Wheel And Axle 712h1i

Wheel and axle From Wikipedia, the free encyclopedia Jump to: navigation, search

A windlass, a well known application of the wheel and axle. The wheel and axle is one of six simple machines developed in ancient times and is in the category of a first-class lever.[1] In its simplest form it consists of a rod attached to a wheel so that their movements are coupled when one of the parts is turned. The wheel and axle is used either as a force multiplier (such as a doorknob, steering wheel or fishing reel) or as a distance multiplier (such as on a bicycle or the driven wheels of a car). In the first kind of application, the larger wheel is used to create more torque (in the axle) with less force. In the second kind of application, when the axle is turned, the outside of the wheel turns at a greater linear speed that is proportional to the ratio of the radii of the wheel and axle. For example, if a bike wheel has a gear that turns eight inches in one second, and the wheel circumference is eighty inches, the wheel rotates through a distance ten times greater than the gear (and reducing the number of rotations of the pedals required). By varying the radii of the axle and/or wheel, any amount of mechanical advantage may be gained.[2]

Turning a doorknob creates torque with little force required.

Contents [hide]     

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1 Description 2 History 3 Uses/Examples 4 Misconceptions 5 Calculating mechanical advantage o 5.1 Ideal mechanical advantage o 5.2 Actual mechanical advantage 6 More Examples 7 References 8 Additional Resources

[edit] Description The wheel and axle is a simple machine that is generally is classified as a lever and provides mechanical advantage. The mechanical advantage is the ratio of the resistance to the effort.[3] It consists of a rod attached to a wheel so that their movements are coupled when one of the parts is turned. When the axle is turned, the outside of the wheel turns at a greater linear speed because the rotational speed is the same. This principle is used in cars to gain more distance by applying a large torque (from the engine) to the axle, causing the wheels, which have a much larger radius, to turn. In the reverse case, when a force is applied to the wheel, more torque is created with less force. The result is proportional to the ratio of the radii. For example, if a sailor is pushing a capstan bar, pushing closer to the center is harder because he makes use of the wheel and axle as if it were a lever. Because the longer a lever is, the less force you have to use, the longer the bar the less effort is required.

A ship’s crew creates a wheel and axle when they insert capstan bars into the capstan – this reduces the effort required to lift the anchor.

[edit] History

It is not known for certain who created the wheel and axle, it is known that it was used in ancient times. The oldest wheel publicized by archaeologists was found in 2002 in Ljubljana.[citation needed] Austrian experts established that the wheel is between 5,100 and 5,350 years old and is therefore at least a century older than those found in Switzerland and southern .[citation needed] The wheel was made of ash and oak and had a radius of 70 cm. The axle is 120 cm long and made of oak.[4]

[edit] Uses/Examples The wheel and axle has many uses on many size scales and there are many examples. Common examples include the lift mechanism on a well, doorknob, a rotary telephone dial, a rotary egg beater, faucet handles, a wheel on which torque acts in a car, a fishing reel, a screw driver, a steering wheel, and even a simple top. In a top, the highest part of the top is spun so that the edge turns rapidly and keeps it upright. These examples are simple applications of a wheel and axle, yet they are great innovations. Examples described in further detail on Wikipedia include the following: See crank (mechanism) for useful images. Note that wheels and axles in several applications are often operated with a crank. See flywheel for a specific type of wheel and axle used to store rotational energy. See Reaction wheel for an application of a flywheel for controlling spacecraft and satellites. See gyroscope for another application of a wheel and axle. See windlass is an example (similar to the capstan and capstan bar) of a wheel and axle created by inserting rods into an axle.

[edit] Misconceptions One misconception about the wheel and axle is that any wheel on a cylinder is a wheel and axle. This is not so. To be a true wheel and axle, the wheel must be firmly attached to the axle so that if one is turned the other turns with it.

[edit] Calculating mechanical advantage The mechanical advantage of a simple machine like the wheel and axle is computed as the ratio of the resistance to the effort. The larger the ratio the greater the multiplication of force (torque) created or distance achieved. By varying the radii of the axle and/or wheel, any amount of mechanical advantage may be gained.[5] In this manner, the size of the wheel may be increased to an inconvenient extent. In this case a system or combination of wheels (often

toothed, that is, gears) are used. As a wheel and axle is a type of lever, a system of wheels and axles is like a compound lever.[6]

[edit] Ideal mechanical advantage The ideal mechanical advantage of a wheel and axle is calculated with the following formula:

[edit] Actual mechanical advantage The actual mechanical advantage of a wheel and axle is calculated with the following formula:

where R = resistance force, i.e. the weight of the bucket in this example. Eactual = actual effort force, the force required to turn the wheel.

