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# Exploratory Research Mechanism - Analysis

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For the opening post of this thread I think a summary of the analysis up to this point, immediately followed by my response to CraigD's last post in the now defunct thread "Gravity Driven Mechanisms" (which is devoted to classing the mechanism) will make for a relatively smooth transition to this thread devoted to analysis. It'll help if comments, questions or objections are accompanied by a diagram from the analysis ( http://thecolemechanism.blogspot.com/ ) showing what's being commented on, questioned or objected to....

Using vectors, the diagram (below) illustrates both the direction and magnitude of the various forces arising from the various moving parts of the mechanism individually and shows (FIG. 4) how they ultimately cancel each other out.

FIG. 1 - Schematic representation of the Chassis.

FIG. 2 - The Chassis is fixed in this schematic. The diagram shows the downward force A of the Pendulum and the resulting force B on the Planet Sprocket.

FIG. 3 - The Sun Sprocket is fixed in this schematic. The Chassis and the Planet Sprocket are free to rotate. The diagram shows the downward force D of the planet sprocket. The force C on the Planet Sprocket is the result of the force D after the force E from the oppositely situated Counter Weight (fixed to the chassis) is subtracted, or.... D minus E equals C.

FIG. 4 - The Sun Sprocket is fixed in this schematic. The Planet Sprocket with its attached Pendulum and the Chassis are free to rotate. The equal and opposite forces B and C acting on the Planet Sprocket effectively cancel each other out and equilibrious balance F is the result.

A series of schematic diagrams (below) show how the equal and opposite forces B and C cancel each other out at various points around 360 degrees (the sun sprocket is fixed for this part of the analysis), presented here as an animation....

In order to render the mechanism purturbable the sun sprocket must be free to move. When it's free to move the mechanism's equilbrium (which was stable at all points around 360 degrees when the sun sprocket was fixed) can be purturbed via the chain by a slight change in the position of the sun sprocket by means of the control lever, which is fixed to the same axle as the sun sprocket. This is also the condition in which four distinct positions of equlibrium emerge. I found a video of an older model (balanced the very same way as the current model) that clearly demonstrates the four possible positions of equilibrium that arise when the sun sprocked is freed to rotate (two stable and two un-stable), appearing in the same order as listed below the video. The video also shows how the mechanism can be caused to rotate as easily in one directon as the other....

1. Pendulum horizontal to the left, stable equilibrium.... the mechanism can't be caused to rotate by the action of the control lever from this position.

2. Pendulum horizontal to the right, stable equilibrium.... the mechanism can't be caused to rotate by the action of the control lever from this position.

3. Pendulum down vertically, un-stable equilibrium.... the mechanism can be caused to rotate by the action of the control lever from this position.

4. Pendulum up vertically, un-stable equilibrium.... the mechanism can be caused to rotate by the action of the control lever from this position.

This constitutes a perturbable form of balance that can result in immediate onset of rotation (in either direction), presented here as animations....

Pendulum up....

Pendulum down....

A problem then arises as a direct result of the sun sprocket being freed to rotate for the purpose of perturbing the mechanism's equilibrium via the chain. The varying forces arising from changing mass distribution during rotation that were formerly transmitted directly to the stand when the sun sprocket was fixed now come to bear on the control lever instead. The diagram (below) shows the downward force D on the Planet Sprocket. The force H on the Sun Sprocket is the result of the force D, and the force I on the Control Lever is the result of the force H. The Mechanism is not balanced or in equilibrium in this diagram because there is no equal and opposite force to counter the force I.

That's where the calibrated spring comes in.... it's mounted on the back of the Mechanism (depicted to the right in the diagram below). The lower end X is fixed to the stand the mechanism is mounted on. The upper end Y is connected to the Control Lever. The diagram (below) shows how the equal and opposite forces I and J effectively cancel each other out and equilibrious balance Q is the result, or.... I minus J equals Q. The Mechanism is in a state of compensated equilibrium, the sum of all forces acting on the control lever is zero.

I want to minimize the magnitude of the input force needed to perturb the system.... the calibrated spring variably compensates for and cancels out the varying force coming to bear on the control lever due to changing mass distribution. The sum of the equal and opposite forces I and J coming to bear on the control lever equals zero at all times during rotation as shown (below). This constitutes a compensatory form of balance. It reduces the input force needed to cause immediate onset of rotation to the level of that needed to overcome only inertial and frictional resistance, presented here as an animation....

