A simple machine is a mechanical device that changes the direction or magnitude of a force.[1] In general, they can be defined as the simplest mechanisms that use mechanical advantage (also called leverage) to multiply force.[2] Usually the term refers to the six classical simple machines that were defined by Renaissance scientists:[3][4][5]
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. 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 mechanical advantage.
Simple Machines
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Simple machines can be regarded as the elementary "building blocks" of which all more complicated machines (sometimes called "compound machines"[6][7]) are composed.[2][8] For example, wheels, levers, and pulleys are all used in the mechanism of a bicycle.[9][10] The mechanical advantage of a compound machine is just the product of the mechanical advantages of the simple machines of which it is composed.
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 machines are composed, which arose in the Renaissance as a neoclassical amplification of ancient Greek texts. The great variety and sophistication of modern machine linkages, which arose during the Industrial Revolution, is inadequately described by these six simple categories. Various post-Renaissance authors have compiled expanded lists of "simple machines", often using terms like basic machines,[9] compound machines,[6] or machine elements to distinguish them from the classical simple machines above. By the late 1800s, Franz Reuleaux[11] had identified hundreds of machine elements, calling them simple machines.[12] Modern machine theory analyzes machines as kinematic chains composed of elementary linkages called kinematic pairs.
During the Renaissance the dynamics of the mechanical powers, 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 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), in which he showed the underlying mathematical similarity of the machines as force amplifiers.[17][18] He was the first to explain that simple machines do not create energy, only transform it.[17]
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.
Although each machine works differently mechanically, the way they function is similar mathematically.[20] In each machine, a force F in {\displaystyle F_{\text{in}}} is applied to the device at one point, and it does work moving a load F out {\displaystyle F_{\text{out}}} at another point.[21] 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 mechanical advantage
Simple machines do not contain a source of energy,[22] so they cannot do more work than they receive from the input force.[21] A simple machine with no friction or elasticity is called an ideal machine.[23][24][25] Due to conservation of energy, in an ideal simple machine, the power output (rate of energy output) at any time P out {\displaystyle P_{\text{out}}} is equal to the power input P in {\displaystyle P_{\text{in}}}
So in non-ideal machines, the mechanical advantage is always less than the velocity ratio by the product with the efficiency {\displaystyle \eta } . 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.
A compound machine is a machine 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 bench vise consists of a lever (the vise's handle) in series with a screw, and a simple gear train consists of a number of gears (wheels and axles) connected in series.
In many simple machines, if the load force F out {\displaystyle F_{\textrm {out}}} on the machine is high enough in relation to the input force F in {\displaystyle F_{\textrm {in}}} , the machine will move backwards, with the load force doing work on the input force.[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 self-locking, nonreversible, or non-overhauling machine.[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.
Simple machines are elementary examples of kinematic chains that are used to model mechanical systems 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 kinematic pair 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.
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.
However, a more successful strategy was identified by Franz Reuleaux, 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.[32]
Throughout history, humans have developed several simple machines to make work easier. The most notable of these are known as the "six simple machines": the wheel and axle, the lever, the inclined plane, the pulley, the screw, and the wedge, although the latter three are actually just extensions or combinations of the first three, according to Encyclopedia Britannica.
Simple machines are devices with no, or very few, moving parts that make work easier. Many of today's complex tools are just combinations or more complicated forms of the six simple machines, according to the University of Colorado at Boulder. For instance, we might attach a long handle to a shaft to make a windlass, or use a block and tackle to pull a load up a ramp. While these machines may seem simple, they continue to provide us with the means to do many things that we could never do without them.
The other five machines all help humans increase and/or redirect the force applied to an object. In their book "Moving Big Things," Janet L. Kolodner and her co-authors write, "Machines provide mechanical advantage to assist in moving objects. Mechanical advantage is the trade-off between force and distance." In the following discussion of the simple machines that increase the force applied to their input, we will neglect the force of friction, because in most of these cases, the frictional force is very small compared to the input and output forces involved.
