Hi there,
I am currently in my final year working on my final year project. My project entails numerical analysis with comparison to results from Working Model 2D. Would like to know if it is possible to obtain the formulas and basic principles which WM2d uses in the program?
Eg. A block falling at 1metre. I need to calculate it's angular velocity upon impact with the ground. I want to know what principles WM2d uses. Isit possible?
Thkz
Help With WM2D
Moderator: scott
re: Help With WM2D
Lumjx, welcome to the forum.
Your questions confuse me.
You can see some of the formulas that WM2D uses by setting up meters. For instance, WM2D will show the angular momentum of circle 1 as:
Hope this helps.
PS. As far as I can determine, WM2D calculates the movement of all the objects then checks for conservation of energy. It then adjust the movement of the objects so as to satisfy conservation of energy. This is why I feel that WM2D will never find a working wheel. On the other hand WM2D has some quirks relating to collisions that sometimes cause it to gain energy when it shouldn't.
Your questions confuse me.
Do you mean the block falls a distance of 1 metre? Or do you mean the block is falling at one metre per second?lumjx wrote:Eg. A block falling at 1metre.
Do you really mean angular velocity? This would mean the weight is rotating around a center point. Or do you mean vertical velocity? In which case the weight would be falling and would impact the ground.lumjx wrote:I need to calculate it's angular velocity upon impact with the ground.
WM2D uses standard physics formulas that can be found in any physics text book.lumjx wrote:I want to know what principles WM2d uses. Is it possible?
You can see some of the formulas that WM2D uses by setting up meters. For instance, WM2D will show the angular momentum of circle 1 as:
To view this formula first select the object by clicking on it (in this case circle 1) then select Measure and Angular Momentum from the menu to create a output meter. Then select the meter and select Window and Properties from the menu. The properties window will show the above equation or one similar if different than SI units are being used.9.54929659e+000*(Body[1].moment * Body[1].v.r*1.04719755e-001)
Hope this helps.
PS. As far as I can determine, WM2D calculates the movement of all the objects then checks for conservation of energy. It then adjust the movement of the objects so as to satisfy conservation of energy. This is why I feel that WM2D will never find a working wheel. On the other hand WM2D has some quirks relating to collisions that sometimes cause it to gain energy when it shouldn't.
re: Help With WM2D
I have attached a WM2D example. The rectangular block 1 is dropped at an angle of approximately 20 degrees from a height of 1 metre and lands on the ground. It is to be noted that Rectangular Block 6 is pin joint to it. My Final Year Project involves the numerical anaylsis of the drop impact of these 2 blocks. I would need to find the angular momentum and angular velocity of these 2 blocks by performing numerical anaylsis and compare it with the results obtained from WM2D.
However, I am interested to know if there is a possible way to obtain the equations leading to the value of "v.r." (which is the angular velocity in WM2D)?
Yesh Jim, I agree with the quirks relating to the collisions. :)
However, I am interested to know if there is a possible way to obtain the equations leading to the value of "v.r." (which is the angular velocity in WM2D)?
Yesh Jim, I agree with the quirks relating to the collisions. :)
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Haha jim_mich. I don't think wm2d gives a rats ass about conservation of energy. It uses Newtonian physics which doesn't deal with CoE. Basically most physics simulations require a numerical integration. There are many algorithms out there to do this, some are faster but less accurate while others are slower but more accurate. Probably the most famous one is the Euler method.
Wm2d uses Euler method as well as Kutta-Merson method (which I haven't heard of). You can see this by opening the accuracy panel and choosing "custom". You can choose between these two integrators.
But do mind you these integrators only handle motion with initial boundary values. They don't incorporate collision detection and proper handling of it. In order to write down what wm2d is doing at that small instance, you'll need a lot of paper :p. Usually motion handling and collision detection are two completely independent systems software wise.
When the box falls it's still easy. The moment collision is registered a new force comes into play and things go haywire :D. You might try by heavy approximation but it will get nasty very quick and you'll start to think why you started on it in the first place :D. If you still want to go on I would suggest you to not use elastic collision. Turn the elasticity for both ground and box to 0.
Wm2d uses Euler method as well as Kutta-Merson method (which I haven't heard of). You can see this by opening the accuracy panel and choosing "custom". You can choose between these two integrators.
But do mind you these integrators only handle motion with initial boundary values. They don't incorporate collision detection and proper handling of it. In order to write down what wm2d is doing at that small instance, you'll need a lot of paper :p. Usually motion handling and collision detection are two completely independent systems software wise.
When the box falls it's still easy. The moment collision is registered a new force comes into play and things go haywire :D. You might try by heavy approximation but it will get nasty very quick and you'll start to think why you started on it in the first place :D. If you still want to go on I would suggest you to not use elastic collision. Turn the elasticity for both ground and box to 0.
re: Help With WM2D
broli's right - the quirks are from the integration method you choose so sometimes it pays to change to the other for comparison & double checking - also the accuracy steps can make a big difference but more accurate [more frames per time unit] slows everything down, but if you have an interesting artifact in a sim that's probably the first thing I would do - & yes, it is based on standard Newtonian physics.
