A lever is a simple machine consisting of a beam or rigid rod pivoted at a fixed hinge , or fulcrum . A lever is a rigid body capable of rotating on a point on itself. On the basis of the locations of fulcrum, load and effort, the lever is divided into three types . It is one of the six simple machines identified by Renaissance scientists. A lever amplifies an input force to provide a greater output force, which is said to provide leverage , which is mechanical advantage gained in the system, equal to the ratio of the output force to the input force. As such, the lever is a mechanical advantage device , trading off force against movement.
34-439: A fulcrum ( pl. : fulcra or fulcrums ) is the support about which a lever pivots. Fulcrum may also refer to: Lever The word "lever" entered English around AD 1300 from Old French : levier . This sprang from the stem of the verb lever , meaning "to raise". The verb, in turn, goes back to Latin : levare , itself from the adjective levis , meaning "light" (as in "not heavy"). The word's primary origin
68-638: A ( F A ⋅ e A ⊥ ) − b ( F B ⋅ e B ⊥ ) = a F A − b F B , {\displaystyle F_{\theta }=\mathbf {F} _{A}\cdot {\frac {\partial \mathbf {v} _{A}}{\partial {\dot {\theta }}}}-\mathbf {F} _{B}\cdot {\frac {\partial \mathbf {v} _{B}}{\partial {\dot {\theta }}}}=a(\mathbf {F} _{A}\cdot \mathbf {e} _{A}^{\perp })-b(\mathbf {F} _{B}\cdot \mathbf {e} _{B}^{\perp })=aF_{A}-bF_{B},} where F A and F B are components of
102-466: A compound lever system, though in rare situations the geometry may suit a specific purpose. The distances used in calculation of mechanical advantage are measured perpendicular to the force. In the example of a nail clipper on the right (a compound lever made of a class 2 and a class 3 lever), because the effort is applied vertically (that is, not perpendicular to the lever), distances to the respective fulcrums are measured horizontally, instead of along
136-415: A lever is the ratio of output force to input force. M A = F 2 F 1 = a b . {\displaystyle MA={\frac {F_{2}}{F_{1}}}={\frac {a}{b}}.\!} This relationship shows that the mechanical advantage can be computed from ratio of the distances from the fulcrum to where the input and output forces are applied to the lever, assuming
170-423: A rigid bar connected to a ground frame by a hinged joint called a fulcrum. The lever is operated by applying an input force F A at a point A located by the coordinate vector r A on the bar. The lever then exerts an output force F B at the point B located by r B . The rotation of the lever about the fulcrum P is defined by the rotation angle θ in radians. Let the coordinate vector of
204-406: A system of levers acts as effort for the next, and thus the applied force is transferred from one lever to the next. Almost all scales use some sort of compound lever to work. Other examples include nail clippers and piano keys. A lever arm uses the fulcrum to lift the load using and intensifying an applied force . In practice, conditions may prevent the use of a single lever to accomplish
238-405: A weight of 7.5 lb (or 7.5 kg). Alternatively, if the position of the fulcrum on lever AA' were moved so that A1 = 4 units and A2 = 9 units, then the mechanical advantage W/F is calculated as 4 / 9 × 9 / 4 = 1, meaning that an applied force will lift an equivalent weight and there is no mechanical advantage. This is not usually the goal of
272-415: A weightless lever and no losses due to friction, flexibility or wear. This remains true even though the "horizontal" distance (perpendicular to the pull of gravity) of both a and b change (diminish) as the lever changes to any position away from the horizontal. Levers are classified by the relative positions of the fulcrum, effort and resistance (or load). It is common to call the input force "effort" and
306-407: Is a remark attributed to Archimedes, who formally stated the correct mathematical principle of levers (quoted by Pappus of Alexandria). One of the earliest examples of a compound lever is from Han dynasty (202 BC - 220 AD) crossbow trigger mechanisms which featured a triple compound lever. Such a mechanism was placed within the crossbow stock itself. The idea of the compound lever is attributed to
340-428: Is given by: M A = F B F A = a b . {\displaystyle MA={\frac {F_{B}}{F_{A}}}={\frac {a}{b}}.} This is the law of the lever , which was proven by Archimedes using geometric reasoning. It shows that if the distance a from the fulcrum to where the input force is applied (point A ) is greater than the distance b from fulcrum to where