Edited by Aemilius
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CraigD "By saying you’ve done “a great descriptive job”, I mean you’ve described your machine clearly – the only deduction I had to make is that the two weights on the end of its arms have equal mass, which I didn’t find explicitly stated anywhere, but was able to understand from one of your videos."

The reason no mass is explicitly stated anywhere in the analysis is because I didn't see the need. The length of a line represents the magnitude of a force and the arrow itself represents the direction of a force. For example....

The situation graphically depicted in the diagram below won't change as long as any arbitrarily stated magnitude of force for the vector A is uniformly applied as a standard. In other words.... Whether one arbitrarily states for the vector A a magnitude of force equal to two ounces or sixteen pounds the resulting diagramatically shown vector proportions won't change in any way, and the diagram will remain an accurate representation for both scenarios (two ounces or sixteen pounds). So, since any arbitrarily stated magnitude of force for the vector A will result in an identical diagram and identical vector proportions, for the purpose of analysis, there's no need to state any specific magnitude of force for the vector A in the diagram.

It's the same for all of the scale drawings in the analysis. For example....

The situation graphically depicted in the scale diagram below won't change as long as any arbitrarily stated magnitude of force for the vector D is uniformly applied as a standard. In other words.... Whether one arbitrarily states a magnitude of force equal to two ounces or sixteen pounds for the vector D, the resulting diagramatically shown vector proportions in the scale drawing won't change in any way, and the diagram will remain an accurate representation of both scenarios (two ounces or sixteen pounds). Again, since any arbitrarily stated magnitude of force for the vector D will result in an identical diagram and identical vector proportions, for the purpose of analysis, there's no need to state any specific magnitude of force for the vector D in the diagram.

Whenever an arbitrarily stated magnitude of force for the vector D (or any other vector in the diagram) is uniformly applied as a standard, the magnitude of force associated with any of the other vectors in the scale drawings of the analysis can be quickly and easily derived. For example....

If the vector D is made to equal one inch and the arbitrarily stated magnitude of force associated with it is two ounces (one inch equals two ounces), then....

A.... 3/8 inch equals 0.75 ounces

B.... 3/4 inch equals 1.50 ounces

C.... 3/4 inch equals 1.50 ounces

E.... 3/8 inch equals 0.75 ounces

F.... ....F = C + B.......0 ounces

If, instead, the vector D is made to equal one inch and the arbitrarily stated magnitude of force associated with it is sixteen pounds (one inch equals sixteen pounds), then....

A.... 3/8 inch equals ..6 pounds

B.... 3/4 inch equals 12 pounds

C.... 3/4 inch equals 12 pounds

E.... 3/8 inch equals ..6 pounds

F.... ...F = C + B.......0 pounds

As you can see, for the purpose of analysis the very same numerically un-adorned diagram serves to describe both of the above scenarios equally well.

In the examples given above, there's no difficulty of description nor is there any appeal to intuition (provided we're using the same definition of "intuition"). Of course, one could go ahead and arbitrarily state this or that magnitude of force for the vector D and then carry out a thorough numerical analysis of the diagram, but that wouldn't change the result already shown diagramatically or the relative proportions of any of the various vectors depicted in the scale drawings of the analysis, it would only be a more specific confirmatory restatement of the generalized result already shown.

CraigD "The difference, I hope is obvious, between this kind of analysis and the drawing-based kind you’ve done in this thread, Aemilius, is the use of numbers."

I see the difference, but a properly conducted vector analysis can't be said to be any more or less credible than its numeric counterpart (or can it?).... it would seem we're playing the same tune on different instruments.

CraigD "I’ve not wanted just to interject natural language comments, but to give a reasonably complete description of at least a few special cases of a numeric, classical physics description of your machine, like the simple example above."

Oddly enough, you seem to be employing in your example the very same technique I've been describing. As you've shown in your example, the two weights are of equal but unspecified mass, yet your numeric calculation works just as well without explicitly stating any specific mass for either of the weights depicted. As long as they're equal no explicitly stated mass is required to arrive at the solution of 36.87 degrees. Just as with the vector proportions in the scale drawings, this solution (36.87 degrees) won't change either as long as any arbitrarily stated mass for the two weights is uniformly applied. In other words.... Whether one arbitrarily states a mass for each of the weights equal to two ounces or sixteen pounds, all things being equal, the result will always be 36.87 degrees, and the diagram will remain an accurate representation of both scenarios (two ounces or sixteen pounds for each of the weights). So for the purpose of analysis, just as there's no need to state any specific mass for the weights in your example, neither is there any need to state any specific magnitude of force for the vectors in the scale drawings of the analysis.

