Two wheels on a single axle...

[raj]

A larger wheel(1) ad a smaller wheel(2) half its diameter, rotating on a single axle(3) with cylindrical weights(4) on arms(5) pivoting on pegs(6) and resting on pegs(7) at 45 degrees intervals on smaller wheel(2) and resting/rolling on outside of rim of larger wheel(1) providing angular momentum and net torque on the clockwise side of the wheels, continuously.

TRUE OR FALSE?

Raj

[Fletcher]

Doesn't look like anyone else wants to step up Raj.

I'll be the devils advocate and say FALSE !

And here's why I think so ..

Using your two lever-weight (lw) wheel you built in Physion as the example of the concept.

The first thing is that if I were to imagine a radius circle around each lws pivot point then I'd have two separate possible paths for the lws to move along (restrained by lever length). But that is not the only constraint as the roller weights will collide with the large radius wheel rim if they have contact.

On the rhs the blocking pin is in contact with the rhs lever. So the lw can't move in relation to the background large wheel and applies its torque as you suggest.

On the lhs the blocking pin is above the lever shaft and does not make contact with it.

But there must be a small clearance between the lhs roller weight and the large wheel rim. So the lhs lw will fall CCW around its pivot. But the path is constrained by the radius i.e. lever shaft length. Therefore the lhs lw will move downwards a short distance and then come in full contact with the background large wheel rim and stop.

Overall I anticipate that the background large wheel would initially turn CW a few degrees then the acceleration would reverse and it turn a few degrees CCW i.e. the wheel would oscillate until friction robbed it of energy and it came to a stop i.e. NO continuous torque capability !

IOW's the whole of wheel CoM would initially drop below the axle and to one side, then the wheel would oscillate until the CoM was directly below the axle (Center of Rotation). This would be the wheels position of least GPE/CoM.

Sorry to be long winded but hopefully you can follow my thoughts in detail on what I anticipate would happen with the two lw design.

[raj]

Hello Fletcher!
Many thanks for your input.

Watch this video I made in a hurry to show you and tell us what you make of it.

https://youtu.be/hoqCsxXmGT0

Raj

[Silvertiger]

False. Once the wheel settles, which doesn't take long, the torque angles on both sides will be equal and opposite, with both masses coming to rest at a point beneath the center of the wheel, resulting in a net torque of zero. With the weight on the right resting on a peg, its moment arm goes to the center of the wheel. Likewise, for the weight on the left, once it comes to rest against the outer wheel, its moment arm also goes to the center of the wheel.

Let's say that the length of the moment arm is 12 inches, well then the weights will settle at different positions at different angles from center level. So you need to calculate your torque angles to get your new effective leverage lengths for the new torques. Start by drawing a line from the center of the wheel to the center of one of the weights. Then you draw a vertical line from the end of the moment arm to intersect the level line at 180. Using the formula to solve for a right triangle, you can calculate the new length of the effective torque leverage after you have the torque angles.

Addendum: Increasing or decreasing the radius of the weights will result in, respectively, lesser or greater torque angles, and thus lesser or greater effective torque leverage lengths. And so, regardless of the final outcome, whatever those new leverage lengths come out to be...they will be equal lengths, and thus still yield a net torque of zero. :)


First Pic: Here, in its starting position, the length of the moment arm is the same as the effective torque leverage length...12 inches. Both torque angles are zero degrees from level.

Second Pic: Here, after the wheel has come to rest, the new length for the effective torque leverage is 11.67 inches on both sides. The torque angles are different as a result of being pinned in different locations on the inner wheel. The weight on the left is pivoting from its pinned location, while the weight on the right is barred from pivoting by a peg, thus causing it to pivot at the center of the wheel. This causes different torque angles, but the effective torque leverage lengths are equal regardless. The reason for this is that, if you will notice, the weight on the right is further from the center of the wheel than the weight on the left, but the difference is made up for by the fact that the weight on the left sits higher than the weight on the right, satisfying "height for width."

[raj]

Silvertiger, I am so pleased that you have joined me on this discussion.
Thank you.

Your drawings are showing the positions of the two weights correctly.
Their distance from the center are equal.

BUT:
The weight on the right is resting,acting on and turning only the small wheel.
The weight on the left is trying to act and turn the small wheel while RESTING on the outer larger wheel.

Therefore the counter-clockwise torque by the weight on the left will be always slightly less than the clockwise torque by the weight on the right.

Raj

[Fletcher]

Hello Fletcher!
Many thanks for your input.

Watch this video I made in a hurry to show you and tell us what you make of it.

https://youtu.be/hoqCsxXmGT0

Raj

I slowed it right down Raj and watched it start moving at about 8 secs. I have problems with what it is showing you.

At start everything is in equilibrium and the system CoM is located at the axle, which is the Center of Rotation (CoR).

When you run the sim the lhs lw drops due to gravity, until the roller weight impacts the large wheel rim. In effect it should jam against it. But it doesn't and I'll come back to that.

Because the lhs lw is initially falling the equilibrium of forces (torque) is unbalanced, and the rhs lw which is still applying its gravity weight torques the wheel CW.

Then then lhs roller weight impacts the wheel rim, AND BOUNCES up again (like a full 100% elastic collision). IMO it shouldn't do this, it should 'jam' as I said, and come to rest in full contact.

Then the system CoM would be below the CoR/axle and slightly to one side or other of the vertical beneath the axle, which causes a slight torque. The larger rear wheel (in sim world) perhaps would continue to turn in a direction if there were no pins frictions etc i.e. no losses from frictions (the perfect ideal case).

