N3-Break Whilst Lifting?

[MrVibrating]

Here's a kind of split Roberval balance:



The two grey plunger-weights turn cranks counterposed via a conrod (green system).

Although the conrod is a linear actuator, it's currently at fixed length for now.

The masses of the two plungers are exposed with input variables, so we can make one heavier or lighter, over or under-balancing that side.

The Roberval is however actually comprised of two cars, able to move sideways independently of one another. The left side is anchored stationary, but the 'Trolley Speed' input variable is applied to the initial x-velocities of the right-side car components, as well as the green and blue actuators connecting the cars:



Note that this is treating the system as if it's already in motion when the actual sim begins - so we're not interested in the energy spent on that initial linear acceleration; as you can see we're just metering the delta-GPE and delta-KE from the balancing action, as well as the work done by the two actuators, here a zero sum.

The two cars are separating at 25 cm/sec, and the two actuators are expanding at that same speed.

The blue actuator is resisting the acceleration of the right-side car, because without it, both plungers would drop, accelerating the right car beyond the selected speed.

The green actuator is basically now a dynamic conrod, in homeostatic equilibrium; if it were expanding any slower than 25 cm/sec, both plungers would drop; any faster and both would rise. Because its speed is equal however, no net work is being performed.

So we have successfully counter-balanced two weights against one another, even though each resides in a different velocity reference frame.

This is an interesting situation, which, with a little more variation, could get more interesting..

For now, let's just check it actually still functions correctly as a balance:



..and yes, all delta-GPE converts to delta-KE between the two interacting plungers, with no net work performed by or against either actuator, or thus between the cars themselves; it's basically an ordinary Roberval-type balance, but for the fact that the interacting GPE loads lie in different velocity reference frames.

It may be awkward to actually build of course, but then so's a Lexus. Point is, we're not breaking any laws, yet..

And so you can probably see where this is going...

Q: What if these were instead elevator cars moving up and down in parallel lift shafts, rather than just moving sideways?

Going vertical should compound the velocity vectors; ie. suppose the right-side car were rising at constant speed instead of translating horizontally, while the left-side car again remains stationary:

• You'd now have a Roberval split between two lift cars

• Rising or falling at constant speed, gravity in each car will remain exactly 1 G

• The vertical load on the blue actuator should reflect the dGPE of the rising car

• The load on the green actuator should remain neutral

• The input and output dGPEs and dKEs on the plungers however now seem susceptible to a divergence from an effective N3 break during the lift, because the plunger in the rising car is moving a greater absolute speed and distance than the one in the static car


I've demonstrated it sideways first just to get the concept across, and to test the hypothesis and initial proof of principle. The only difference between horizontal and vertical - as far as i can currently see - is that GPE is not a function of horizontal displacement..

What will happen if this is tried vertically?

[MrVibrating]

Still mulling how best to try this, but have realised an additional feature that might be worth implementing - a variable fulcrum or leverage ratio, so that ie. 1 kg can be balanced against 4 kg having one-quarter the displacement or whatever.

"One pound can cause the raising of more than one pound".

"I don't want to go into the details here of how suddenly the excess weight is caused to rise. You can't comprehend these matters, or see how true craftsmanship can rise above innate lowly tendencies (as does a weight above the point of application of a lever)"

Together with the 'quarters' riddle in AP, all the clues seem to point to some kind of N3 break whilst lifting, so being able to experiment with different input / output displacement heights may be desirable.

The basic premise remains the same - a Roberval-type balance split between static and dynamic velocity frames, the latter now rising instead of just sliding sideways.

The potential exploit here is that the weight being lifted in the rising car is not being pushed upwards against the floor of the car itself, but is instead being pushed upwards by the descending weight in the static car; in other words the reaction mass is in a different velocity FoR to the mass being thrust upwards. The intention is that the constant rising velocity of the elevator car might then add to the velocity of the weight lift occurring inside it, the absence of recoil applied back to the rising car adding free height and thus GPE to the output side of the 'lever'.

Gobbledygook no doubt. I think i know what i mean anyway, just need to carefully plan how to implement it..