374-414: Is no friction in the hinge or bending in the beam. In this case, the power into the lever equals the power out, and the ratio of output to input force is given by the ratio of the distances from the fulcrum to the points of application of these forces. This is known as the law of the lever . The mechanical advantage of a lever can be determined by considering the balance of moments or torque , T , about
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#1732791472954408-612: Is the Proto-Indo-European stem legwh- , meaning "light", "easy" or "nimble", among other things. The PIE stem also gave rise to the English word "light". The earliest evidence of the lever mechanism dates back to the ancient Near East c. 5000 BC , when it was first used in a simple balance scale . In ancient Egypt c. 4400 BC , a foot pedal was used for the earliest horizontal frame loom . In Mesopotamia (modern Iraq) c. 3000 BC ,
442-481: Is the generalized coordinate that defines the configuration of the lever, and the generalized force associated with this coordinate is given by F θ = F A ⋅ ∂ v A ∂ θ ˙ − F B ⋅ ∂ v B ∂ θ ˙ =
476-402: Is the output force. The distances a and b are the perpendicular distances between the forces and the fulcrum. Since the moments of torque must be balanced, T 1 = T 2 {\displaystyle T_{1}=T_{2}\!} . So, F 1 a = F 2 b {\displaystyle F_{1}a=F_{2}b\!} . The mechanical advantage of
510-422: The eardrum to the oval window of the cochlea . The lever is a movable bar that pivots on a fulcrum attached to a fixed point. The lever operates by applying forces at different distances from the fulcrum, or a pivot. As the lever rotates around the fulcrum, points further from this pivot move faster than points closer to the pivot. Therefore, a force applied to a point further from the pivot must be less than
544-443: The shadouf , a crane-like device that uses a lever mechanism, was invented. In ancient Egypt , workmen used the lever to move and uplift obelisks weighing more than 100 tons. This is evident from the recesses in the large blocks and the handling bosses which could not be used for any purpose other than for levers. The earliest remaining writings regarding levers date from the 3rd century BC and were provided, by common belief, by
578-451: The 3rd class lever. A compound lever comprises several levers acting in series: the resistance from one lever in a system of levers acts as effort for the next, and thus the applied force is transferred from one lever to the next. Examples of compound levers include scales, nail clippers and piano keys. The malleus , incus and stapes are small bones in the middle ear , connected as compound levers, that transfer sound waves from
612-515: The Greek mathematician Archimedes , who famously stated "Give me a lever long enough and a fulcrum on which to place it, and I shall move the world." Autumn Stanley argues that the digging stick can be considered the first lever, which would position prehistoric women as the inventors of lever technology. A lever is a beam connected to ground by a hinge, or pivot, called a fulcrum. The ideal lever does not dissipate or store energy, which means there
646-409: The desired result, e.g., a restricted space, the inconvenient location of the point of delivery of the resultant force, or the prohibitive length of the lever arm needed. In these conditions, combinations of simple levers, called compound levers, are used. Compound levers can be constructed from first, second and/or third-order levers. In all types of compound lever, the rule is that force multiplied by
680-414: The elbow-joint press, which is used in printing, molding or handloading bullets, minting coins and medals, and in hole punching. Compound balances are used to weigh heavy items. These all use multiple levers to magnify force to accomplish a specific purpose. The train brake translates the force of pushing back the stick to the levers and they rub against the wheels, using friction to slow and eventually stop
714-552: The force arm equals the weight multiplied by the weight arm. The output from one lever becomes the input for the next lever in the system, and so the advantage is magnified. The figure on the left illustrates a compound lever formed from two first-class levers, along with a short derivation of how to compute the mechanical advantage. With the dimensions shown, the mechanical advantage, W/F can be calculated as 10 / 3 × 9 / 4 = 7.5, meaning that an applied force of 1 pound (or 1 kg) could lift
SECTION 20
