Gearing MoIs

[ME]

I am not trying to use gravity and leverage (or forces with leverage in the usual way) for so long I forgot to think about it like this. But actually I am leveraging MoI against another MoI, so resistance against resistance and not standard forces. When the system is just coasting and there are no outside forces acting on any part of it, plus it is always balanced in gravity field, then what...

Euh.. Leverage, gear leverage, wheel-piston-combos all work perfectly without gravity and in carousel-mode... but all having a leverage in force (F=m·a)

• Inertia is the resistance of any physical object to any change in its state of motion; this includes changes to its speed, direction, or state of rest.

By definition an acceleration is needed to change the velocity of some mass, even so an angular acceleration is needed to change an angular velocity of rotational inertia. And that's Torque, which is accelerating rotational inertia and also some force at a distance: τ = r x F = I · α
When there are no more forces and the system coasts at a certain speed then...
..then it theoretically stays that way and there's no leverage.. and the velocities end-up with the same ratio's as set by those radii. And they do have some (angular-)momentum but that does not matter only until that is (or need to be) changed and forces apply again.
In case of a coasting wheel-piston there's remains an oscillating transfer in force.
Perhaps things are better expressed with "frequency"?

Oh gosh, I have written a code which based on my initial criteria can loop through billions of parameter combinations and find me hundreds of different approximate solutions for an otherwise quite complicated system of integral equations. Then what?

As usual: Get yourself a definition on what you consider optimal and let your code filter the best combi.

Good luck :-)

[Gregory]

Euh.. Leverage, gear leverage, wheel-piston-combos all work perfectly without gravity and in carousel-mode... but all having a leverage in force (F=m·a)

Inertia is the resistance of any physical object to any change in its state of motion; this includes changes to its speed, direction, or state of rest.


By definition an acceleration is needed to change the velocity of some mass, even so an angular acceleration is needed to change an angular velocity of rotational inertia. And that's Torque, which is accelerating rotational inertia and also some force at a distance: τ = r x F = I · α
When there are no more forces and the system coasts at a certain speed then...
..then it theoretically stays that way and there's no leverage.. and the velocities end-up with the same ratio's as set by those radii. And they do have some (angular-)momentum but that does not matter only until that is (or need to be) changed and forces apply again.
In case of a coasting wheel-piston there's remains an oscillating transfer in force.
Perhaps things are better expressed with "frequency"?

Hey Marchello,

Right, I got that. It's just confusing cause in my design there are only radial movements of masses (gravity balanced), and the only force/torque is the resulting "reactionless torque". So I calculated how much one part of the machine accelerates, but as it is connected to the system in the MoI calculations I also had to represent all the system MoI via the gearing and such to get the correct speed/acceleration of that one mechanism in question. This is why a changing gearing/leverage ratio was a problem, because that in itself acts like a changing MoI, and in the process screws up the calculation. I wanted to escape the horror of coding reference frame inside reference frame inside reference frame, so i simplified things, and now I can't use that changing ratio, need to average it...

But it's looking good, and you just gave me a new idea. I haven't focused for torque, but I can simply calculate it in every iteration as I*a, and write it out in a table to have a look on it.
For me that will be I * dV/dA, I think...
Inside the loop that should look something like this? (newV - oldV) / newI
With radians/s^2, meters, kgs... should arrive at Nm.

Bedankt!

[ME]

But it's looking good, and you just gave me a new idea. I haven't focused for torque, but I can simply calculate it in every iteration as I*a, and write it out in a table to have a look on it.
For me that will be I * dV/dA, I think..

Örömmel.
I have only a guessing clue on what you're trying but I advice to cross-check the validity of such formula before concluding spectacular stuff.
The newness sounds a bit weird when I just 'assumed' that force is what starts it all (either by gravity or a push) and affects those lower derivatives 'down the chain'.
The usual co-dependence of force on position makes it tricky to determine the next location without a solver. But when you already know the path then calculating the needed acceleration (and forces) should become easier (or found to be impossible).
Jó szerencsét!

[Gregory]

I have only a guessing clue on what you're trying but I advice to cross-check the validity of such formula before concluding spectacular stuff.
The newness sounds a bit weird when I just 'assumed' that force is what starts it all (either by gravity or a push) and affects those lower derivatives 'down the chain'.
The usual co-dependence of force on position makes it tricky to determine the next location without a solver. But when you already know the path then calculating the needed acceleration (and forces) should become easier (or found to be impossible).

I tried, but couldn't find a good source to check this stuff. Although I am watching Khanacademy time to time.

