Routine for Decomposition of Vectors

[lizp]

@SEANT,

 

The torque-generating force can only be derivable from the given weight. No surface this given weight might be in contact with can generate more mass (respectively weight) than the given circular weight. Therefore, for a given circular weight and a given length of the arm the resulting toque in the presence of surfaces the observed weight is contact with can only be less than the torque when such surfaces are absent and never greater than the torque in absence of touching surfaces.

[Lee Mac]

Wow, you’ve put also the leads. Looks great on most places but at places where the resultant vectors are too short (as at the bottom) it appear somewhat messy because the arrows happen to be of the same, even greater length than the resultant vector itself.

 

I wanted to keep all the leads the same size for consistency, and at the same time not make them too small to see.

 

Let me know how you would like to proceed with this one.

 

Also, the broken lines which appear upon the first click turn into solid lines after the second click. Can they be retained as broken lines in the final drawing? In the meantime (when clicking the second time) I also get an error message saying HIDDEN Linetype could not be Found. Is this to be expected or something is going wrong?

 

I wasn't sure what linetypes you had in your drawings, so I made a prompt to let you know if the linetype I had chosen could not be found in the drawing. Hence the reason they stayed as solid lines upon mouse-click.

 

What linetype would you like to use for these lines?

[lizp]

Actually, one of the cool things about many of the “Vector” based calculations in physics is that they can be computed graphically. Say there was two forces applied to an object, one 10 kilos at 60 degrees, another 15 kilos at 150 degrees.

 

Even if I were "math impaired”, the resultant force and direction could be determined with a line from the origin @10

 

Notice, you're talking about two weights here, and what you're saying is correct. When you have one weight only, however, and we know what this weight unobstructed by surfaces is, any torque which this weight can give rise to can never be of greater magnitude than the product of the arm and the component of that mentioned known force, perpendicular to the arm.

[Lee Mac]

By, the way - is the file being written correctly?

 

Is the drawing name being broken down correctly?

[lizp]

I wanted to keep all the leads the same size for consistency, and at the same time not make them too small to see.

 

Let me know how you would like to proceed with this one.

 

Now, that's a tough one. I know you told me it's a hassle to place these leads and I can imagine it would be even a greater hassle to have them scaled and never allow them to be longer than, say 1/4th of the corresponding vector. It looks so good with the leads but if they cannot somehow be scaled (or probably eliminated) when the vectors are too short, then they probably should be eliminated altogether.

 

I wasn't sure what linetypes you had in your drawings, so I made a prompt to let you know if the linetype I had chosen could not be found in the drawing. Hence the reason they stayed as solid lines upon mouse-click.

 

What linetype would you like to use for these lines?

 

Let these final ones be represented by broken lines after the second click, the same broken lines as are those after the first click.

[Lee Mac]

Now, that's a tough one. I know you told me it's a hassle to place these leads and I can imagine it would be even a greater hassle to have them scaled and never allow them to be longer than, say 1/4th of the corresponding vector. It looks so good with the leads but if they cannot somehow be scaled (or probably eliminated) when the vectors are too short, then they probably should be eliminated altogether.

 

I am using a different method to insert these leads - they are scaled anyway upon creation, this scaling factor can be changed willy-nilly.

 

Would you like the smaller ones scaled, them all scaled, or the smaller ones just eradicated?

 

Let these final ones be represented by broken lines after the second click, the same broken lines as are those after the first click.

 

No can do (well... not that I know of, anyway!)

The broken lines present on the first click are created by the grvecs function and are a special instance of this function, however, after the second click, the lines are drawn permanently and need to be given a linetype, whether that be continuous or otherwise

[lizp]

By, the way - is the file being written correctly?

 

Is the drawing name being broken down correctly?

 

All works just fine. I tried it twice and the data from the second run were added to the data from the first run in both files.

 

The only little thing is that the name of the net torque file shouldn't contain the numerical value of the degrees corresponding to the first data file because the data in the final net torque file will be gathered from all the files processed, corresponding (and having it in their name too) from all the degrees studied.

[lizp]

Here's a problem regarding the final net torque file. Suppose I'm determining the individual torques in a drawing W30.dxf. The code places all the data from that file in a file W30.csv while the data from the file for the net torque is placed by the code in a file W30_NET.csv. So far, so good. And it will continue to be good if the next file I work with has also the name W30.dxf -- that data obtained from the second determination will be added to the files W30.csv and W30_NET.csv.

 

However, suppose now I make determination on the drawing in file W20.dxf. The code will place all the data for the individual torques in a file W20.csv. That's fine.

