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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.
If a and b are distances from the fulcrum to points A and B and the force F A applied to A is the input and the force F B applied at B is the output, the ratio of the velocities of points A and B is given by a/b, so we have the ratio of the output force to the input force, or mechanical advantage, is given by: = =.
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. The device trades off input forces against movement to obtain a desired amplification in the output force.
The input force from this equation is the force needed to hold the load motionless on the inclined plane, or push it up at a constant velocity. If the input force is greater than this, the load will accelerate up the plane. If the force is less, it will accelerate down the plane.
If the input force F A is applied to the edge of the wheel A and the force F B at the edge of the axle B is the output, then the ratio of the velocities of points A and B is given by a/b, so the ratio of the output force to the input force, or mechanical advantage, is given by = =.
The rotational force applied to the screw is actually a torque =. Because of this, the input force required to turn a screw depends on how far from the shaft it is applied; the farther from the shaft, the less force is needed to turn it. The force on a screw is not usually applied at the rim as assumed above.
This means the input force on the rope is F A =F B /n. Thus, the block and tackle reduces the input force by the factor n. A double tackle has two pulleys in both the fixed and moving blocks with four rope parts (n) supporting the load (F B) of 100 N. The mechanical advantage is 4, requiring a force of only 25 N to lift the load.
The input force multiplied by the distance moved by the smaller piston is equal to the output force multiplied by the distance moved by the larger piston; this is one more example of a simple machine operating on the same principle as a mechanical lever.