mechanical advantage - Mechanical advantage, Type of mechanical advantage, Example, graphically shown

The ratio of the resistance or load to the applied force or effort of a machine; for example, the weight lifted by a lever divided by the effort required. It is an essential property of a machine, which can be less than, equal to, or greater than 1. The actual mechanical advantage of a working machine is always less than that predicted because some extra effort is always needed to overcome frictional resistance.

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. This is due to the momentum created by vector force "A" counterclockwise (momentum A*a) being in equlibrium with momentum created by vector force "B" clockwise (momentum B*b). This ratio is called the mechanical advantage. 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. 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. 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. 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.

Block and tackle: MA = 3

Inclined plane: MA = length of slope ÷ height of slope

Generally, the mechanical advantage is calculated thus:

MA = (the distance over which force is applied) ÷ (the distance over which the load is moved)

also, the Force exerted IN to the machine × the distance moved IN will always be equal to the force exerted OUT of the machine × the distance moved OUT. 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 load 1 foot. Workin will be greater than Workout

Mechanical advantage also applies to 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 '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.

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

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 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.