:
attached to or positioned on or across a fixed point. The lever operates by applying forces at different distances from the fulcrum, or pivot. The location of the fulcrum determines a lever's
104:. An ideal mechanism transmits power without adding to or subtracting from it. This means the ideal machine does not include a power source, is frictionless, and is constructed from
2168:
1923:
991:
Mechanisms consisting of two sprockets connected by a chain, or two pulleys connected by a belt are designed to provide a specific mechanical advantage in power transmission systems.
2643:
373:
The requirement for power input to an ideal mechanism to equal power output provides a simple way to compute mechanical advantage from the input-output speed ratio of the system.
108:
that do not deflect or wear. The performance of a real system relative to this ideal is expressed in terms of efficiency factors that take into account departures from the ideal.
1758:
1105:
735:
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The mechanical advantage of a block and tackle equals the number of sections of rope that support the moving block; shown here it is 2, 3, 4, 5, and 6, respectively.
1928:
The negative sign shows that the velocity of the load is opposite to the velocity of the applied force, which means as we pull down on the rope the load moves up.
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For an ideal block and tackle system there is no friction in the pulleys and no deflection or wear in the rope, which means the power input by the applied force
500:
258:
92:
or machine system. The device trades off input forces against movement to obtain a desired amplification in the output force. The model for this is the
2277:
2179:
983:(Force multiplier). In this case, because the output gear must have more teeth than the input gear, the speed reducer will amplify the input torque.
1334:
1244:
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1443:
1221:
drive, the number of teeth on the sprocket can be used. For friction belt drives the pitch radius of the input and output pulleys must be used.
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1951:
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2577:
2389:(IMA). In operation, deflection, friction and wear will reduce the mechanical advantage. The amount of this reduction from the ideal to the
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46:
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This shows that for an ideal mechanism the input-output speed ratio equals the mechanical advantage of the system. This applies to all
3147:
68:
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The ideal mechanical advantage is the ratio of the force out of the machine (load) to the force into the machine (effort), or
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424:
2637:
Applying the constant power relationship yields a formula for this ideal mechanical advantage in terms of the speed ratio:
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is constant through the machine and force times velocity into the machine equals the force times velocity out—that is,
1419:
the power through the system in friction heat, deformation and wear, in which case the efficiency of the drive is 95%.
2898:
190:
As the lever pivots on the fulcrum, points farther from this pivot move faster than points closer to the pivot. The
39:
33:
153:
149:
2720:{\displaystyle {\mathit {IMA}}={\frac {F_{\text{out}}}{F_{\text{in}}}}={\frac {v_{\text{in}}}{v_{\text{out}}}}.}
50:
2933:
1767:
is the constant length of rope that passes over the pulleys and does not change as the block and tackle moves.
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1875:
2473:
losses such as rope stretch. Subtracting those losses from the IMA or using the first ratio yields the AMA.
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The ratio of the output force to the input force is the mechanical advantage of an ideal gun tackle system,
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If the output gear of a gear train rotates more slowly than the input gear, then the gear train is called a
101:
2746:
The AMA of a machine is calculated as the ratio of the measured force output to the measured force input,
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The ratio of the experimentally determined mechanical advantage to the ideal mechanical advantage is the
2945:
2816:
1224:
The mechanical advantage of a pair of a chain drive or toothed belt drive with an input sprocket with
593:
972:
the input torque. And, if the output gear has fewer teeth than the input gear, then the gear train
2998:
2883:
3122:
3142:
1718:
1193:{\displaystyle {\frac {\omega _{A}}{\omega _{B}}}={\frac {r_{B}}{r_{A}}}={\frac {N_{B}}{N_{A}}}.}
823:{\displaystyle {\frac {\omega _{A}}{\omega _{B}}}={\frac {r_{B}}{r_{A}}}={\frac {N_{B}}{N_{A}}}.}
157:
137:
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2913:
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89:
3002:
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load, the operator of an ideal system would be required to pull the rope six feet and exert
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1670:
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The use of velocity in the static analysis of a lever is an application of the principle of
183:
143:
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be the distance from the axle of the fixed block to the axle of the moving block, which is
2928:
630:
of the point of contact on the pitch circles is the same on both gears, and is given by
252:
so the ratio of the output force to the input force, or mechanical advantage, is given by
191:
574:{\displaystyle {\mathit {MA}}={\frac {T_{B}}{T_{A}}}={\frac {\omega _{A}}{\omega _{B}}}.}
2267:
This analysis generalizes to an ideal block and tackle with a moving block supported by
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of the chain or belt is the same when in contact with the two sprockets or pulleys:
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2918:
1218:
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105:
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be the distance from the axle of the fixed block to the end of the rope, which is
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The mechanical advantage of a pair of meshing gears for which the input gear has
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3070:
2358:{\displaystyle {\mathit {MA}}={\frac {F_{B}}{F_{A}}}={\frac {V_{A}}{V_{B}}}=n.\!}
2257:{\displaystyle {\mathit {MA}}={\frac {F_{B}}{F_{A}}}={\frac {V_{A}}{V_{B}}}=2.\!}
100:
Machine components designed to manage forces and movement in this way are called
2908:
368:
3007:. Harvard University Press (reprinted by Dover Publications 1988). p. 94.