CraigD "Because I’m out of practice, short of free time (the two combine, as my lack of practice means it might take me hours to get up to speed enough to start) and a pretty severe procrastinator, I haven’t yet, but will try to soon."

Believe me, I know about being short of free time.... I provide 24/7 care for my 86 year old mom and also 24/7 supervision of my 58 year old schizophrenic brother (they both live with me). As far as being out of practice goes, at least you have some.... I'm facing a vertical learning curve here man!

CraigD "I gotta' lay much of the blame for this on myself (and other readers out there who know how) for not bringing some numeric physics into the discussion, and hope to remedy this failing soon."

I'd like that very much! Maybe Turtle was right.... maybe you are my horse in this race. If you should decide to undertake it though, I was thinking it would be most effective if you were to go ahead and superimpose your numeric calculations over my scale vector diagrams (it would also save you the trouble of having to draw any diagrams).

CraigD "This “at a glance” step is what I mean by “appeal to intuition”, and hope to replace with “appeal to arithmetic”."

The "at a glance" remark was a reference to simplicity and ease of understanding, not an "appeal to intuition" as suggested.

CraigD "I’m truly interested in what you believe, because it informs about what you’re interested in showing via an analysis of any kind."

Hah! I'm going to pass on that one. If there's one thing I've learned from "Gravity Driven Mechanisms" it's to avoid any mention of subjective beliefs, opinions and analogies like the plague. Just as with religion and philosophy.... beliefs, opinions and analogies are a perfect recipe for endless bickering that doesn't solve a damn thing! What I'm doing fits the definition of exploratory research.

CraigD "Classical physics assumes laws like conservation of energy, AKA “you can’t get more work out of a machine than you put into it”, so it’s important up front to state that you’re trying to show that a particular work output (eg: that could be extracted from the moving arms of you machine) exceeds what’s put into it (eg: the work exerted on the tilting lever by your hand), because it means some “hidden” work input must be included in the analysis (eg: something involving gravity)"

Well, exploratory research assumes as little as possible. I want to try and get out from under the stigma attached to the mechanism that it was designed as a perpetual motion or over unity machine. When it comes to the notion of self rotation though, I did say at one point that if the needed input force appears to be less than the output force I would try it. Why not? I'm in this for the fun of it so what's the harm? It's not, however, the stated goal of the research.... I have a couple of possible applications in mind for it.... I'm just not there yet.

CraigD "I don’t really need this yet, but like to know where everyone’s hoping to eventually go, even early in the trip."

The best I can do is to say that.... I'm conducting exploratory research generally aimed at designing and constructing a mechanism that rotates as forcefully as possible for the least amount of input as possible.

CraigD "....but find your machine truly beautiful."

Thanks man.... and regardless of how this pans out, thanks again for humoring an old eighth grade dropout!

Edited by Aemilius
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Just a quick question (when you have a minute) CraigD. You recently said here in reference to my vector analysis that....

CraigD "The difference, I hope is obvious, between this (trigonometric) kind of analysis and the drawing-based (graphical) kind you’ve done in this thread, Aemilius, is the use of numbers." and "As I hope I’ve conveyed above, my main objection is that what you’ve done so far aren’t “calculations” of the sort I understand to be in the domain of physics, because they don’t have equations and numbers based on natural laws in them."

Of the two methods of vector analysis and resolution being discussed.... the Graphical Method which employs accurately drawn scale diagrams and the Trigonometric Method which employs trigonometric functions.... you say you don't recognize the Graphical Method I'm using as being calculations of the sort understood to be in the domain of physics compared to the Trigonometric Method you're suggesting be used instead. Are you saying that the Graphical Method of vector analysis I'm using is invalid because it doesn't use numbers? I'm just curious as to how you could see the Graphical Method as being somehow inferior to the Trigonmetric Method and why, especially since when properly carried out they both appear to be equally effective techniques (methods of calculation).

Edited by Aemilius
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especially since when properly carried out they both appear to be equally effective techniques (methods of calculation).
Appearances can be deceiving. Thought you were going to try to avoid subjective data this round and focus on objective means of analysis.
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From the opening post.... It'll help if comments, questions or objections are accompanied by a diagram from the analysis ( http://thecolemechanism.blogspot.com/ ) showing what's being commented on, questioned or objected to....

From the rules.... If you want to refute someone's claims, please stay calm and point out where you think they went wrong, and what kind of proof you base your own opinion on.

Statements like "I just know that this is the way it is" are considered ignorant and might be deleted.