Where the extra energy sometimes appears to come from after collisions is an annoying hiccup that you may have to manage - Rainer tells me that it is to do with the accuracy of the integration steps & for example, if you have two objects coming together rapidly then rebounding, if their intersecting velocities is to fast for the number of steps you are using the surfaces will pass thru each other [overlap error] before the integration will register that that has happened & presto you get anomalous energy results - also, depending on the integration method will cause some rounding assumptions, up in some circumstances & down using other methods - while this is not normally a show stopper when you are looking for very small differences in energy etc then it can give a heart palpitation or two & cause you to spontaneously pull your hair out by the roots :7)
It's to do with the fact that physic sim programs can only be discreet frames, one following another & building on the conditions before - unlike real world where there is perceived continuity - nevertheless, as long as you are aware of these constraints you can adjust setting & calculation method etc to take out the anomalies & have a pretty fair & reliable approximation of the Newtonian world view that you can trust.
At least that's how Rainer has explained it to me over the years but I'm pretty average with the program - put it in the hands of an expert & it can sing & dance so it's only as good as the inputs & the users expertise !
Where the extra energy sometimes appears to come from after collisions is an annoying hiccup that you may have to manage - Rainer tells me that it is to do with the accuracy of the integration steps & for example, if you have two objects coming together rapidly then rebounding, if their intersecting velocities is to fast for the number of steps you are using the surfaces will pass thru each other [overlap error] before the integration will register that that has happened & presto you get anomalous energy results - also, depending on the integration method will cause some rounding assumptions, up in some circumstances & down using other methods - while this is not normally a show stopper when you are looking for very small differences in energy etc then it can give a heart palpitation or two & cause you to spontaneously pull your hair out by the roots :7)
It's to do with the fact that physic sim programs can only be discreet frames, one following another & building on the conditions before - unlike real world where there is perceived continuity - nevertheless, as long as you are aware of these constraints you can adjust setting & calculation method etc to take out the anomalies & have a pretty fair & reliable approximation of the Newtonian world view that you can trust.
At least that's how Rainer has explained it to me over the years but I'm pretty average with the program - put it in the hands of an expert & it can sing & dance so it's only as good as the inputs & the users expertise !
Wm2d has many parameters for tweaking the accuracy to your heart's content (there's always a limit of course). Fletcher the "bugs" you talk about are correct but usually their error is in the micro range. So if you see your energy is increasing by micro steps then yes it's probably due to the lack of accuracy. But I believe simulating a besller setup should be fully possible as the energy is not due a bug but a clever overall setup. Wm2d will act as it's told. That is to integrate the path for you using the given boundary values and forces applied.
The only way it can do the CoE check is to measure the initial total energy of the system and each frame compare the current total energy with the initial value (this even goes out of the window with friction applied). If it's bigger than a certain error margin then all it can do is give you a message about it in form of an error or something. There's no way wm2d will be able to "correct" itself. As it would not know which body should have what amount of energy, due to the thousands of collision that can happen and conversion/exchange of energy between bodies and everything else you can imagine. There's not a single physics engine that I've worked with that has had such a system. It would be "impossible" to do let alone in real time. All physics engine use newtonian physics which is vectorized calculus.
Basically the conclusion is that I trust wm2d. And am fully confident that w/e wheel build out of real material runs in real life will run in wm2d.
The only way it can do the CoE check is to measure the initial total energy of the system and each frame compare the current total energy with the initial value (this even goes out of the window with friction applied). If it's bigger than a certain error margin then all it can do is give you a message about it in form of an error or something. There's no way wm2d will be able to "correct" itself. As it would not know which body should have what amount of energy, due to the thousands of collision that can happen and conversion/exchange of energy between bodies and everything else you can imagine. There's not a single physics engine that I've worked with that has had such a system. It would be "impossible" to do let alone in real time. All physics engine use newtonian physics which is vectorized calculus.
Basically the conclusion is that I trust wm2d. And am fully confident that w/e wheel build out of real material runs in real life will run in wm2d.
re: Help With WM2D
Good points broli - in summary no two objects in wm2d can occupy the same space so if overlap occurs then it 'explodes' & we've all seen that annoying little distraction.
I also agree that they programs can't start from a condition of CoE then calculate backwards or adjust as it goes along - they are input driven [bottom up modeling] - for example, you can add a 'fake force' at any time to get asymmetric torque about the axle & get a runner, even with other losses to the system loaded up to simulate real world conditions - but finding the real world equivalent of the fake force is the trick & it comes down to whether it is adequately described by Newtonian vectors & calculus that the program uses as its building blocks ?!
Personally, I am not looking for small variances or artifacts but largish forces that could be tamed & used in a wheel environment - that's because JB's wheels could accelerate & self sustain after accounting for ordinary/common system losses AND do external work - in other words they had the ability to restore their Pe each revolution AND do external work over & above [well & truly OU] - this would indicate to me that the force he found & used was by no means small or minor but 'in your face' large so not likely to be a small artifact or quirk of Newtonian physics - but I do think it could be explained in Newtonian terms - paraphrased: 'children played with it in the streets & one word could give it all away' clearly indicates that it was a common principle, so it was obviously of this physical world & therefore likely to be able to be simulated by physics software.