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1408:{\displaystyle {\mathit {MA}}={\frac {T_{B}}{T_{A}}}={\frac {r_{B}}{r_{A}}}.}
1318:{\displaystyle {\mathit {MA}}={\frac {T_{B}}{T_{A}}}={\frac {N_{B}}{N_{A}}}.}
944:{\displaystyle {\mathit {MA}}={\frac {r_{B}}{r_{A}}}={\frac {N_{B}}{N_{A}}}.}
1945:
be positive upwards, so this relationship can be written as the speed ratio
156:
to the section by replacing the section with a link and a summary or by
1506:{\displaystyle {\mathit {MA}}={\frac {F_{B}}{F_{A}}}={\frac {7}{13}}=0.54.}
3022:
2561:{\displaystyle P=F_{\text{in}}v_{\text{in}}=F_{\text{out}}v_{\text{out}}.}
169:
2025:{\displaystyle {\frac {V_{A}}{V_{B}}}={\frac {\dot {S}}{-{\dot {R}}}}=2,}
2802:{\displaystyle {\mathit {AMA}}={\frac {F_{\text{out}}}{F_{\text{in}}}},}
2627:{\displaystyle {\mathit {IMA}}={\frac {F_{\text{out}}}{F_{\text{in}}}}.}
2470:
318:{\displaystyle {\mathit {MA}}={\frac {F_{b}}{F_{a}}}={\frac {a}{b}}.}
2035:
where 2 is the number of rope sections supporting the moving block.
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applied to the drive pulley which rotates at an angular velocity of
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formulated using geometric reasoning. It shows that if the distance
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This shows that the force exerted by an ideal block and tackle is
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where the input and output forces are determined experimentally.
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is the number of sections of rope that support the moving block.
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the pulley and brought back up to be knotted to the fixed block.
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circles and the ratio of the number of teeth on each gear, its
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The mechanical advantage for friction belt drives is given by
121:
18:
2867:{\displaystyle \eta ={\frac {\mathit {AMA}}{\mathit {IMA}}}.}
3048:
p 129-130, 12th century AD, translation by
Francis R. Walton
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from the fulcrum to where the input force is applied (point
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Measure of the force amplification achieved by using a tool
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from fulcrum to where the output force is applied (point
2973:
Uicker, John J.; Pennock, G. R.; Shigley, J. E. (2011).
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are related by the constant length of the rope, that is
1217:
is the number of teeth on the output sprocket. For a
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meshes with this chain or belt along the pitch radius
1064:{\displaystyle v=r_{A}\omega _{A}=r_{B}\omega _{B},\!}
696:{\displaystyle v=r_{A}\omega _{A}=r_{B}\omega _{B},\!}
484:{\displaystyle P=T_{A}\omega _{A}=T_{B}\omega _{B},\!}
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is the output, the ratio of the velocities of points
3096:(Revised 1994 ed.), Courier Dover Publications,
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meshes with the chain or belt along the pitch radius
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How to Dunk a
Doughnut: The Science of Everyday Life
2420:
of force to lift the load one foot. Both the ratios
1859:{\displaystyle {\dot {L}}=2{\dot {R}}+{\dot {S}}=0,}
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480:
3090:United States Bureau of Naval Personnel (1971),
2448:show that the IMA is six. For the first ratio,
404:Because the power flow is constant, the torque
376:The power input to a gear train with a torque
840:is the number of teeth on the input gear and
622:Two meshing gears transmit rotational motion.