#1732791472954748-421: The force located at a point closer in, because power is the product of force and velocity. If a and b are distances from the fulcrum to points A and B and the force F A applied to A is the input and the force F B applied at B is the output, the ratio of the velocities of points A and B is given by a/b , so we have the ratio of the output force to the input force, or mechanical advantage,
782-400: The forces that are perpendicular to the radial segments PA and PB . The principle of virtual work states that at equilibrium the generalized force is zero, that is F θ = a F A − b F B = 0. {\displaystyle F_{\theta }=aF_{A}-bF_{B}=0.\,\!} Thus, the ratio of the output force F B to
816-542: The fulcrum to the input point A and to the output point B , respectively. Now introduce the unit vectors e A and e B from the fulcrum to the point A and B , so r A − r P = a e A , r B − r P = b e B . {\displaystyle \mathbf {r} _{A}-\mathbf {r} _{P}=a\mathbf {e} _{A},\quad \mathbf {r} _{B}-\mathbf {r} _{P}=b\mathbf {e} _{B}.} The velocity of
850-399: The fulcrum. If the distance traveled is greater, then the output force is lessened. T 1 = F 1 a , T 2 = F 2 b {\displaystyle {\begin{aligned}T_{1}&=F_{1}a,\quad \\T_{2}&=F_{2}b\!\end{aligned}}} where F 1 is the input force to the lever and F 2
884-426: The input force F A is obtained as M A = F B F A = a b , {\displaystyle MA={\frac {F_{B}}{F_{A}}}={\frac {a}{b}},} which is the mechanical advantage of the lever. This equation shows that if the distance a from the fulcrum to the point A where the input force is applied is greater than the distance b from fulcrum to
918-401: The key. The malleus , incus and stapes are small bones (ossicles) in the middle ear , connected as compound levers, that transfer sound waves from the eardrum to the oval window of the cochlea . The earliest remaining writings regarding levers date from the 3rd century BC and were provided by Archimedes . " Give me a place to stand, and I shall move the earth with a lever "
952-400: The lever. In this example, W/F is 7 + 1 / 1 × 6 / 6 + 2 = 6. Note that (7 + 1) cm = 8 cm is the distance from the point of application of the effort to the fulcrum of the first lever, perpendicular to the applied effort. A few examples of the compound lever are the scale, train brakes , and a common type of nail clippers . Another example is
986-409: The output force "load" or "resistance". This allows the identification of three classes of levers by the relative locations of the fulcrum, the resistance and the effort: These cases are described by the mnemonic fre 123 where the f fulcrum is between r and e for the 1st class lever, the r resistance is between f and e for the 2nd class lever, and the e effort is between f and r for
1020-399: The output force is applied (point B ), then the lever amplifies the input force. On the other hand, if the distance a from the fulcrum to the input force is less than the distance b from the fulcrum to the output force, then the lever reduces the input force. The use of velocity in the static analysis of a lever is an application of the principle of virtual work . A lever is modeled as
1054-416: The point B where the output force is applied, then the lever amplifies the input force. If the opposite is true that the distance from the fulcrum to the input point A is less than from the fulcrum to the output point B , then the lever reduces the magnitude of the input force. Compound lever The compound lever is a simple machine operating on the premise that the resistance from one lever in
Fulcrum - Misplaced Pages Continue
1088-416: The point P that defines the fulcrum be r P , and introduce the lengths a = | r A − r P | , b = | r B − r P | , {\displaystyle a=|\mathbf {r} _{A}-\mathbf {r} _{P}|,\quad b=|\mathbf {r} _{B}-\mathbf {r} _{P}|,} which are the distances from
1122-562: The points A and B are obtained as v A = θ ˙ a e A ⊥ , v B = θ ˙ b e B ⊥ , {\displaystyle \mathbf {v} _{A}={\dot {\theta }}a\mathbf {e} _{A}^{\perp },\quad \mathbf {v} _{B}={\dot {\theta }}b\mathbf {e} _{B}^{\perp },} where e A and e B are unit vectors perpendicular to e A and e B , respectively. The angle θ
1156-446: The train. These are everyday applications of this mechanism. A piano key is a compound lever of the first-class, since the fulcrum is between the weight to be moved and the power. The purpose of this lever is to translate a small movement (depression of the key) into a larger and fast movement of the hammer on the strings. The quality of the resulting tone depends on whether the final speed is brought about by gradual or sudden movement of
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