Is it possible to have it so that that the rubber bands become more tense as the load increases?
In a passive intake?
The only thing I could say is that I’m assuming your wanting this for a lift and in that case all I can say is that you have your rubber banding set up to where it is supporting the lift rather than just helping the motors. And have a motor hold set up so that the rubber bands are doing most of the work but the motors are keeping up the extra load.
If you have a cap on the cubes (that expands to fit the number of cubes in the intake, I’d say that its plausible. I still hold my reservations about capping your stacks though.
Yes, it’s the primary characteristic of springs: F = kd. The force, F, is proportional to the distance the spring has been stretched or compressed times the spring constant, k. So by adding more load to a spring, you will stretch or compress it until the force is equal to the load (or until the spring breaks or otherwise permanently deforms).
Now if you want additional force without comparable deflection, you’re out of luck.
@John_TYler is correct that if you have a claw with sides rubber-banded together then your force is fixed by width of the claw .
However, if you set it up such that entire claw could move up/down, relative to the rest of the lift, stretching the rubber bands depending on the weight of what it holds, then you could have variable force.
Another way to achieve your goal would be combine rubber bands with something like this:
Similar principle is used in panel carriers.