In
physicsPhysics is a natural science; it is the study of matter and its motion through spacetime and all that derives from these, such as energy and force...
and
engineeringEngineering is the discipline, art and profession of acquiring and applying technical, scientific and mathematical knowledge to design and implement materials, structures, machines, devices, systems, and processes that safely realize a desired objective or inventions.The American Engineers' Council...
,
mechanical advantage (
MA) is the factor by which a mechanism multiplies the
forceIn physics, a force is any agent that causes a change in the motion of a free body, or that causes stress in a fixed body. It can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a...
or
torqueTorque, also called moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....
put into it. Generally, the mechanical advantage is calculated as follows:
or more simply:
The first equation shows that the force exerted IN to the machine multiplied by the distance moved IN will always be equal to the force exerted OUT of the machine multiplied by the distance moved OUT. For example, using a block and tackle with 6 ropes, and a 600 pound load, the operator would be required to pull the rope 6 feet, and exert 100 pounds of force to lift the 600 pound load 1 foot.
The second equation is a simplified formula based just on the forces in and out. Using the example above, 100 pounds of force IN results in 600 pounds of force OUT, an MA of 6. Both of these equations calculate only the ideal mechanical advantage (IMA) and ignore any losses due to friction. The actual mechanical advantage (AMA) includes those frictional losses. The difference between the two is the
mechanical efficiencyIn physics, mechanical efficiency is the effectiveness of a machine and is defined asMechanical Efficiency is the ratio of work input to work output. It is often expressed as a percentage...
of the system.
Types
There are two types of mechanical advantage: ideal mechanical advantage (IMA) and actual mechanical advantage (AMA).
Ideal mechanical advantage
The
ideal mechanical advantage (IMA), or
theoretical mechanical advantage, is the mechanical advantage of an
ideal machineAn 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...
. It is usually calculated using physics principles because there is no ideal machine.
The IMA of a machine can be found with the following formula:
where
- DE equals the 'effort distance' (the distance from the fulcrum to where the effort is applied)
- DR equals the resistance distance (the distance from the fulcrum to where the resistance is applied)
Actual mechanical advantage
The
actual mechanical advantage (AMA) is the mechanical advantage of a real
machineA simple machine is a mechanical device that changes the direction or magnitude of a force.In general, they can be defined as the simplest mechanisms that use mechanical advantage to multiply force. A simple machine uses a single applied force to do work against a single load force...
. Actual mechanical advantage takes into consideration real world factors such as energy lost in friction.
The AMA of a machine is calculated with the following formula:
where
- R = resistance force
In physics, resistance force is the force which an effort force must overcome in order to do work on an object. Resistance force, like most other forces, is measured in newtons or in pound-forces.Resistance force can be expressed as:where:...
- Eactual = actual effort force
There are six simple machines: screw, inclined plane, wheel and axle, pulley, lever, and wedge!
Simple machines
The following
simple machineA simple machine is a mechanical device that changes the direction or magnitude of a force.In general, they can be defined as the simplest mechanisms that use mechanical advantage to multiply force. A simple machine uses a single applied force to do work against a single load force...
s exhibit a mechanical advantage:
- The beam shown is in static equilibrium around the fulcrum. This is due to the moment
In physics, the term "moment" can refer to many different concepts:*Moment of force is a synonym for torque, an important basic concept in physics, civil engineering, and mechanical engineering. In the context of mechanical engineering, the terms are not necessarily interchangeable, but one or the...
created by vector force "A" counterclockwise (moment A*a) being in equilibrium 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 leverIn physics, a lever 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....
.
- Wheel and axle
The wheel and axle is a simple machine. A wheel and axle is a butt that rotates in a circle around a center point or fulcrum. The larger wheel rotates around the smaller wheel . Bicycle wheels, ferris wheels and gears are all examples of a wheel and axle...
motion (e.g. screwdriverThe screwdriver is a device specifically designed for the insertion and tightening of screws. The screwdriver is made up of a head or tip, which engages with a screw, a mechanism to apply torque by rotating the tip, and some way to position and support the screwdriver...
s, doorknobs): 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 frictionFriction is the force resisting the relative lateral motion of solid surfaces, fluid layers, or material elements in contact. It is usually subdivided into several varieties:...
is overwhelmed by the rotational force of the wheel multiplied by the mechanical advantage.
- Pulley
A pulley, also called a sheave or a drum, is a mechanism composed of a wheel on an axle or shaft that may have a groove between two flanges around its circumference. A rope, cable, belt, or chain usually runs over the wheel and inside the groove, if present...
: Pulleys change the direction of a tension force on a flexible material, e.g. a rope or cable. In addition, a Block and tackleA block and tackle is a system of two or more pulleys with a rope or cable threaded between them, usually used to lift or pull heavy loads.- Overview :...
of multiple pulleys creates mechanical advantage, by having the flexible material looped over several pulleys in turn. Adding more loops and pulleys increases the mechanical advantage.
- Screw
A screw, or bolt, is a type of fastener characterized by a helical ridge, known as an external thread or just thread, wrapped around a cylinder. Some screw threads are designed to mate with a complementary thread, known as an internal thread, often in the form of a nut or a object that has the...
: A screw is essentially an inclined planeThe inclined plane is one of the original six simple machines; as the name suggests, it is a flat surface whose endpoints are at different heights. By moving an object up an inclined plane rather than completely vertical, the amount of force required is reduced, at the expense of increasing the...
wrapped around a cylinder. The run over the rise of this inclined plane is the mechanical advantage of a screw.
Pulleys
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 pulley. It has an 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 an 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 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 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
A block and tackle is a system of two or more pulleys with a rope or cable threaded between them, usually used to lift or pull heavy loads.- Overview :...
: MA = 3
Screws
The theoretical mechanical advantage for a screw can be calculated using the following equation:
where
- dm = the mean diameter of the screw thread
- l = the lead
Lead is the axial advance of a helix for one complete turn on a gear, especially worm and helical gears. The lead for a screw thread is the axial travel for a single revolution....
of the screw thread
Note that the actual mechanical advantage of a screw
system is greater, as a screwdriver or other screw driving system has a mechanical advantage as well.
- Inclined plane
The inclined plane is one of the original six simple machines; as the name suggests, it is a flat surface whose endpoints are at different heights. By moving an object up an inclined plane rather than completely vertical, the amount of force required is reduced, at the expense of increasing the...
: MA = length of slope รท height of slope
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