DFINITLYDISTRUBD "Appearances can be deceiving."

Can you at least make some effort here to explain why you're saying that? Show how and why accurately drawn scale diagrams like those shown above are deceiving.

DFINITLYDISTRUBD "Thought you were going to try to avoid subjective data this round and focus on objective means of analysis."

Right.... I started this thread to try and get away from the kind of comment you're making here. Can you at least try to point out some aspect of a diagram that appears to you to be subjective data and explain why you see it that way? Feel free to post marked up reproductions of any of the diagrams. Blanket statements just labeling the whole thing as being subjective amount to an "I just know that this is the way it is" type of comment. That's just distracting and doesn't contribute anything to the thread.

Edited by Aemilius
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You proved my point more than adequately when you said

especially since when properly carried out they both appear to be equally effective techniques (methods of calculation).
which I quoted in the post you so eagerly attacked. Appear and ARE are two different things need i point out the fiasco that is the other thread. Where clearly what appeared to you to be an effective ideal way of providing data about your project in reality as can be ascertained from the posts was far from it. Edited by DFINITLYDISTRUBD
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My asking CraigD why he prefers the trigonometric method over the graphical one I'm using doesn't magically render all the accurately drawn scale diagrams of the analysis or the information they convey subjective.

You're confusing this analysis with petty semantics. You're not addressing any of the diagrams. If you can't point out some aspect of a diagram that appears to you for some reason or other to be subjective and explain why you see it that way for the purpose of discussion (without resorting to semantics), it's just an off topic distraction that doesn't contribute anything to the thread. If you continue with it I'll report you and let the moderator decide.

Edited by Aemilius
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While I find your rantings mildly amusing, I grow bored with your same old routine carried over from the other thread.

You gripe that everybody forced you to use vector graphics...You gripe that you use that "language" and nobody even understands it..though oddly enough nobody even asked you too...and in fact explained the preferred language to you.

When asked to use actual equations you scoff and say the drawings that have already proven ineffective at conveying information repeatedly requested are the same thing.

You get asked straight forward questions and promptly dodge them by tap dancing in circles while saying look at my pictures I've already shown you dozens of times! Are you to stupid to figure them out? Trust me they're just as good as the data you keep requesting, Would I lie to you?

In your own words you promised actual numbers, real equations and to refrain from the subjective.

You want to report me, report me. If they feel I'm being unfair to you by expecting you to live up to your statements as to the purpose of this thread as mentioned in both threads I'm sure they'll let me know.

EDIT: speeling ers

Edited by DFINITLYDISTRUBD
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DFINITLYDISTRUBD "While I find your rantings mildly amusing, I grow bored with your same old routine carried over from the other thread."

Well, I'm glad it at least had some redeeming entertainment value for you.... as you said yourself, you don't understand junior high school level vectors so it really makes perfect sense that you would quickly become bored.... all those meaningless, irritating little arrows!

DFINITLYDISTRUBD "You gripe that everybody forced you to use vector graphics...You gripe that you use that "language" and nobody even understands it..though oddly enough nobody even asked you too...and in fact explained the preferred language to you."

Yeah man.... I can see now it was really reaching for me to actually think that graphically represented scale vectors might be considered any kind of suitable "language" that would be understood by the "physics-aware folk" here. What the hell was I thinking? If someone of your obvious caliber with a (now legendary) "firm understanding of physics and engineering" doesn't recognize graphically represented scale vectors I definitely made a huge mistake!

DFINITLYDISTRUBD "When asked to use actual equations you scoff and say the drawings that have already proven ineffective at conveying information repeatedly requested are the same thing."

The other thread is locked into classing which is a mess. I said they're accurately drawn scale diagrams and they're still accurately drawn scale diagrams.... they're going to stay accurately drawn scale diagrams too whether you understand that they're accurately drawn scale diagrams or not.

DFINITLYDISTRUBD "You get asked straight forward questions and promptly dodge them by tap dancing in circles while saying look at my pictures I've already shown you dozens of times!"

Well, I don't know about dozens of times. Going a bit overboard there aren't you? I get what you're saying though.... since you don't understand scale vectors it just makes them even more boring and even more irritating.... I feel you man!

DFINITLYDISTRUBD (mockingly) "Are you to stupid to figure them out?"

Well.... are you?

DFINITLYDISTRUBD "In your own words you promised actual numbers, real equations and to refrain from the subjective."

