Mechanical advantage

In physics and engineering mechanical advantage (MA) is the factor by which a machine multiplies the force put into it. The mechanical advantage can be calculated for the following simple machines by using the following formulas:

• Lever: MA = length of effort arm ÷ length of resistance arm.

• 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 an equally large mechanical advantage. This is why even simple wheels with wooden axles running in wooden blocks will still turn freely, because the friction is overwhelmed by the rotational force of the wheel multiplied by the mechanical advantage.

• Pulley: Pulleys are wheels that are connected together with ropes. In doing so the direction of the force on the rope can be changed, with little loss in force due to friction (for the same reasons as the wheel). However pulleys can be "added together" to create additional mechanical advantage by having the rope looped over several pulleys in turn. A pulley with one rope (single fixed pulley) has an MA = 1, that is, no advantage (or disadvantage). A pulley with two ropes (single moveable pulley) has a MA = 2. A pulley with 6 ropes (block and tackle) has a MA = 6.

• Inclined Plane: MA = length of slope ÷ height of slope

Most 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. 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 load 1 foot, therefore:

• (force in 100 × distance in 6) = (force out 600 × distance out 1)

or more basic, WORK_in = WORK_out

This requires an ideal simple machine, meaning that there are no losses due to friction or elasticity. If friction or elasticity exist in the system efficiency will be lower; Work_in will be greater than Work_out

Mechanical advantage also applies to torque. A simple gearset is able to multiply torque.

There are two types of mechanical advantage:

1. Ideal mechanical advantage (IMA)
2. Actual mechanical advantage (AMA)