When a force is applied over a distance, it produces work. Mathematically, this is expressed as W = F D. For example, to lift an object, we must do work to overcome the force due to gravity and move the object upward. To lift an object that is twice as heavy, it takes twice as much work to lift it the same distance. It also takes twice as much work to lift the same object twice as far, according to Auburn University. As indicated by the math, the main benefit of machines is that they allow us to do the same amount of work by applying a smaller amount of force over a greater distance.
As simple as pulleys are, they are still finding use in the most advanced new machines. For example, the Hangprinter, a 3D printer that can build furniture-sized objects, employs a system of wires and computer-controlled pulleys anchored to the walls, floor, and ceiling.
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Stephannie BehrensTable of Contents 2 Mechanisms and Simple Machines tag_hash_108_________: the fundamental physical or chemical processesinvolved in or responsible for an action, reaction or other naturalphenomenon. tag_hash_109_______: an assemblage of parts that transmit forces, motionand energy in a predetermined manner. tag_hash_110______________: any of various elementary mechanisms havingthe elements of which all machines are composed. Included inthis category are the lever, wheel and axle, pulley, inclined plane,wedge and the screw. The word mechanism has many meanings. In kinematics, a mechanism is a means oftransmitting, controlling, or constraining relative movement (Hunt 78). Movements which areelectrically, magnetically, pneumatically operated are excluded fromthe concept of mechanism. The central theme for mechanisms is rigidbodies connected together by joints. A machine is a combination of rigid or resistant bodies,formed and connected so that they move with definite relative motionsand transmit force from the source of power to the resistance to beovercome. A machine has two functions: transmitting definite relativemotion and transmitting force. These functions require strengthand rigidity to transmit the forces. The term mechanism is applied to the combination ofgeometrical bodies which constitute a machine or part of a machine. Amechanism may therefore be defined as a combination ofrigid or resistant bodies, formed and connected so that they move withdefinite relative motions with respect to one another (Ham et al. 58). Although a truly rigid body does not exist, many engineeringcomponents are rigid because their deformations and distortions arenegligible in comparison with their relative movements. The similarity between machines and mechanisms isthat they are both combinations of rigid bodies the relative motion among the rigid bodies are definite. The difference between machine and mechanism isthat machines transform energy to do work, while mechanisms so notnecessarily perform this function. The term machinerygenerally means machines and mechanisms. Figure 2-1 shows a picture of the main part of a diesel engine. Themechanism of its cylinder-link-crank parts is a slider-crankmechanism, as shown in Figure 2-2. Figure 2-1 Cross section of a powercylinder in a diesel engineFigure 2-2 Skeleton outline2.1 The Inclined Plane Figure 2-3a shows an inclinedplane, AB is the base, BC is the height and AC the inclinedplane. With the use of the inclined plane a given resistance canbe overcome with a smaller force than if the plane is not used. Forexample, in Figure 2-3b, suppose we wish to raisea weight of 1000 lb. through the vertical distance BC = 2 ft. If thisweight were raised vertically and without the use of the inclinedplane the force 1000 lb. would have to be exerted through the distanceBC. If, however, the inclined plane is used and the weight is movedover its inclined plane AC, a force of only 2/3 of 1000 lb. or 667lb. is necessary, although this force is exerted through a distance ACwhich is greater than distance BC. Figure 2-3 Inclined planeUsing an inclined plane requires a smaller force exertedthrough a greater distance to do a certain amount of work. Letting F represent the force required to raise a given weight onthe inclined plane, and W the weight to be raised, we have the proportion:(2-1)2.1.1 Screw Jack One of