# Modulating Output of a Pulley with Variable Inputs

I am working on a recreational project to take variable inputs and convert them to a constant output without substantially altering the force required to achieve such a task. The best way to visualize the problem is with the classic case of using a simple pulley to raise a bucket of water. I am wondering if there is a mechanism that would allow someone to pull the rope variable distances ( 1ft, 2 ft, 3ft, 4 ft, etc) all while lifting the bucket to the same height each time (1 ft). Ideally, it would not take any more or less force to perform the task. From my understanding of gears, increasing the distance of the input would decrease the force required to raise the bucket. I am wondering if there is a known mechanism or way to offset this in order to make the input force requirement relatively constant or if there is potentially a better way to accomplish the task? Thank you for your help! My knowledge of engineering is rudimentary at best and was wondering if something like this is even physically possible.

• (1) "... to pull on one end of the pulley at variable distances". I think we need a diagram. Usually we pull on the rope, not the pulley. (Search for "block and tackle" images.) (2) To lift a load a fixed amount will require $energy = mgh$ where $m$ is mass (kg), $g$ is gravity (10 m/s/s approx.) and $h$ is height (m). (3) By using gears, levers, hydraulics or pulleys you can reduce the force but you will have to increase the distance the force acts over to do the same amount of work. (4) Can you edit to explain the real problem you are trying to solve. Commented Feb 16, 2022 at 22:47
• To make the input relatively constant, add a lot of friction to your pulley. To make the distance traveled limited to a fixed value, add a mechanical stop and have the load on a limited slip connection to the line and have lots of extra line beyond that point Commented Feb 17, 2022 at 1:04

What if you wanted to be able to pull only 1 inch and lift the bucket the same 1 foot? You needed to pull the rope with a force 12 times the weight of the bucket.

The pulley or a lever or a crane all they do is change the mechanical advantage. They can not and never will change the amount of work needed.

Work, energy are nonvariant fundamental concepts.

If you need more mechanical advantage you end up increasing the travel distance of a smaller force. and vice versa.

Figure 1. Your drawing shows four identical systems. Pulling a rope down by a certain distance will cause each of the loads to move up by the same distance.

Figure 2. To get mechanical advantage you need to use a block and tackle system.

This gives a mechanical advantage equal to an integral multiple of the pulling force. Note that the mechanical advantage is equal to the number of ropes supporting the load because the load weight is spread between the supporting ropes. In the case of the 1:2 setup there are two vertical ropes supporting 100 N so each takes 50 N.

Work = force x distance.

You want the amount of force to be constant, regardless of the distance that the user will pull the rope. So the amount of work the user does is variable. But the work done on the bucket in lifting it 1ft remains constant. This is a rather strange requirement.

The only way I can see that would work is to change the mechanical advantage (see the answer by Transistor), but then deliberately add or remove friction. So if the user sets the system to 1:4, then you add a load of friction so that it's just as hard to pull the rope as it was at 1:1.