 

However, instead of adding the data for the net torque determined for W20.dxf to the file W30_NET.csv, where we're putting together all the data for the net torques obtained from these individual files W30.dsf, W20.dxf, W10.dsf etc. the code creates a separate file W20_NET.csv where it places the data for the obtained net torque from W20dxf. That should't be. As I mentioned, all the data for the net torque should go into one and only file -- in our case W30_NET.csv.

 

Now, because this W30_NET.csv should contain the net torques from all the individual files: W30.dxf, W20.dxf, W10.dxf ..., it should not contain the number '30' in its name but the name should probably be just _NET.csv or all_net_torques.csv or anything you deem convenient for such general name.

[SEANT]

Notice, you're talking about two weights here, and what you're saying is correct..

 

The two weight example was only to demonstrate a "Graphical" method of Vector addition, and didn't have any relevance to this threads primary setup.

 

. . . .any torque which this weight can give rise to can never be of greater magnitude than the product of the arm and the component of that mentioned known force, perpendicular to the arm.

 

This is the crux separating of our repective opinions. I hoped that the Basic.dwg I posted earlier isolated the most fundamental aspect of that separation. I believe, also, that the diagram is in accordance with Classical Physics.

[lizp]

The two weight example was only to demonstrate a "Graphical" method of Vector addition, and didn't have any relevance to this threads primary setup.

 

 

 

This is the crux separating of our repective opinions. I hoped that the Basic.dwg I posted earlier isolated the most fundamental aspect of that separation. I believe, also, that the diagram is in accordance with Classical Physics.

 

The fact that the only torque-generating force is that provided by the circular weight is exactly in accordance with Classical Physics. Guides, contact surfaces etc. cannot generate more mass (respectively weight) to cause torque than the mass that is given. That's the pivotal point.

 

Of course, you may draw all kinds of other forces, reactive forces and so on but the torque-generating force can never be greater than that derived from the given mass.

[SEANT]

I’m certainly not suggesting that contact with the surfaces generates additional mass. I’m saying that the contact with the other surface essentially “wedges” the circular weight. In the Basic.dwg, the free rolling weight (10 Kilos) requires a 10 Kilo counter force to hold it in position.

 

The angled force applied by the lever arm has to have a vertical component equal to 10; the horizontal component is the side effect at applying the force at an angle other than straight up. The solid wall applies a force counter to that horizontal component but, because the wall is vertical, none of that contributes to the required vertical 10 kilos.

 

The consequence of that angled application of force is a torque requirement twice that compared to the lever arm rotated horizontally and roller at the same displacement from fulcrum. As in example addendum attached.

BasicPlus.dwg

[lizp]

@SEANT,

 

You’re saying:

 

I’m certainly not suggesting that contact with the surfaces generates additional mass.

 

but in the same breath you’re also saying that

 

The angled force applied by the lever arm has to have a vertical component equal to 10; the horizontal component is the side effect at applying the force at an angle other than straight up.

...

The consequence of that angled application of force is a torque requirement twice that compared to the lever arm rotated horizontally and roller at the same displacement from fulcrum.

 

In other words, you’re claiming that for a given length of the arm L the same mass providing a force of 10kg (Red vector) yielding a torque of 10L in the right-hand side illustration of BasicPlus.dwg (“the lever arm rotated horizontally and roller at the same displacement from fulcrum”) will somehow become greater than 10L in the left-hand side illustration of BasicPlus.dwg just because “[t]he angled force applied by the lever arm has to have a vertical component equal to 10”. This means nothing else but claiming that contact with the surface (left-hand side illustration) creates additional mass compared to the mass in the right-hand illustration, which is a contradiction with your first above-cited statement.

 

You may also notice that in the left-hand side illustration of BasicPlus.dwg the sense of the force you claim is creating the torque, additional to the torque created by the mass, is opposite to the torque created by that mass. The two torques are subtracted rather than summed up, as you claim. So, even from pure vector addition perspective it doesn’t follow that torque requirement will be “twice that compared to the lever arm rotated horizontally and roller at the same displacement from fulcrum”, as you conclude. Your proposal will lead to a torque of even lower value than the correctly calculated one in the left-hand side illustration.

[SEANT]

I would not suggest inferring “. . . creates additional mass . . .”. The issue is creating sufficient force to counter a given mass.

 

A given mass, in the presence of gravity, will produce a particular force. The compensating force can, but does not necessarily need to be, a comparable mass.

 

If the compensating force is applied at an angle other than 180 degrees offset, the magnitude of the force needs to increase. As a general example (not exactly like the threads primary setup, but directly applicable) this link shows how a combined 120 lbs is required to support 100 lbs (lower left) and how 14 lbs is required to support 10 lbs (upper right). The discrepancy is an internal stress balanced by the two connecting points.