the most common application of the principle of the inclined plane is in the screwjack which is used to overcome a heavy pressure or raise aheavy weight of W by a much smaller force F applied atthe handle. R represents the length of the handle and Pthe pitch of the screw, or the distance advances in onecomplete turn. Figure 2-4 The screw jackNeglecting the friction the following rule is used: The force Fmultiplied by the distance through which it moves in one complete turnis equal to the weight lifted times the distance through which it islifted in the same time. In one complete turn the end of the handledescribes a circle of circumference 2R. This is thedistance through which the force F is exerted. Therefore from the rule above(2-2)and(2-3)Suppose R equals 18 in., P equals 1/8 in. and the weightto be lifted equals 100,000 lb., then the force required at Fis then 110 lb. This means that, neglecting friction, 110 lb. atF will raise 100,000 lb. at W, but the weight liftedmoves much slower than the force applied at F. 2.2 Gears A gear, or toothed wheel, when in operation, may actually beconsidered as a lever with the additional feature that it can be rotatedcontinuously, instead of rocking back and forth through a shortdistance. One of the basic relationships for a gear is the numberof teeth, the diameter, and the rotary velocity of gears. Figure 2-5 shows the ends of two shafts A and Bconnected by 2 gears of 24 and 48 teeth respectively. Notice that thelarger gear will make only one-half turn while the smaller makes acomplete turn. That is, the ratio of speeds (velocity ratio) of thelarge to the smaller is as 1 to 2. Figure 2-5 GearsThe gear that is closer to the source of power is called thedriver, and the gear that receives power from the driver iscalled the driven gear.2.2.1 Gear Trains A gear train may have several drivers and several driven gears.Figure 2-6 Gear trainWhen gear A turns once clockwise, gear B turns 4 timescounter-clockwise and gear C turns once clockwise. Hence gear B doesnot change the speed of C from what it would have been if geareddirectly to gear A, but it changes its direction from counterclockwiseto clockwise. The velocity ratio of the first and last gears in a train of simple gearsdose not changed by putting any number of gears between them.Figure 2-7 shows compound gears in whichtwo gears are on the middle shaft. Gears B and D rotate at the samespeed since they are keyed (fixed) to the same shaft. The number ofteeth on each gear is given in the figure. Given these numbers, ifgear A rotates at 100 r.p.m. clockwise, gear B turns 400r.p.m. (rotations per minute) counterclockwise and gear C turns 1200r.p.m. clockwise. Figure 2-7 Compound gears2.2.2 Gear Ratios It is important when working with gears to know what number of teeththe gears should have so that they can mesh properly in a gear train.The size of the teeth for connecting gears must be match properly.2.3 Belts and Pulleys Belts and pulleys are an important part ofmost machines. Pulleys are nothing but gears withoutteeth and instead of running together directly they are made to driveone another by cords, ropes, cables, or belting of some kinds. As with gears, the velocities of pulleys are inversely proportional totheir diameters. Figure 2-8 Belts and pulleysPulleys can also be arranged as a block and tackle.2.4 Lever2.5 Wheel and Axle2.6 Wedge2.7 Efficiency of MachinesIn working out the problems on levers, belts andpulleys, inclined planes and so forth, we have not takenaccount of friction or other sources of energy loss. In other words,we have supposed them to be perfect, when in fact they are not. Tomeasure the performance of a machine, we often find itsefficiency, which is defined as(2-4)where = the efficiencyof a machine,Win = the input work to a machine, andWout = the output work of a machine.Table of Contents Complete Table of Contents1 Introduction to Mechanisms2 Mechanisms and Simple Machines 2.1 The Inclined Plane 2.1.1 Screw Jack 2.2 Gears 2.2.1 Gear Trains 2.2.2 Gear Ratios 2.3 Belts and Pulleys 2.4 Lever 2.5 Lever 2.6 Wedge 2.7 Efficiency of Machines3 More on Machines and Mechanisms4 Basic Kinematics of Constrained Rigid Bodies5 Planar Linkages6 Cams7 Gears8 Other MechanismsIndexReferences
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