I never promised any numeric equation analysis (show me a quote), but I did give you a simple procedure for easily deriving any arbitrarily stated numeric mass/force value for any vector in any of the diagrams by the application of a simple standard (from post number two of this thread)....

Whenever an arbitrarily stated magnitude of force for the vector D (or any other vector in the diagram) is uniformly applied as a standard, the magnitude of force associated with any of the other vectors in the scale drawings of the analysis can be quickly and easily derived. For example....

If the vector D is made to equal one inch and the arbitrarily stated magnitude of force associated with it is two ounces (one inch equals two ounces), then....

A.... 3/8 inch equals 0.75 ounces

B.... 3/4 inch equals 1.50 ounces

C.... 3/4 inch equals 1.50 ounces

E.... 3/8 inch equals 0.75 ounces

F.... ....F = C + B.......0 ounces

If, instead, the vector D is made to equal one inch and the arbitrarily stated magnitude of force associated with it is sixteen pounds (one inch equals sixteen pounds), then....

A.... 3/8 inch equals ..6 pounds

B.... 3/4 inch equals 12 pounds

C.... 3/4 inch equals 12 pounds

E.... 3/8 inch equals ..6 pounds

F.... ...F = C + B.......0 pounds

DFINITLYDISTRUBD "You want to report me, report me. If they feel I'm being unfair to you by expecting you to live up to your statements as to the purpose of this thread as mentioned in both threads I'm sure they'll let me know."

Well, not yet, this was more fun! Bottom line, you (and a few others here) can say whatever you like, but unless CraigD locks this thread or bans this old "self imagined genius" I'm going to complete this analysis (timing, accceleration, etc.).

Edited by Aemilius
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And again your nifty drawings while showing direction of force, leave out the forces themselves as well as the mass of the components the forces are acting upon. Overall your own understanding of the use of vectors is flawed as you don't seem to grasp that the graphical representations are intended to function as a visual aid to be used in conjunction with proper mathematical representation, not instead of.

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QuoteI started the vector analysis in an effort to shift the focus from the subjective (what I believe, suspect or think) to the objective (vectors that can easily be seen at a glance as either correct or incorrect).

<br style="color: rgb(8, 8, 8); font-size: 13px; line-height: 20px; background-color: rgb(250, 251, 252); ">CraigD-This “at a glance” step is what I mean by “appeal to intuition”, and hope to replace with “appeal to arithmetic”.

Hmmm, so I'm not the only one to repeatedly ask for proper mathematical representation.

QuoteIn terms of the analysis, it no longer matters what anyone thinks, what anyone suspects, what anyone believes or what anyone claims. With the ongoing vector analysis the only thing that matters is whether or not the calculations are correct. No one (including you) has challenged the calculations to date or shown them to be incorrect in any way.... I can't even get anyone to discuss them!

<br style="color: rgb(8, 8, 8); font-size: 13px; line-height: 20px; background-color: rgb(250, 251, 252); ">

CraigD- As I hope I’ve conveyed above, my main objection is that what you’ve done so far aren’t “calculations” of the sort I understand to be in the domain of physics, because they don’t have equations and numbers based on natural laws in them. I gotta' lay much of the blame for this on myself (and other readers out there who know how) for not bringing some numeric physics into the discussion, and hope to remedy this failing soon.

Though the request have been piling up and thus far ignored or scoffed at.
By “classical mechanical analysis”, I mean the work of writing a collection of equations able to describe the state of a numeric representation of the machine as a function of time. This is more-or-less what classical physicists do – reduce physical systems, which are difficult to describe without appeals to intuition, with numeric ones, which a computer or a person capable of following a program using arithmetic can compute, using no intuition.
I never promised any numeric equation analysis (show me a quote), but I did give you a simple procedure for easily deriving any arbitrarily stated numeric mass/force value for any vector in any of the diagrams by the application of a simple standard (from post number two of this thread)....
I'll start another thread called "Exploratory Research Mechanism - Analysis" devoted exclusively to analysis, and I'll format it in such a way as to prevent any beliefs, opinions, analogies or comparisons from entering the discussion.
With the ongoing vector analysis the only thing that matters is whether or not the calculations are correct. No one (including you) has challenged the calculations to date or shown them to be incorrect in any way.... I can't even get anyone to discuss them!
And still as of yet no calculations provided for analysis.

DFINITLYDISTRUBD "Among key details conveniently left out, the force you are applying, the mass of the weights, distance to the fulcrums, and distance of any concentric offsets from center. What information a person can glean from a few sketches with arrows is not nearly enough to make any sort of determination of accurate or not."<br style="color: rgb(8, 8, 8); font-size: 13px; line-height: 20px; background-color: rgb(250, 251, 252); ">

That remark's relevant to the analysis.... I'll respond to it over in the "Exploratory Research Mechanism - Analysis" thread.