Lever From Wikipedia, the free encyclopedia Jump to: navigation, search This article is about the simple machine. For other uses, see Lever (disambiguation).

Lever

Levers can be used to exert a large force over a small distance at one end by exerting only a small force over a greater distance at the other. Classification

Simple machine

Industry

Construction

In physics, a lever (from French lever, "to raise", cf. a levant) is a rigid object that is used with an appropriate fulcrum or pivot point to either multiply the mechanical force (effort) that can be applied to another object or resistance force (load), or multiply the distance and speed at which the opposite end of the rigid object travels. This leverage is also termed mechanical advantage, and is one example of the principle of moments. A lever is one of the six simple machines.

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1 Early use 2 Force and levers 3 Classes 4 In the real world 5 See also 6 Notes 7 References 8 External links

[edit] Early use 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"[note 1] is a remark of Archimedes who formally stated the correct mathematical principle of levers (quoted by Pappus of Alexandria).[1] It is assumed that in ancient Egypt, constructors used the lever to move and uplift obelisks weighting more than 100 tons.[2]

[edit] Force and levers The force applied (at end points of the lever) is proportional to the ratio of the length of the lever arm measured between the fulcrum (pivoting point) and application point of the force applied at each end of the lever. Mathematically, this is expressed by M = Fd, where F is the force, d is the perpendicular distance between the force and the fulcrum, and M is the turning force known as the moment or torque.

[edit] Classes There are three classes of levers representing variations in the relative locations of the fulcrum, the load and the force:[3]  

Class 1: The fulcrum is located between the applied force and the load, for example, a crowbar or a pair of scissors or a seesaw. Class 2: The load is situated between the fulcrum and the force, for example, a wheelbarrow or a nutcracker.

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Class 3: The force is applied between the fulcrum and the load, for example, a pair of tweezers or the human mandible

[edit] In the real world For the classical mechanics formulas to work, or to be a good approximation of real world applications, the lever must be made from a combination of rigid bodies, (i.e., a beam) and a rigid fulcrum. Any bending or other deformation must be negligible.

Simple machine From Wikipedia, the free encyclopedia Jump to: navigation, search This article is about the concept in physics. For the Internet forum software, see Simple Machines Forum.

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

Simple machines are the elementary "building blocks" of which all more complicated machines (sometimes called "compound machines"[5]) are composed.[3][6] For example, wheels, levers, and pulleys are all used in the mechanism of a bicycle. The mechanical advantage of a compound machine is just the product of the mechanical advantages of the simple machines of which it is composed. 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).

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1 History 2 Alternate definitions 3 Frictionless analysis 4 Friction and efficiency 5 Self-locking machines o 5.1 Derivation 6 Compound machines 7 References

[edit] History The idea of a "simple machine" originated with the Greek philosopher Archimedes around the 3rd century BC, who studied the "Archimedean" simple machines: lever, pulley, and screw. [3][7]

He discovered the principle of mechanical advantage in the lever.[8] Hellenistic Greek scientists defined the classic five simple machines (excluding the inclined plane) and were able to roughly calculate their mechanical advantage, although the calculations for the wedge and screw, which have large frictional losses, were not very accurate.[9] Heron of Alexandria (ca. 10–75 AD) in his work Mechanics lists five mechanisms that can "set a load in motion"; lever, windlass, pulley, wedge, and screw,[7] and describes their fabrication and uses.[10] However the Greeks' understanding was limited to the statics of simple machines; the balance of forces, and did not include dynamics; the tradeoff between force and distance, or the concept of work. During the Renaissance the dynamics of the Mechanical Powers, as the simple machines were called, began to be studied from the standpoint of how much useful work they could perform, leading eventually to the new concept of mechanical work. In 1586 Flemish engineer Simon Stevin 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 Galileo Galilei in 1600 in Le Meccaniche ("On Mechanics").[11][12] He was the first to understand that simple machines do not create energy, only transform it.[11] The classic rules of sliding friction in machines were discovered by Leonardo da Vinci (1452– 1519), but remained unpublished in his notebooks. They were rediscovered by Guillaume Amontons (1699) and were further developed by Charles-Augustin de Coulomb (1785).[13]