 

http://books.google.com/books?id=N97zPAvogxoC&pg=PA279&lpg=PA279&dq=force+vector+diagrams+in+tension&source=bl&ots=cGCwsff-kr&sig=QINF645dpOnpxMYodirtsa24HsI&hl=en&ei=Cr8TSpZZjaO2B6PjgJkE&sa=X&oi=book_result&ct=result&resnum=5

 

I'm not sure if these additional comments will change any opinions. If not, that’s okay. Difference of opinions is generally a good thing, as long as everyone remains civil. And, I think we’ve both been models of civility.

[Lee Mac]

Now, because this W30_NET.csv should contain the net torques from all the individual files: W30.dxf, W20.dxf, W10.dxf ..., it should not contain the number '30' in its name but the name should probably be just _NET.csv or all_net_torques.csv or anything you deem convenient for such general name.

 

This can be easily changed - this aspect slipped my mind

[Lee Mac]

What linetype would you like to use for these lines?

 

You've been having quite a discussion overnight I see about torque - but my query is still the above ^^

 

As I have said, I cannot use the same highlighted lines as used upon first click - as these are grvecs specific.

[lizp]

You've been having quite a discussion overnight I see about torque - but my query is still the above ^^

 

As I have said, I cannot use the same highlighted lines as used upon first click - as these are grvecs specific.

 

Honestly, I haven't even understood what you're asking me and I thought you might be able to retain the broken line. Isn't there a linetype, different from the one you used, but still appearing as a broken line?

[Lee Mac]

When you draw a line, you have to assign it a linetype - the default being continuous linetype.

 

The lines that are created when you click for the first time are not permanent lines, but are just vectors created by a LISP function. - this function can highlight these lines (as you see them broken), as a special case.

 

However, upon second click, the program draws these lines permanently, as if you had drawn them yourself. And so they need to have a linetype to be broken lines.

 

I do not know what linetypes you use in your drawings - I picked one that I had in my drawings and hoped that you had it too. But that is obviously not the case.

[lizp]

@SEANT,

 

I'm ready to change my opinion at once if I see convincing reason for that. However, your last post still doesn't provide such and continues with the implicit inferring that there might be a way something else, other than the given weight, to contribute to the torque. I already pointed out that even from a pure vector perspective the additional torque you're showing in your example has the opposite sign to the sign of the torque generated by the weight itself thus the calculated overall torque in your way would be even smaller (if not zero) compared to the correctly calculated torque.

 

You may think of the weight immovably attached to the arm, thus becoming part of the arm. In this way the distracting notion of a surface of contact disappears and the standard way of calculating torque from a force derived only from the given weight and the length of the arm affirms itself.

[lizp]

When you draw a line, you have to assign it a linetype - the default being continuous linetype.

 

The lines that are created when you click for the first time are not permanent lines, but are just vectors created by a LISP function. - this function can highlight these lines (as you see them broken), as a special case.

 

However, upon second click, the program draws these lines permanently, as if you had drawn them yourself. And so they need to have a linetype to be broken lines.

 

I do not know what linetypes you use in your drawings - I picked one that I had in my drawings and hoped that you had it too. But that is obviously not the case.

 

Well, these are subtleties that are beyond me. So, as far as I understand, I have to know what the linetypes are that are included in my version of AutoCAD. I have no clue, however. Wouldn't there be something universal that would look like a broken line, and if not, how can I check what linetypes I have, to see if there's anything looking like a broken line?

[SEANT]

@SEANT,

 

I'm ready to change my opinion at once if I see convincing reason for that. However, your last post still doesn't provide such and continues with the implicit inferring that there might be a way something else, other than the given weight, to contribute to the torque. I already pointed out that even from a pure vector perspective the additional torque you're showing in your example has the opposite sign to the sign of the torque generated by the weight itself thus the calculated overall torque in your way would be even smaller (if not zero) compared to the correctly calculated torque.

 

You may think of the weight immovably attached to the arm, thus becoming part of the arm. In this way the distracting notion of a surface of contact disappears and the standard way of calculating torque from a force derived only from the given weight and the length of the arm affirms itself.

 

 

Theoretically, the weight in the “Basic” diagram is supposed to be free to rotate and travel without friction.

 

The diagram does not convey the concept I was trying to describe as well as I had hoped, apparently. This should not be distressing to anyone, especially the diagrams inability to change opinions.

 

The best summation I could make at this point is to say:

 

If you are correct, and the physical prototype acts accordingly, you’ll make quite a stir.

 

If, on the other hand, the prototype does not behave as the calculations suggest, perhaps a revisit to this thread will offer focus on potential problem areas.