Ok, so promised should be replaced with implied, you got me there...but then you keep implying that you would like for a reader any reader to prove or disprove your "calculations" which as of yet you've not provided.

calculate

[ˈkælkjʊˌleɪt]

vb1. (Mathematics) to solve (one or more problems) by a mathematical procedure; compute. To perform a mathematical process

1.

To determine by mathematics, especially by numerical methods:

cal·cu·la·tion

(klky-lshn)

n.1.a. The act, process, or result of calculating.

1.

(Mathematics) the act, process, or result of calculating

http://en.wikipedia....iki/Calculation

http://www.britannic...vector-analysis

http://en.wikipedia....Vector_calculus

http://en.wikipedia....ential_geometry

Edited by DFINITLYDISTRUBD
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I don't know why you're rehashing all that.... reminds me of Turtle endlessly waving around the "Lock" thing. I said a long time ago I wouldn't be able to carry out a numeric analysis. CraigD has already said though that he's looking forward to doing it at some point in the near future and also that I've at least given a good enough description that he (or anyone else who's interested) could work with it.... and I said "I'd like that very much!"

I'm going to go on with what I've been doing to create an even more complete "scaffolding" for anyone who's interested to work with.

Edited by Aemilius
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Just a quick question (when you have a minute) CraigD. You recently said

The main difference, I hope is obvious, between this [trigonometric] kind of analysis and the drawing-based kind you’ve done in this thread, Aemilius, is the use of numbers.

As I hope I’ve conveyed above, my main objection is that what you’ve done so far aren’t “calculations” of the sort I understand to be in the domain of physics, because they don’t have equations and numbers based on natural laws in them.

Of the two methods of vector analysis and resolution being discussed.... the Graphical Method which employs accurately drawn scale diagrams and the Trigonometric Method which employs trigonometric functions.... you say you don't recognize the Graphical Method

I recognize, and when convenient use, “graphical methods” like yours, Aemilius. For example, in my flying model hobbyist youth, I often used the common practice of finding the center of lateral resistance of a model by tracing the shadow cast by it from a bright lamp on a sheet of thick paper, cutting out the resulting silhouette, and balancing it on a sharp straight edge – a true “analog calculation”, and not at all an “illegitimate” technique. (To my delight, I found the printed manual where I leaned this technique online in this PDF file)

Rather than calling numeric calculations “numeric” or naming them for a specific kind of mathematical function used, such as trigonometric, I think it’s edifying to classify them as digital, and contrast that to analog (AKA graphical) approaches.

I'm using as being calculations of the sort understood to be in the domain of physics compared to the Trigonometric Method you're suggesting be used instead. Are you saying that the Graphical Method of vector analysis I'm using is invalid because it doesn't use numbers? I'm just curious as to how you could see the Graphical Method as being somehow inferior to the Trigonmetric Method and why, especially since when properly carried out they both appear to be equally effective techniques (methods of calculation).

Analog approaches – sometimes called analog calculations, more often analog computations or modeling – have the advantage that they can be more intuitive to read (that is, view), and in some cases, such as my anecdote above, are easier than numeric models, and accurate enough for practical purposes.

Digital techniques – are nice because they are usually more precise than any practical need, and easy to write or type than the drawing and other handcraftiness for analog.

Consider the simple “find angle a” problem I gave as an example in my above post. Although you could solve it by making precise drawings and measurements, it’s not only more precise, but quicker, to just write down the essentials of the system, and solve mathematically, especially since calculators to do the once-laborious trig calculation involved are now ubiquitous.

I challenge you, Aemilius, to find the answer to that simple problem graphically – not seriously – it’d be a waste of your time and pencil lead – but I think you can pretty quickly see my point about the difference in effort and accuracy of analog vs. digital computation for this system.

The example of vector addition you gave in post #9 (nice animated gif – did you make that, or find it somewhere?) shows that analog calculations can work well for some surprisingly complex problems – a careful person with compass and/or ruler and protractor could perform it without even entertaining the concept of a digitally represented quantities (roughly AKA numbers)

Where this approach gets troublesome is when you’re dealing not with simple, line-using force, velocity, or similar vectors applied to point bodies, but when we need to use angle-using torques for rigid bodies that rotate, like my simple problem, and your Cole Mechanism. While it’s not impossible to represent torques graphically, it’s less easy and intuitive than representing linear vectors. Numbers and trigonometry quickly become your friends in these kinds of calculations.

