Utilizing Weight Force in Various Systems
Note. This paper is still under revision. It is placed here by arrangement for a few interested people, but as presented here, does not represent my complete thoughts or data on this matter.
The idea of utilising a weight force as an important contributer to the operation of a mechanism is not new. The idea of a "counter weight" is universally understood. A counter weight hanging from a flexible cable will apply a force to that cable that is constant whatever the displacement, as long as the counter weight is not accelerating. This constant force is often convenient, and counter weights find many applications.
Counter weights can also be used in applications where the force required is not constant, but is required to vary with displacement according to some law. One application in which a linear relationship between displacement and force would be required is the suspension of a container of liquid so that the level of the surface of the liquid stays the same as the quantity of the liquid changes. If the container shape is such that the free surface area of the liquid is constant, then it can be seen that a linear relationship between force and displacement is required.
Consider my crude drawing of three jars. These three jars are identical and contain different amounts of liquid.
Jar A contains the most liquid, and is supported by a tensile force in the support cable of magnitude Fa. I have shown the three jars having the same liquid level. Of course these three depictions could represent a single jar in three different states as the liquid is drawn from the jar. You will be able to see that if the force F varies with displacement in just the right manner, then the liquid level can be kept constant.
Can we use a counter weight to provide this force?
It is easy to attange a counter weight to apply a force that varies with displacement, but there would still be the question of whether the force can be made to vary with displacemnt as required.
Here is an arrangement that will give a force that varies with displacement.
The force F pulls the weight through an arc centred on the "fixed point". You can see that when the weight is directly below the "fixed point", the force in the cable is zero. As the pendulum is pulled to the side, the force becomes greater and greater as the displacement increases.
Here is an application.
The jar here is just as we have seen before, except that a flexible tube is attached to the bottom and leads water to the water dish. Can we choose a geometry of the penduum and the pulley so that the water level in the dish remains constant as the water is used?
Perhaps not, but a more practical question would be could we choose a geometry that would give substantially constant water level in the dish?
Here is another application
This is a garage door made of multiple panels. This particular style of door lifts to clear the doorway and moves up into the ceiling. The door panels move on wheels on tracks. It will be seen that when the door is nearly shut, the counter weight force required will be the weight of the door, but when the door is nearly open, most of the door rests on tracks that are level, and the counterweight force required is very small. When the door is roughly half open, the force required will be roughly half that required when the door is closed.
I had an actual application for this idea, and wrote a BASIC program to optimize the pendulum geometry to the counterweight requirements for the particular door. The results were satisfactory. The developement of the program will be described here in a subsequent version of this.
The pendulum counterweight was not ultimately used for the door counterweight. The reason for this had nothing to do with my ability to make it work. It was not used because of safety considerations. There is a huge amount of energy stored in the pendulum when elevated, and what would happen to this in the case of a cable break or release was a concern. (The pendulum would swing within the building smashing everything it encountered.)