Information about Mechanical Advantage
In physics and engineering, mechanical advantage (MA) is the factor by which a mechanism multiplies the force put into it. Following are simple machines where the mechanical advantage is calculated.
A single movable pulley has a MA of 2 (assuming frictionless bearings in the pulley). Consider a pulley attached to a weight being lifted. A rope passes around it, with one end attached to a fixed point above, e.g. a barn roof rafter, and a pulling force is applied upward to the other end with the two lengths parallel. In this situation the distance the lifter must pull the rope becomes twice the distance the weight travels, allowing the force applied to be halved. Note: if an additional pulley is used to change the direction of the rope, e.g. the person doing the work wants to stand on the ground instead of on a rafter, the mechanical advantage is not increased.
By looping more ropes around more pulleys we can continue to increase the mechanical advantage. For example if we have two pulleys attached to the rafter, two pulleys attached to the weight, one end attached to the rafter, and someone standing on the rafter pulling the rope, we have a mechanical advantage of four. Again note: if we add another pulley so that someone may stand on the ground and pull down, we still have a mechanical advantage of four.
Here are examples where the fixed point is not obvious:
A man sits on a seat that hangs from a rope that is looped through a pulley attached to a roof rafter above. The man pulls down on the rope to lift himself and the seat. The pulley is considered a movable pulley and the man and the seat are considered as fixed points; MA = 2.
A velcro strap on a shoe passes through a slot and folds over on itself. The slot is a movable pulley and the MA =2.
Two ropes laid down a ramp attached to a raised platform. A barrel is rolled onto the ropes and the ropes are passed over the barrel and handed to two workers at the top of the ramp. The workers pull the ropes together to get the barrel to the top. The barrel is a movable pulley and the MA = 2. If the there is enough friction where the rope is pinched between the barrel and the ramp, the pinch point becomes the attachment point. This is considered a fixed attachment point because the rope above the barrel does not move relative to the ramp. Alternatively the ends of the rope can be attached to the platform.
Block and tackle: MA = 3
Mechanical advantage also applies to torque. A simple gearset is able to multiply torque.
The IMA of a machine can be found with the following formula:
where
The AMA of a machine is calculated with the following formula:
where
The vertical vector force "V" is transmitted through the bars (with a vector force "F") of which one is anchored on the right side and the other pushes away a block on the left against a vector force "H". The angle α should be relatively small, say less than 5 degrees, for best performance. The ratio "H/V" equals the mechanical advantage MA.
In the equations the friction on the block on the left (illustrated by normal vector force "N") is ignored, as is friction in the hinges. The friction in the hinges will have less influence on the mechanical advantage with a large 'bar length'/'hinge pin diameter' ratio. However, in that case one has to be increasingly aware of material deformation.
Calculation: for angle α=0.5 degree the MA=57.3; α=1 > MA=28.6; α=2 > MA=14.3; α=3 > MA=9.5; α=5 > MA=5.7
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)
Beam balanced around fulcrum.
- The beam shown is in static equilibrium around the fulcrum. This is due to the moment created by vector force "A" counterclockwise (moment A*a) being in equlibrium with the moment created by vector force "B" clockwise (moment B*b). The relatively low vector force "B" is translated in a relatively high vector force "A". The force is thus increased in the ratio of the forces A : B, which is equal to the ratio of the distances to the fulcrum b : a. This ratio is called the mechanical advantage. This idealised situation does not take into account friction. For more explanation, see also lever.
- Wheel and axle: A wheel is essentially a lever with one arm the distance between the axle and the outer point of the wheel, and the other the radius of the axle. Typically this is a fairly large difference, leading to a proportionately large mechanical advantage. This allows even simple wheels with wooden axles running in wooden blocks to still turn freely, because their friction is overwhelmed by the rotational force of the wheel multiplied by the mechanical advantage.
- Pulley: Pulleys change the direction of a tension force on a flexible material, e.g. a rope or cable. In addition, pulleys can be "added together" to create mechanical advantage, by having the flexible material looped over several pulleys in turn. More loops and pulleys increases the mechanical advantage.
Mechanical advantage
Consider lifting a weight with rope and pulleys. A rope looped through a pulley attached to a fixed spot, e.g. a barn roof rafter, and attached to the weight is called a single fixed pulley. It has a MA = 1 (assuming frictionless bearings in the pulley), meaning no mechanical advantage (or disadvantage) however advantageous the change in direction may be.A single movable pulley has a MA of 2 (assuming frictionless bearings in the pulley). Consider a pulley attached to a weight being lifted. A rope passes around it, with one end attached to a fixed point above, e.g. a barn roof rafter, and a pulling force is applied upward to the other end with the two lengths parallel. In this situation the distance the lifter must pull the rope becomes twice the distance the weight travels, allowing the force applied to be halved. Note: if an additional pulley is used to change the direction of the rope, e.g. the person doing the work wants to stand on the ground instead of on a rafter, the mechanical advantage is not increased.
By looping more ropes around more pulleys we can continue to increase the mechanical advantage. For example if we have two pulleys attached to the rafter, two pulleys attached to the weight, one end attached to the rafter, and someone standing on the rafter pulling the rope, we have a mechanical advantage of four. Again note: if we add another pulley so that someone may stand on the ground and pull down, we still have a mechanical advantage of four.
Here are examples where the fixed point is not obvious:
A man sits on a seat that hangs from a rope that is looped through a pulley attached to a roof rafter above. The man pulls down on the rope to lift himself and the seat. The pulley is considered a movable pulley and the man and the seat are considered as fixed points; MA = 2.
A velcro strap on a shoe passes through a slot and folds over on itself. The slot is a movable pulley and the MA =2.