418:of the output gear must satisfy the relation
8:
2090:must equal the power out acting on the load
168:The lever is a movable bar that pivots on a
847:is the number of teeth on the output gear.
3123:Nice demonstration of mechanical advantage
2060:on the moving block. Like the velocities
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206:are distances from the fulcrum to points
69:Learn how and when to remove this message
2968:
2966:
2163:{\displaystyle F_{A}V_{A}=F_{B}V_{B}.\!}
1918:{\displaystyle {\dot {S}}=-2{\dot {R}}.}
1519:
88:amplification achieved by using a tool,
32:This article includes a list of general
2962:
1697:where the input force is applied. Let
2977:. New York: Oxford University Press.
7:
2393:(AMA) is defined by a factor called
2461:
2451:
2412:
1074:where the input sprocket or pulley
961:has more teeth than the input gear
954:This shows that if the output gear
3128:Mechanical advantage — video
3004:A History of Mechanical Inventions
1231:teeth and the output sprocket has
1085:and the output sprocket or pulley
38:it lacks sufficient corresponding
14:
2975:Theory of machines and mechanisms
3093:Basic machines and how they work
2487:theoretical mechanical advantage
126:
23:
3046:Book of Histories (Chiliades) 2
857:teeth and the output gear has
344:) is greater than the distance
2045:be the input force applied at
1:
2404:with six rope sections and a
2372:times the input force, where
2049:the end of the rope, and let
1708:The total length of the rope
2940:On the Equilibrium of Planes
1423:Example: bicycle chain drive
717:and meshes with output gear
2899:Mechanical advantage device
2741:actual mechanical advantage
2735:Actual mechanical advantage
2391:actual mechanical advantage
1753:{\displaystyle L=2R+S+K,\!}
1705:where the load is applied.
140:the scope of other articles
3164:
3059:ConstructionKnowledge.net
2483:ideal mechanical advantage
2477:Ideal mechanical advantage
2458:of force input results in
2387:ideal mechanical advantage
2067:is directed downwards and
1938:be positive downwards and
1521:Speed ratios and total MA
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3148:Mechanisms (engineering)
2934:Transmission (mechanics)
2400:As an example, using a
225:is the input force and
53:more precise citations.
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968:, then the gear train
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3075:, Arcade Publishing,
2946:Mechanical efficiency
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2817:mechanical efficiency
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2074:is directed upwards.
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987:Chain and belt drives
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411:and angular velocity
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158:splitting the content
152:and help introduce a
3069:Fisher, Len (2003),
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84:is a measure of the
82:Mechanical advantage
2884:Outline of machines
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160:into a new article.
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2819:η of the machine,
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1712:can be written as
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1543:crank-wheel ratio
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1503:
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1315:
1238:teeth is given by
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976:the input torque.
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864:teeth is given by
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693:
624:
586:mechanical systems
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481:
315:
188:
150:discuss this issue
3118:Gears and pulleys
3103:978-0-486-21709-3
3082:978-1-55970-680-3
3014:978-0-486-14359-0
2984:978-0-19-537123-9
2914:Belt (mechanical)
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1019:
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1008:
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1000:
999:
997:
994:The velocity
992:
986:
984:
982:
981:speed reducer
977:
975:
971:
964:
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931:
927:
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680:
674:
670:
666:
661:
657:
651:
647:
643:
640:
633:
632:
631:
629:
626:The velocity
620:
616:
614:
607:
599:
597:
595:
591:
588:ranging from
587:
568:
561:
557:
551:
547:
541:
534:
530:
524:
520:
514:
497:
496:
495:
494:which yields
477:
472:
468:
462:
458:
454:
449:
445:
439:
435:
431:
428:
421:
420:
419:
417:
410:
402:
400:
389:
382:
374:
370:
362:
360:
358:
353:
351:
347:
343:
339:
335:
331:
312:
307:
304:
299:
292:
288:
282:
278:
272:
255:
254:
253:
251:
247:
243:
239:
235:
231:
224:
220:
214:and if force
213:
209:
205:
201:
196:
193:
185:
181:
177:
175:
171:
159:
155:
154:summary style
151:
145:
141:
139:
135:This section
133:
124:
123:
119:
111:
109:
107:
103:
99:
97:
91:
87:
83:
73:
70:
62:
52:
48:
42:
41:
35:
30:
21:
20:
3092:
3071:
3057:Ned Pelger,
3053:
3045:
3043:John Tzetzes
3038:
3026:. Retrieved
3003:
2999:Usher, A. P.