[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 exclude the wedge from the list of simple machines, as it is a moving inclined plane.[3] The screw, being a helical inclined plane,[14] is sometimes also excluded.[15] This position is less accepted because a screw converts a rotational force (torque) to a linear force. It has been said that the pulley, and wheel and axle can be viewed as unique forms of levers, leaving only the lever and the inclined plane as simple machines from which all others can be derived.[16][17][18][19] Hydraulic systems can also provide amplification of force, so some say they should be added to the list.[18][20][21]

[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, [22] 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,[23] so they cannot do more work than they receive from the input force.[22] A simple machine with no friction or elasticity is called an ideal machine.[24] In an ideal simple machine, 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 [19] moves, , must be equal to the load force, times the distance the load moves, :

So the ratio of output to input force, the mechanical advantage, of a frictionless machine is equal to the "distance ratio"; the ratio of input distance to output distance moved:[22][24]

(Ideal Mechanical Advantage) 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] Friction and efficiency All actual machines have some friction. When friction is included, the mechanical advantage of a simple machine is no longer equal to the "distance ratio" but also depends on the machine's efficiency.[24][25][26][27] Due to conservation of energy, in a machine with friction all the work done on the machine by the input force, Win goes into either moving the load Wout or is dissipated as heat by friction Wfric.

The efficiency η of a machine is a number between 0 and 1 defined as the ratio of output work to input work

Work is defined as the force multiplied by the distance moved, so , and thus

and

(Actual Mechanical Advantage) So in all practical machines, the mechanical advantage is always less than the distance ratio, and equal to the distance ratio din/dout multiplied by the efficiency η.[26][27] So a real machine, with friction, will not be able to move as large a load as a corresponding ideal frictionless machine using the same input force.

[edit] Self-locking machines In many simple machines, if the load force Fout on the machine is high enough in relation to the input force Fin, the machine will move backwards, with the load force doing work on the input force.[28][29] 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 "reversible", "non-locking" or "overhauling" machines, and the backward motion is called "overhauling". 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 "selflocking", "nonreversible", or "non-overhauling" machine.[26][29] 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. Self-locking occurs mainly in those machines which have large areas of sliding and therefore large frictional losses: the screw, inclined plane, and wedge: 





The most common example is a screw. In most screws, applying torque to the shaft can cause it to turn, moving the shaft linearly to do work against a load, but no amount of axial load force against the shaft will cause it to turn backwards. In an inclined plane, a load can be pulled up the plane by a sideways input force, but if the plane is not too steep and there is enough friction between load and plane, when the input force is removed the load will remain motionless and will not slide down the plane, regardless of its weight. A wedge can be driven into a block of wood by force on the end, such as from hitting it with a sledge hammer, forcing the sides apart, but no amount of compression force from the wood walls will cause it to pop back out of the block.

A machine will be self-locking if and only if its efficiency η is below 50%:[26][29]

Whether a machine is self-locking depends on both the friction forces (coefficient of static friction) between its parts, and the distance ratio din/dout (ideal mechanical advantage). If both the friction and ideal mechanical advantage are high enough, it will self-lock.

[edit] Derivation 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[30][31]

When it moves backward from point 2 to point 1 with the load force doing work on the input force, the work lost to friction Wfric is the same

When the input force is removed, the machine will self-lock if the work dissipated in friction is greater than the work done by the load force moving it backwards

From (1)

[edit] Compound machines A compound machine is a machine made up of a number of simple machines connected in series, with the output force of each providing the input force for the next. For example a bench vise consists of a lever (the vise's handle) in series with a screw, and a car's transmission consists of a number of gears (wheels and axles) in series. The mechanical advantage of the compound machine MAcompound is defined as the output force applied to the load by the last machine, divided by the input force applied to the first machine. As the force propagates through the machine, each simple machine scales the force by its own mechanical advantage, so the mechanical advantage of the compound machine is equal to the product of the mechanical advantages of each simple machine of which it is composed

Proof:

Since the output force of each machine is the input of the next:

, so

Similarly, the efficiency of the compound machine is equal to the product of the efficiencies of the simple machines