I’ll close with a note on hypography culture. Our page banner says “SCIENCE FOR EVERYONE”, which is as close to an official motto as we have. I love that folk like Aemillus, who can draw and handcraft masterfully, but never completed a mathematical physics course in school, and I and other folk with traditional academic science training, can share stuff here. That said, I think some tension and mutual suspicion between “picture” and “numbers” folk is unavoidable. I, for example, am pretty sure of my suspicion that Aemillus is keeping secret hopes of demonstrating an over-unity device, something that tends to drive mathic folk crazy. Our “science for everyone” creed, though, promises that if we can all keep it friendly, we can all have fun, and learn stuff.

We also have the not-specifically-stated rule that if, after honest effort to communicate with 'em, some folk turn out to be irredeemable trolls, we thrash ‘em and ban ‘em. I’m pretty confident nobody involved in the 2 Cole Mechanism threads is one of these loathsome beings, so it won’t come to that. :)

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I don't know why you're rehashing all that.... reminds me of Turtle endlessly waving around the "Lock" thing. I said a long time ago I wouldn't be able to carry out a numeric analysis. CraigD has already said though that he's looking forward to doing it at some point in the near future and also that I've at least given a good enough description that he (or anyone else who's interested) could work with it.... and I said "I'd like that very much!"

I'm going to go on with what I've been doing to create an even more complete "scaffolding" for anyone who's interested to work with.

Now wait a minute here. You have had what appears to have been such a marvelous time attacking the credibility and intellect of nearly everyone that couldn't use your vector drawings as a sole source of data. If you can't translate them into relevant data useful for calculations and thereby achieve an accurate result how the heck do you expect anyone else to? Also. By what right do you attack anyone else for not being able to use or determine the validity of information you refuse to provide due to your inability to translate it?

Edited by DFINITLYDISTRUBD
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DFINITLYDISTRUBD "Blah blah blah...."

Sketch me a parallelogram.

Edited by Aemilius
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DFINITLYDISTRUBD "Blah blah blah...."

Sketch me a parallelogram.

Demonstrate the manner in which a mature adult would act.

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CraigD "I recognize, and when convenient use, “graphical methods” like yours, Aemilius."

Graphical methods like mine? I thought it was just the graphical method.

CraigD "For example, in my flying model hobbyist youth, I often used the common practice of finding the center of lateral resistance of a model by tracing the shadow cast by it from a bright lamp on a sheet of thick paper, cutting out the resulting silhouette, and balancing it on a sharp straight edge – a true “analog calculation”, and not at all an “illegitimate” technique."

That's a good example of a (non-numeric) analog calculation and it does resemble the graphical method in the sense of your tracing out an accurate profile using the silhouette of the plane as a template (scale drawing), but that's where the similarity ends. In other words.... The method you used to establish a one-to-one behavioural correspondence between the source system (the profile cut-out) and the target system (the model plane) was accomplished in a different way (manual balancing of a physical object) than the graphical vector method. It definitely shows though that there are also other forms of non-numeric calculation that can be useful for practical purposes in spite of the lack of great precision.

CraigD "Rather than calling numeric calculations “numeric” or naming them for a specific kind of mathematical function used, such as trigonometric, I think it’s edifying to classify them as digital, and contrast that to analog (AKA graphical) approaches."

I can appreciate that, but I think I'll stick with the old numerical/graphical description. Why semantically re-evaluate and re-classify the relevant terms "numerical" and "graphical" if there's no need to? Besides, ultimately aren't all models really just variations of the analog target system where a source system (numerical, graphical, physical, etc.) is formulated to accurately represent a target system for the purpose of establishing one-to-one behavioural correspondences to aid analysis?

CraigD "Analog approaches – sometimes called analog calculations, more often analog computations or modeling – have the advantage that they can be more intuitive to read (that is, view), and in some cases, such as my anecdote above, are easier than numeric models, and accurate enough for practical purposes."

So (amazingly) we actually do seem to agree here that non-numeric vector calculations consisting of accurately drawn scale diagrams really can be practically useful and easier to understand than numerical calculations for some applications, and even that there are other forms of non-numeric calculations that can also be practically useful and easier to understand than numeric methods of calculation (such as your anecdote).