One thing I have learnt from Rainer/Tinhead is 'the golden rule' - simplify, simplify, simplify - wm2d is 2 dimensional by necessity - whenever I have an idea I always start off too complex with too many parts [contrary to what you might think would happen] - Rainer hacks it to pieces & reduces the number & complexity of components until it is a mere distillation of its former self, but it contains all the essential elements [experience is invaluable there] - we then try to physically test real world components & then tweak the sim to give the same results [if required] but generally the predictions are close anyway - that way it is in my mind accurate, reliable & trustworthy, as far as can be determined in advance of a complete build i.e. this way you can reduce the effect of compounding errors creeping in thru lack of computing skill or if mechanical aptitude &/or visualization could be found wanting.
Bessler Field of Dreams :- "find the principle & the rest will come" LOL.
I also agree that they programs can't start from a condition of CoE then calculate backwards or adjust as it goes along - they are input driven [bottom up modeling] - for example, you can add a 'fake force' at any time to get asymmetric torque about the axle & get a runner, even with other losses to the system loaded up to simulate real world conditions - but finding the real world equivalent of the fake force is the trick & it comes down to whether it is adequately described by Newtonian vectors & calculus that the program uses as its building blocks ?!
Personally, I am not looking for small variances or artifacts but largish forces that could be tamed & used in a wheel environment - that's because JB's wheels could accelerate & self sustain after accounting for ordinary/common system losses AND do external work - in other words they had the ability to restore their Pe each revolution AND do external work over & above [well & truly OU] - this would indicate to me that the force he found & used was by no means small or minor but 'in your face' large so not likely to be a small artifact or quirk of Newtonian physics - but I do think it could be explained in Newtonian terms - paraphrased: 'children played with it in the streets & one word could give it all away' clearly indicates that it was a common principle, so it was obviously of this physical world & therefore likely to be able to be simulated by physics software.
One thing I have learnt from Rainer/Tinhead is 'the golden rule' - simplify, simplify, simplify - wm2d is 2 dimensional by necessity - whenever I have an idea I always start off too complex with too many parts [contrary to what you might think would happen] - Rainer hacks it to pieces & reduces the number & complexity of components until it is a mere distillation of its former self, but it contains all the essential elements [experience is invaluable there] - we then try to physically test real world components & then tweak the sim to give the same results [if required] but generally the predictions are close anyway - that way it is in my mind accurate, reliable & trustworthy, as far as can be determined in advance of a complete build i.e. this way you can reduce the effect of compounding errors creeping in thru lack of computing skill or if mechanical aptitude &/or visualization could be found wanting.
Bessler Field of Dreams :- "find the principle & the rest will come" LOL.
re: Help With WM2D
Try here broli - a thread called Christian Wagner's Critiques - it's in there IIRC.
http://www.besslerwheel.com/forum/viewt ... s+critique
Steve often mentions how the witness reports are the only really reliable source of information that doesn't venture too far into speculation, such as the clues we often see quoted - I place at least equal value on Wagner's critique & Bessler's reply to his points raised, perhaps even more, as Wagner was both a mathematician & a practical builder/mechanic who built his own clock work wheel - he did want to catch JB out & asked some pointed questions & made some intelligent observations so worth a read of the thread imo.
If they are both not in there then perhaps someone else can point the way ;)
cheers
http://www.besslerwheel.com/forum/viewt ... s+critique
Steve often mentions how the witness reports are the only really reliable source of information that doesn't venture too far into speculation, such as the clues we often see quoted - I place at least equal value on Wagner's critique & Bessler's reply to his points raised, perhaps even more, as Wagner was both a mathematician & a practical builder/mechanic who built his own clock work wheel - he did want to catch JB out & asked some pointed questions & made some intelligent observations so worth a read of the thread imo.
If they are both not in there then perhaps someone else can point the way ;)
cheers
re: Help With WM2D
Appreciate the insight which you guys have shared :)
Recently have been reading up on Baraff and Chris Hecker's articles on rigid body collisions for dynamic simulations.
In the case when only one box collide with the ground, I understand that I could easily obtain the angular velocities by using coeff of restitution, conservation of momentum etc.
However, I have not come across any article pertaining to linkages where eg. in the WM2d which I have posted, the 2 rectangular boxes are pin joint together, I would like to know the method of finding the angular velocities of both boxes when one of the boxes collide with the ground first. Is there any simplified method based on 1st principles?
Thanks!
Recently have been reading up on Baraff and Chris Hecker's articles on rigid body collisions for dynamic simulations.
In the case when only one box collide with the ground, I understand that I could easily obtain the angular velocities by using coeff of restitution, conservation of momentum etc.
However, I have not come across any article pertaining to linkages where eg. in the WM2d which I have posted, the 2 rectangular boxes are pin joint together, I would like to know the method of finding the angular velocities of both boxes when one of the boxes collide with the ground first. Is there any simplified method based on 1st principles?
Thanks!