Two ropes laid down a ramp attached to a raised platform. A barrel is rolled onto the ropes and the ropes are passed over the barrel and handed to two workers at the top of the ramp. The workers pull the ropes together to get the barrel to the top. The barrel is a movable pulley and the MA = 2. If the there is enough friction where the rope is pinched between the barrel and the ramp, the pinch point becomes the attachment point. This is considered a fixed attachment point because the rope above the barrel does not move relative to the ramp. Alternatively the ends of the rope can be attached to the platform.
Block and tackle: MA = 3
- Inclined plane: MA = length of slope ÷ height of slope
- MA = (the distance over which force is applied) ÷ (the distance over which the load is moved)
Mechanical advantage also applies to torque. A simple gearset is able to multiply torque.
Type of mechanical advantage
There are two types of mechanical advantage:- Ideal mechanical advantage (IMA)
- Actual mechanical advantage (AMA)
Ideal mechanical advantage
The ideal mechanical advantage is the mechanical advantage of an ideal machine. It is usually calculated using physics principles because there is no ideal machine. It is 'theoretical.'The IMA of a machine can be found with the following formula:
where
- DE equals the effort distance
- DR equals the resistance distance.
Actual mechanical advantage
The actual mechanical advantage is the mechanical advantage of a real machine. Actual mechanical advantage takes into consideration real world factors such as energy lost in friction. In this way, it differs from the ideal mechanical advantage, which is a sort of 'theoretical limit' to the efficiency of the MA.The AMA of a machine is calculated with the following formula:
where
- R is the resistance force,
- Eactual is the actual effort force.
Example, graphically shown
)
Mechanical advantage in mechanism.
In the equations the friction on the block on the left (illustrated by normal vector force "N") is ignored, as is friction in the hinges. The friction in the hinges will have less influence on the mechanical advantage with a large 'bar length'/'hinge pin diameter' ratio. However, in that case one has to be increasingly aware of material deformation.
Calculation: for angle α=0.5 degree the MA=57.3; α=1 > MA=28.6; α=2 > MA=14.3; α=3 > MA=9.5; α=5 > MA=5.7
See also
External links
Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
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Engineering is the applied science of acquiring and applying knowledge to design, analysis, and/or construction of works for practical purposes. The American Engineers' Council for Professional Development, also known as ECPD,[1] (later ABET [2]
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simple machine is any device that only requires the application of a single force to work. Work is done when a force is applied and results in movement over a set distance. The work done is the product of the force and the distance.
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- Principle of Moments redirects here. For the Robert Plant album, see The Principle of Moments. See also Moment (mathematics) for a more abstract concept of moments that evolved from this concept of physics.
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lever (from French lever, "to raise", c.f. a levant) is a rigid object that is used with an appropriate fulcrum or pivot point to multiply the mechanical force that can be applied to another object.
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wheel is a circular device capable of rotating on its axis, facilitating movement or transportation or performing labour in machines. A wheel together with an axle overcomes friction by facilitating motion by rolling. Common examples are found in transport applications.
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axle is a central shaft for a rotating wheel or gear. In some cases the axle may be fixed in position with a bearing or bushing sitting inside the hole in the wheel or gear to allow the wheel or gear to rotate around the axle.
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Friction is the force of two surfaces in contact. It is not a fundamental force, as it is derived from electromagnetic forces between atoms. When contacting surfaces move relative to each other, the friction between the two objects converts kinetic energy into thermal energy, or
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pulley (also called a sheave or block) is a wheel with a groove between two flanges around its circumference. The groove normally locates a rope, cable or belt. Pulleys are used to change the direction of an applied force, transmit rotational motion, or realize a mechanical
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- This article deals with the physical structure. For related terms see, canal inclined plane, cable railway, funicular, or fixed-wing aircraft (airplane).
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Friction is the force of two surfaces in contact. It is not a fundamental force, as it is derived from electromagnetic forces between atoms. When contacting surfaces move relative to each other, the friction between the two objects converts kinetic energy into thermal energy, or
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Elasticity is a branch of physics which studies the properties of elastic materials. A material is said to be elastic if it deforms under stress (e.g., external forces), but then returns to its original shape when the stress is removed.
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torque (or often called a moment) can informally be thought of as "rotational force" or "angular force" which causes a change in rotational motion. This force is defined by linear force multiplied by a radius.
The SI unit for torque is the newton meter (N m). In U.S.
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The SI unit for torque is the newton meter (N m). In U.S.
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A gear is a component within a transmission device that transmits rotational force to another gear or device. A gear is different from a pulley in that a gear is a round wheel which has linkages ("teeth" or "cogs") that mesh with other gear teeth, allowing force to be fully
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ideal machine is an idealistic system in which there is no loss of energy. Loss of energy may occur through any type of radiation, radiational heat for example. In this article, energy loss refers to losses of energy that are not directly accountable for, as when a space shuttle
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In graph theory, the resistance distance between two vertices of a simple connected graph, G, is equal to the resistance between two equivalent points on an electrical network, constructed so as to correspond to G
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simple machine is any device that only requires the application of a single force to work. Work is done when a force is applied and results in movement over a set distance. The work done is the product of the force and the distance.
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In physics, resistance force is the force which an effort force must overcome in order to do work on an object.
Resistance force can be expressed as
where:
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Resistance force can be expressed as
- b × lR = m × jjE
where:
- R
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In physics, effort force is the force used to move an object over a distance.
Effort force is a component in the following equation,
where
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Effort force is a component in the following equation,
- R × DR = E × DE
where
- R is the resistance force
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The gear ratio is the relationship between the number of teeth on two gears that are meshed or two sprockets connected with a common roller chain, or the circumferences of two pulleys connected with a drive belt.
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