Basically in my analysis and coding I use an angle step (dA) instead of a time step (dt). I think in logic this is essentially the same, as for mathematics it does not matter whether you use time or something else for the base of your analysis... So, I have a loop coded where the angle is incremented with every step of the loop. The amount of increase is my dA, let's say 1 degree for example.

Also, there is a starting velocity and starting orientation, but it is just programmed to start with that, as I choose. If you think about, it does not matter what started it anyway... And actually I am not written this code to simulate some runner. On the contrary, I have written it to simulate an otherwise ordinary interaction (no PM or anything similar intended), but while doing this analysis it is also integrating through some forcefields and collecting different data, which is in parralell used to determine the key parameters for another important mechanism I came up with before. So I already have the mechanisms I wanted, now I only looking for the right setup and parameters, and with only pen and paper the calculations would be hellish, and there is not much help at even where to start looking (lots of input parameters and combonations). That's it, simple :)

But back to the loop steps... The loop works in a discrete step of an angle, and in every iteration lots of physical quantities and variables are calculated/recalculated, like: angularV, Moi, AM, etc. And I just get the idea to let's do the calculation for the torque too. If I have the data, why not. Although, I am not entirely sure what would be the correct way to do this.


As for the "weird newness" of variables, this is how I mean:
With every loop step aka dA, my velocities are recalculated.
Let's say V(0) stands for velocity of a mech in the current step...
And V(-1) means velocity in the previous step (before recalculation). Then V(0) - V(-1) will be my change in speed, aka acceleration, so A(0) or A(-1), right?

I can calculate this and multiply it with the MoI.
Or should I calculate tha change in MoI, and use that instead? For some reason I feel that as logical...

So what will be the torque?
dv/dA * I

Or:
dv/dA * dI/dA

Ahh, my math skills/experience are not so great... I am only good at thinking and seeing a process from the inside as it goes, visualize things, looking for problems or patterns and similar abstract stuff. However, now I realized that sometimes it can be fun to code integrals and such...

Otherwise this torque calc is not really important for me at this point, it was only a "why not tick". And I am almost done with the code, just a little bit more free time and silence to test and finalize everything...

Örömmel

Jó szerencsét!

Haha, thanks! :)

[MrVibrating]

Interesting issue.

What i've come to realise is that "inertia" reduces to how much mass is accelerated thru how much space, in how much time.

For example suppose a rotating mechanism also involves a linear component - such as via a rack and pinion or whatever; the resistance to acceleration we experience on the drive shaft is a function of the total mass / space / time acceleration.

You can 'black box' the conundrum - imagine a lever on a black box, the object is to determine the applied momentum from the felt inertia times displacement over time... it's inherently unsolvable, due to the possibility of the internal mechanism involving both inertia as a function of rest mass, together with angular inertia as a function of RPM at radius squared. If you don't know how much of either contingent you're dealing with, you can only calculate input energy - output momentum could be literally anything at all...

The only common factor between both angular and linear inertias is mass * displacement / time. That's the bottom line.

[mickegg]

Hi Gregory

Then V(0) - V(-1) will be my change in speed, aka acceleration, so A(0) or A(-1), right?

Wouldn't your choosing of dA instead of dt mean the change in velocity
cannot be called acceleration as that quantity is time dependent?

Regards

Mick

[agor95]

Interesting problem.

Mass is short for 'Inertial Mass'

Inertia is the property to resist a force vector.

Like back EMF in a superconductive coil.

You have to use force Voltage to get it moving and the same reverse voltage to stop it's movement.

You know the atoms are all moving in a straight lines even when they are rotating; approximately.

Summary
The amount of energy used to cause movement is the same amount as to stop momentum/movement.
I recommend using small sections of straight line vectors to equate rotation.

[ME]

Hi Gregory

Then V(0) - V(-1) will be my change in speed, aka acceleration, so A(0) or A(-1), right?

Wouldn't your choosing of dA instead of dt mean the change in velocity cannot be called acceleration as that quantity is time dependent?

Hertz.

The loop works in a discrete step of an angle

When you don't know the timestep (besides your animation speed), it seems you can't know the speed as (dA/dt in [rad/s]).
And then you can't know the angular acceleration as (dv/dt in [rad/s²]), or determine (dv/dA) in [Hz]?
Unless you use your animation speed or timestep, but then you find your acceleration (α) to be likely 0.

Basically in my analysis and coding I use an angle step (dA) instead of a time step (dt). I think in logic this is essentially the same, as for mathematics it does not matter whether you use time or something else for the base of your analysis...

"dt" = t₁ - t₀
"dA" = dθ = θ₁ - θ₀ = ω₀·dt + ½ α₀·dt² + [...]
"dv" = dω =ω₁ - ω₀ = α₀·dt + [...]
Useless when (dt) is unknown.

