by Ron Kurtus (28 June 2016)

A machine's distance mechanical advantage shows the effectiveness of the machine in moving an object a greater distance than the input distance. The equation for the distance mechanical advantage is the output distance divided by the input distance.

Note: Most science books only consider force mechanical advantage. However, distance mechanical advantage is just as important.

Examples where distance mechanical advantage is employed include the lever, bicycle, and cranes.

Questions you may have include:

• What is distance mechanical advantage equation?
• How is distance mechanical advantage used with levers?
• What are other examples?

This lesson will answer those questions. Useful tool: Units Conversion

There are times when you want to apply a force a short distance to increase the distance an object moves. The distance mechanical advantage equation is:

where

• DO is the distance the load moves or the output distance
• DI is the distance the effort moves or the input distance

Note that the distance directions are not taken into consideration in the mechanical advantage.

Also note: Friction in the machine does not change the distances moved.

## Relationship with lever arms

The distance mechanical advantage of a lever is also a function of the distances to the lever fulcrum.

(See Increasing Distance Moved with a Lever)

where

• dO is the distance of the output or load to the fulcrum
• dI is the distance of the input or effort to the fulcrum Lever configuration provides distance mechanical advantage

If the input arm was dI = 0.5m and the output arm was dO = 2m, then MAD = 4.

Thus, if the input distance was DI = 3cm, then the output distance would be DO = 12cm.

## Other examples

Other examples of distance mechanical advantage are a bicycle, pulley, and crane.

### Bicycle

One good example is when you ride a bicycle. The distance you move the pedals on a bicycle are much less than the distance moved on the circumference of the tires.

### Pulley

A pulley is an example of a machine where the output distance can be the same as the input distance, except in the opposite direction. For example, if the pulley lifted an object 1.5 meters, you would have to pull on the rope 1.5 meters, such that the mechanical advantage of the pulley would be:

### Crane

Also, cranes are used to lift large items to various heights.

## Summary

To move an object a greater distance than the input distance, you can calculate its distance mechanical advantage (MAD) to show the effectiveness of the machine.

Examples include the lever, bicycle, pulley, and cranes.

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## Resources and references

Ron Kurtus' Credentials

### Websites

The Mechanical Advantage of Machines - Carolina Curriculum (PDF)

Machines Resources

### Books

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