In your Physion sim the lhs lw bounces up again. Why would it do that ? What material would do that ?

Anyways, the system CoM (in your sim) climbs back towards the axle, and then it continues to oscillate up and down each half rotation. The whole system started with zero Rotational Kinetic Energy (RKE) and now has some continuous RKE. Yet the CoM is cycling up and down. The whole system does not gain GPE which can be converted into RKE to sustain its rotation.

So I have severe doubts about the logic of what I am seeing in your sim.

Additionally if the sustained torque imbalance were real then any sim should accelerate (trend over time). I'm not seeing that in your sim tho admittedly I didn't what it all the way thru.

So I conclude the Physion sim is not reliable and has some artifact energy in the system which makes the lhs lw bounce (when it shouldn't) and have RKE, which it shouldn't.

ETA: I just built a simple WM sim of this. The lhs lw falls and the CoM drops below the axle, where it stays. The thing moves a few degrees and stops there. The large background wheel continues to rotate slowly from the first impact but as mentioned that is likely from the lack of pin frictions etc.

ATEOTD Raj its a simple build. If you think the concept has potential for continuous imbalance (the only way IMO that a gravity wheel can possibly work) then build it and test it to see what happens. Then you have something to compare against a sim (and tweak).

As I've always said sims are useful for planning a build, dimensions, masses, placements, etc. If a sim does something outside the known laws, like gaining RKE from nowhere in your case, then suspect the sim is giving you a false positive, either from bugs in the program of from finger trouble.

[Silvertiger]

Not sure what I'm seeing...it looks like you have either drawn in a third wheel on its own separate axle, or repositioned the larger wheel to a different axle. Isn't the title of this thread "Two wheels on a SINGLE axle"? Clarification is welcomed. :)

[raj]

Fletcher, Thanks again.
The idea in this concept is to use the larger wheel JUST as a circular RAMP, to allow the smaller wheel able pull the weight on the ascending side easier upwards, while part of the weight load is free moving on the larger wheel.

Silvertiger, the red circle is showing the circular path the weight on the left would take that would force it to share some of its torque with the larger wheel, thereby reducing some of its counter=clockwise on the smaller wheel,

Raj

[Silvertiger]

It can't Raj, because it contacts that outer wheel, for, as you previously stated: "...and resting/rolling on outside of rim of larger wheel..." Your new drawing now has the (red) circular path of that weight going THROUGH it. (This cannot happen if it is made to rest/roll on the circumference of the outer wheel.) Which is it? :)

[raj]

No, Silvertiger.
The left weight won't take a circular path round its pivot on the smaller wheel.

I drew the red circle only to show that the left weight load will always press on on the larger wheel, thereby reducing its counter torque on the smaller wheel.

Please remember the larger wheel is ONLY a FREE rotating circular RAMP to allow the small wheel to pull the weight on the ascending side easier and faster

Thank again..

Raj

[Silvertiger]

Unfortunately, it doesn't work that way. At the wheel's point of rest, the left weight now has two points of contact: one with the larger wheel where it "rests," and one with the smaller wheel where it is pinned. These two points of contact cause the two wheels to be locked together and made to rotate as one, and so the system still balances with equal and opposite torque angles from the center.

I included a pic of a sim to show you what is happening. The left weight acts like a "brake" using counter-torque. The wheel rotates only until the left weight falls against the outer wheel, and brakes it by locking both wheels together, thus preventing the inner wheel from rotating any further, and so it comes to rest at equilibrium. The fundamental concept here is no different than how the sport of tree-climbing is accomplished. :)

[Fletcher]

I get the same result as ST ..

Here is my sim pics.

I stopped the sim at the second pic because as mentioned the larger background disk keeps rotating CCW, due no pin frictions to use up energy and stop it rotating.

But the rest just oscillates very slightly in the positions shown.

Note : I have made objects transparent and activated the System CoM (small b&w nuclear sign). See it below the axle.

For confirmation I added a separator element (inactivated) between the two roller weights, to indicate equi-distance (shortest distance) between them. This visually confirms System CoM analysis from the program.

[eccentrically1]

What do you think a simulation of a working pm wheel would look like?
Would it also turn for as long as you could stand to watch it? Would you assume it must be operator error, because sim programs aren’t programmed to violate the laws?
🤔

[Fletcher]

A working simulation would start from a standing start, if it were one-directional.

And need a push force to get started if it were bi-directional.

But in both cases the sim would accelerate until some upper threshold in rpm was reached. That would be determined by the actions and range of movement of the internal parts, and gravity force if a gravity only wheel.

If it don't accelerate then you have a sim bug issue, or finger issue.

Whether a kinematic sim like Working Model, or Solid Works, or Physion can actually show a 'gravity only' PM has been debated for some time. I'd like to know the answer to that myself i.e. whether it's bottom up or top down programing, with CoE override. I suspect not.

Therefore if a 'gravity only' PM wheel could exist in nature, in the real world, then there is a strong possibility imo that a sim could also show it's working principle, without violating its programing. Might violate some of the man made Laws however.

[ME]

What do you think a simulation of a working pm wheel would look like?
Would it also turn for as long as you could stand to watch it? Would you assume it must be operator error, because sim programs aren’t programmed to violate the laws?
🤔

This is what I "preach":

http://www.besslerwheel.com/forum/viewt ... 905#166905