For classical mechanics, as I understand it:
The difference between time and space is that a single mass can be at one position at a certain time. But it may be anywhere or even at the same position at different times.
Hence time is usually the unique factor and position a variable for locating an object, how it varies depends on time.

I tried, but couldn't find a good source to check this stuff.
+ Ahh, my math skills/experience are not so great.

You have coding skills... you could build your own source :-)

[Gregory]

Interesting issue.

What i've come to realise is that "inertia" reduces to how much mass is accelerated thru how much space, in how much time.

For example suppose a rotating mechanism also involves a linear component - such as via a rack and pinion or whatever; the resistance to acceleration we experience on the drive shaft is a function of the total mass / space / time acceleration.

Cheers! Interesting viewpoint with the mass-space-acceleration...
A little bit of thinkering deeper into this:
A few times already I have guessed that inertia itself should be not only a property of mass, but similarly as gravity is a curvature of spacetime, also inertia has to be the result of some interaction between mass and spacetime. Later I searched after this, and found that in general relativity it is considered that mass following spacetime geodesics and resist any change in that state. Although, I think this is a very vague description, I could not find anything else, looks like scientist haven't really interested to dig deeper into it yet. I have a very interesting theory of mine, might be even "fantastic", but otherwise I don't have the math expertise to work on that.

You can 'black box' the conundrum - imagine a lever on a black box, the object is to determine the applied momentum from the felt inertia times displacement over time... it's inherently unsolvable, due to the possibility of the internal mechanism involving both inertia as a function of rest mass, together with angular inertia as a function of RPM at radius squared. If you don't know how much of either contingent you're dealing with, you can only calculate input energy - output momentum could be literally anything at all...

A black box, nice thought experiment. In my mech the straight line component is negligible, small mass compared to other components...
But back to the boxes... During the years I developed a technique/thought experiment I called the "gray box" technique. Suppose you have a goal/function/mechanical movement to accomplish, but the solution is unknown. I draw a gray box (either for real or just in immagination) and write inside all the function, purpose, whatever to be accomplished with details. Then slowly the components of the gray box can be worked out step by step, so dividing big problems into smaller ones. I found it to be very useful.

[Gregory]

Hi Gregory

Then V(0) - V(-1) will be my change in speed, aka acceleration, so A(0) or A(-1), right?

Wouldn't your choosing of dA instead of dt mean the change in velocity
cannot be called acceleration as that quantity is time dependent?

Regards

Mick

Good question... But a change in velocity always implies acceleration, doesn't it? Measuring it with respect to this or that does not change the phenomenon. It is possible that dA itself means a non-constant but variable time step, but somehow it is convertibe to a timestep.

Otherwise time itself is an artificial construct in classical physics derived form the motion of celestial bodies in the sky. Like the earth rotates once around its axis every day. Divide it by 24, you get an hour. Divide that by 60 we get a minute. Divide that by 60 again, we have the second... Even with atomic clocks the analogy does not change much, only the precision. Basically we compare the cycle of a (more or less stable/non-changing) mechanical movement to another mechanical movement we choosed to examine...

So as can be deduced, time in this sense does not even exist. I think one second perfectly corresponds to a theta degree of change of the Earth's rotational position around its axis. I am sure Marchello could calculate this any time within a minute. :)

Also, consider the following thought experiment:
Driving on the road and grandma is wrapping fishing line on a spindle on the backseat... In average she makes a full wrap every 1.394781 seconds, with a +- tolerance of 0.25 sec. This is not so good for a measurement, but still it is possible to measure the position/velocity/acceleration of an object with respect to grandma's wrap. :D

It is funny how much we people are 'fooled' by time anyway, became a blind servant of it... Perhaps even some unknown advancment in science is prevented by this stucked viewpoint. Somehow I always got the feeling that this fixed viewpoint is not right in a sense... Although it is true that in relativity and modern physics t becomes something more and something else.

[Gregory]

When you don't know the timestep (besides your animation speed), it seems you can't know the speed as (dA/dt in [rad/s]).
And then you can't know the angular acceleration as (dv/dt in [rad/s²]), or determine (dv/dA) in [Hz]?
Unless you use your animation speed or timestep, but then you find your acceleration (α) to be likely 0.

I have an initial angular velocity value in my code to start with. It's in rpm, but I convert it to rads/sec, by applying: Rpm * 2 * Pi / 60
This means that I can have the velocity in whatever dimension needed, at every point of rotation of my coded mech. I guess having the initial rpm value itself suggest some kind of 't' component, although I only use an angle step to process the motion forward.

Attached a picture of a debug mode list. Mass sliding out radially on a spoke.