Better watch out though CraigD.... if DFINITLYDSTRUBD gets wind of this he'll be coming for you man! You see, he already settled it for everyone.... "vectors are only intended to function as a visual aid to be used in conjunction with proper mathematical representation." As if that wasn't bad enough, just you wait until he gets ahold of your "model airplane shadow paper cut-out balancing technique"! I think Turtle will be alright with it though (it's like a see-saw).

CraigD "Digital techniques – are nice because they are usually more precise than any practical need, and easy to write or type than the drawing and other handcraftiness for analog."

No doubt.... numeric methods of calculation surpass non-numeric methods of calculation when precise calculation is called for (or do they?). In this case though, just as with your anecdote, there's no need for any great degree of precision (open to correction).

CraigD "Consider the simple “find angle a” problem I gave as an example in my above post. Although you could solve it by making precise drawings and measurements, it’s not only more precise, but quicker, to just write down the essentials of the system, and solve mathematically, especially since calculators to do the once-laborious trig calculation involved are now ubiquitous."

You're right, and Wikipedia (Representations-paragraph four) confirms it.... "In order to calculate with vectors, the graphical representation may be too cumbersome."

CraigD "I challenge you, Aemilius, to find the answer to that simple problem graphically – not seriously – it’d be a waste of your time and pencil lead – but I think you can pretty quickly see my point about the difference in effort and accuracy of analog vs. digital computation for this system."

I see your point (and thanks man, I'm really low on pencil lead!), but again, just as with your anecdote, there's no need for any great degree of precision.

CraigD "The example of vector addition you gave in post #9 (nice animated gif – did you make that, or find it somewhere?) shows that analog calculations can work well for some surprisingly complex problems – a careful person with compass and/or ruler and protractor could perform it without even entertaining the concept of a digitally represented quantities (roughly AKA numbers)"

No, I didn't make the animation, I found it here. You're right though, it definitely shows that non-numeric graphical vector calculations (along with other non-numeric methods like your anecdote) can work for solving relatively complex problems and also shows how they can be carried out without the use of numerically represented quantities.... I seem to be the only one that finds that fascinating.

CraigD "I love that folk like Aemillus, who can draw and handcraft masterfully...."

Thanks.... that means a lot to me.

CraigD "I think some tension and mutual suspicion between “picture” and “numbers” folk is unavoidable."

That's the really funny part, I actually thought they (simple vectors) would be welcomed and even seen as complimetary.... talk about a major miscalculation!

CraigD "I, for example, am pretty sure of my suspicion that Aemillus is keeping secret hopes of demonstrating an over-unity device, something that tends to drive mathic folk crazy."

No secret hopes really (though I wouldn't mind if it turned out that way).... I said I'd try it when I get the chance and I will. There's no harm in that, it's just experimentalist curiousty.... otherwise known as fun. I actually do have a couple of possible applications in mind for it I'll get around to sketching up later. I say this is a hobby/exploratory research project generally aimed at achieving maximum output for minimum input (efficiency) and that I don't know how it'll turn out. I don't have any illusions/delusions of grandeur and I'm not some self imagined genius that thinks he knows the grand secret of everything either. The vaunted "Pantheon of Science Gods" is safe!

Most of the stuff being said along those lines just rolls off (I did lose my temper once or twice though). After all, when I think on it, why should I get upset? It turns out that all of the people (with the exception of you and possibly blamski) making the derogatory comments so far about pseudo science, not understanding how locks work, deliberate deception on my part, trying to fool gullible people, etc. either backed out because they (tee-hee) never really agreed to the use of vectors and don't know enough about them (passing the buck on to you), or say that despite their firm understanding of physics and engineering they essentially wouldn't know the magnitude or direction indicated by a vector if they got shot in the *** with one!

Did that turn into a rant? I think that turned into a rant.... sorry.

Just a note....

I hope you'll continue to procrastinate until I finish the graphical analysis before you start that numerical analysis so that you have as complete a "scaffolding" as I can provide. Also, I've recently found there's no need for the calibrated spring when the mechanism is in motion, which would have an impact on the calculations if you were to include it in anything other than a static evaluation. The reason for that will become apparent in upcoming stages of the analysis having to do with timing and acceleration.

And a question....

Reviewing earlier posts you made about the role played by the "weighted bits" and more recently the "find angle a" example you provided.... Are you under the impression that the mechanism as a whole balances as a direct result of these two weights which are of equal mass in the same way as the example you provided?

CraigD "Our “science for everyone” creed, though, promises that if we can all keep it friendly, we can all have fun, and learn stuff."

Diplomatic to the end (much appreciated).... Emile

Edited by Aemilius

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