Fundamentals of Machines: Mechanical Advantage, Velocity Ratio, and Efficiency

A machine is formally defined as a device that enables the user to overcome a large resistance or load by applying a relatively small amount of effort.
In broader terms, a machine can be defined as any device utilized to gain a specific type of advantage during the performance of work.

Mechanical Advantage represents the ratio of the load to the effort applied to the machine.
The mathematical formula for mechanical advantage is: $MA = \frac{\text{load}}{\text{effort}}$
It is also expressed simplified as: $MA = \frac{L}{E}$

The Velocity Ratio is defined as the ratio of the distance traveled by the effort to the distance traveled by the load over the same period.
The mathematical expression for velocity ratio is: $VR = \frac{\text{distance moved by effort}}{\text{distance moved by load}}$

In a situation where a machine is considered frictionless, the mechanical advantage is equal to the velocity ratio.
The relationship for a frictionless machine is stated as: $MA = VR$

Efficiency is the percentage ratio comparing the mechanical advantage to the velocity ratio.
The formula used to calculate efficiency based on mechanical properties is: $\text{Efficiency} = \frac{MA}{VR} \times 100$
Efficiency can also be defined in terms of work performance: $\text{Efficiency} = \frac{\text{useful work output}}{\text{useful work input}} \times 100$
When expanded into components of force and distance, the efficiency formula is: $\text{Efficiency} = \frac{\text{load} \times \text{distance moved by load}}{\text{effort} \times \text{distance moved by output}} \times 100$