2993:
2974:
2938:
2919:Roller chain
2814:
2811:
2745:
2740:
2738:
2729:
2636:
2570:
2493:
2491:
2486:
2482:
2480:
2442:
2435:
2428:
2421:
2399:
2394:
2390:
2386:
2383:
2373:
2369:
2367:
2268:
2266:
2172:
2097:
2091:
2084:
2078:
2076:
2068:
2061:
2057:
2050:
2046:
2039:
2037:
2034:
1939:
1932:
1930:
1927:
1868:
1789:
1785:
1778:
1771:
1769:
1764:
1762:
1709:
1707:
1702:
1698:
1694:
1690:
1688:
1676:
1668:
1659:
1655:
1540:speed ratio
1515:
1435:
1417:
1327:
1232:
1225:
1223:
1219:toothed belt
1211:
1204:
1202:
1098:
1090:
1086:
1079:
1075:
1073:
995:
993:
990:
980:
978:
973:
969:
962:
955:
953:
858:
851:
849:
841:
834:
832:
722:
718:
711:
707:
705:
627:
625:
609:
583:
493:
412:
405:
403:
391:
384:
377:
375:
372:
357:virtual work
354:
349:
345:
341:
337:
329:
328:This is the
327:
249:
245:
244:is given by
241:
237:
233:
226:
222:
215:
211:
207:
203:
199:
197:
189:
178:
167:
136:
106:rigid bodies
93:
81:
80:
65:
56:
37:
2909:Chain drive
2406:600 lb
1629:high speed
729:therefore,
710:has radius
600:Gear trains
369:Speed ratio
363:Speed ratio
232:exerted at
221:applied to
94:law of the
51:introducing
3137:Categories
2957:References
2904:Gear ratio
2485:(IMA), or
2395:efficiency
2380:Efficiency
2103:, that is
1551:low speed
1099:therefore
721:of radius
613:gear ratio
606:Gear train
334:Archimedes
138:duplicates
102:mechanisms
59:April 2017
34:references
3143:Mechanics
2830:η
2460:600
2450:100
2410:100
2005:˙
1996:−
1990:˙
1907:˙
1895:−
1886:˙
1842:˙
1827:˙
1809:˙
1546:total MA
1123:ω
1113:ω
1049:ω
1026:ω
970:amplifies
753:ω
743:ω
681:ω
658:ω
558:ω
548:ω
469:ω
446:ω
3001:(1929).
2878:See also
594:linkages
332:, which
3028:7 April
974:reduces
170:fulcrum
148:Please
47:improve
3100:
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3021:
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2471:energy
1763:where
1603:mid 2
1577:mid 1
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833:where
590:robots
112:Levers
36:, but
2951:Wedge
1650:0.16
1624:0.31
1598:0.33
1572:0.62
1501:0.54.
192:power
174:class
118:Lever
96:lever
86:force
3098:ISBN
3077:ISBN
3030:2013
3019:OCLC
3009:ISBN
2979:ISBN
2739:The
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1644:0.30
1621:0.54
1618:0.57
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1592:0.62
1569:0.54
1566:1.14
240:and
210:and
202:and
2780:out
2708:out
2671:out
2605:out
2551:out
2541:out
2446:out
2425:out
1869:or
592:to
392:P=T
390:is
198:If
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2965:^
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