# Is there a way of "shortening" a mechanical lever, but keeping its mechanical advantage intact someway?

For what I think I know, the mechanical advantage of a lever comes in exchange for the distance the load travels upwards, independent from the type of lever (I think).

So, let's say, in a (class-1) lever with a long area where the load is applied, but the effort is also applied in an even longer area. Is there a way of "shortening" it while maintaining the mechanical advantage?

I thought of putting a lot of small levers in sequence (with different lengths to compensate for the increase of force), one applying effort until the total of levers would make the same amount of force as the long single lever.

Let's say, someone then would organise them in a spiral, so they occupy less space.

Would that even be possible, or it is just a nonsensical question?

By the way, the intention with this question is to lift around 200 kg with the force of a leg.

• Yeah, that would probably work. Jun 10 at 17:31
• Sketch them out in a straight line, calculate the mechanical advantage and the input / output movement ratio and post your findings. Are you hoping to find something magical? (You won't!) Jun 10 at 17:48
• Consider a screw- it is a wedge that has been wrapped around for significant 'shortening' To do the same to a lever may mean multiple pivots such as in a gearbox (this has indeed been done with gears which are essentially levers)
– Abel
Jun 10 at 19:23
• Cascade levers the same way a a gearbox does. Gears are just round levers. That will shorten the levers in one axis while expanding it in the other. Jun 10 at 20:17
• Could you edit your question to include a sketch of what you mean? I'm having a hard time picturing it.
– Wasabi
Jun 11 at 3:29

## 3 Answers

Input force times distance equals output force times distance. There is no way around this except adding power to the system. If you shorten the throw you must increase the force to get the same output because the mechanical sdvantage is less. No amount of smaller levers linked together can help this. All the smaller levers would do is increase losses in the system.

• Explain why not? A 1:9 lever is 10 units long. But two 1:3 levers linked together are 8 units long. Jun 14 at 8:39

Yes. Assume the load and the force are in equilibrium condition initially. You can shift either the load, the force, or both, toward the fulcrum, so the resulting work done (mechanical advantage) by the load and the force are equal, thus the equilibrium condition is re-established. Two cases are shown below.

• this answer changes the mcehanical advantage, which the question wanted to maintain. Jun 13 at 0:26
• @TigerGuy You can simply adjust the weight or force accordingly to maintain the balance while shortening the rod.
– r13
Jun 13 at 1:31
• that is changing the machnical advantage. Jun 13 at 3:29
• Please define the "mechanical advantage" to clarify your disagreement.
– r13
Jun 13 at 3:42
• mechacal advantage has a formula, output force over input force. Wiki has an entry. Moving the fulcrum changes the mechanical advantage. Jun 13 at 4:11

Although you need to move the ends of the lever through the correct distances to get the correct advantage -- work equals force times distance -- you don't need to have the same linear distance to do so. A worm screw does effectively the same, without the long levers.

A simple example is a double lever system where the second lever points back towards you. Two 2:1 levers give you a 4:1 advantage, but the load point is right next to your hand, and the length of the lever system is only 2+1=3, not 4+1=5.