Comments by Member 8736093 (Top 15 by date)

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Very good analysis, Stefan.

You are correct. Translation is not a point. But I said "...translation with respect to each other..." which means two points. After all, the two circles were initially at contact at the 12o'clock position which also denotes two points. So, at any given time, if you create a mark of the location of the original contact points which are now moving, the sum of these marks will be a trace, a curve, that will mark the places there these points were relative to each other during the circles' spins/rotations.

To put it in your terms, it is a trace of a point on the circumference of the smaller inner rotating circle with respect to the moving point on the circumference of the larger rotating circle. This is similar to how cycloid curves are produced except they are a trace of one point carrying out some motion relative to its starting point which remains stationary. Please see the animations in the webpage on Hypocycloids in my original question. Its links have other animated cycloids.

I doubt it is a "manifold" but if it is then it is a simple 2 dimensional (plane) manifold whose trace, I believe, is a pointed tooth or pointed ellipse or diamond/kite shape if the trace produces straight lines.


One way to analyze this is geometrically.
Let point A lie on the large circle and point B on the small circle located such that they are touching at time zero at the 12o'clock position. Connect A & B with a straight segment which terminates at the axis of the large circle and call this point C. After rotating both circles 90 degrees clockwise, in order for the line to connect A-C it has to pass through B which is clearly above A and C. The line has to either sharply bend at B or gradually curve to achieve this. Since this is a continuous motion and not stepped progression, the line segment A-B had to go through a gradual bending as it passed through B - a curve. After 180 degrees of rotation, points A, B, and C will be in line again. This is the trace of half of the curve. It resembles an arc of a circle or exponential curve. The other 180 degrees of rotation should produce a mirror trace which now I think might look like an ELLIPSE with pointed ends, like an American football or rugby ball or perhaps a tear drop.

If it turns out that the first 180 degrees of rotation is not a smooth curve but rather two straight segments joined at a kink, then the complete curve might look like a rhombus http://janbrett.com/games/jan_brett_geometric_shapes_diamond.htm[^] or a kite http://en.wikipedia.org/wiki/Kite_%28geometry%29[^]

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She sun gear analog is good if you keep in mind that the teeth are NOT meshing together, or as you put it, the gears are not in contact. The analog for teeth not meshing is smooth rollers/circles slipping along the point of contact which brings me back to my original description. CIRCLE WITHIN A CIRCLE IN CONTACT AT ONE POINT. Tadaaa!

This particular example is the simplest curve I could think off. In one revolution the curve at the 12o'clock position will be downward pointing tooth. There may be a simpler curve that is produced by other parameters but that is not what I seek.

What is the problem you ask? As I stated at the beginning of my question "...I have a need to generate a set of curves which are completely novel. I am looking for both, the exact mathematical solution and its programing/graphic solution to produce the visual end product." Not knowing anything about programing and not having used higher mathematics in 30 years means that I am not up to the task. I am stuck and seeking avenues to resolve my problem. As you said, it should not be a challenge of a principle difficulty (to someone who works in those fields). I am very technically knowledgeable but not a master of all crafts. No one is. That is why I need help from the experts in those fields.


{Da, da, tavarish. I was born in Czechoslovakia and left 43 years ago at 10 years of age. I only remember a few words}

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сэр Kryukov

As I wrote in my question, yes it is a form of cycloid where there is slippage occurring at the point of contact, which in my example is at the 12o'clock position (top).

Your "planetary gear" example is perfect BUT the gears do not "gear up" (In English we say: mesh). (I used the same example in my question :-D )

Here is an example of the type of slipping that I am talking about.
http://www.pumpschool.com/principles/vane_ani.htm
Now imagine the case/housing also rotating on its own axis in the same direction as the inner rotor. If they have the same revolutions per second or minute then there will slippage at the point of contact (12o'clock point) because the speed of each circle's circumference is different.

Понимаешь?

мистер Kryukov

Thank you for replying.

I would be satisfied with any answer in any format that I can get. Its the answer/solution I need, irregardless of the form it comes in.

You are correct in asserting/saying that it is easy to create a new set of curves because there is a near infinite combinations of equations. Mine is not a novel approach or idea. It is simply a set of curves which I've not been able to find anywhere and therefore, by definition, "new or novel".

"...Let me understand this: do you mean two curves "rolling" one by another without sliding..." It seems your definition of "rolling without friction" includes translation then I say NO that's not what is happening. Your description would fall under my definition of ORBIT in my posted question which I defined as NOT being present (not happening) in this scenario. In mechanical terms, the axis of the two circles are set in roller bearings which are set in concrete or welded to a steel plate.

To answer your question of "...Why?..." Again you are correct. I can not disclose/say it at this time. I wish I could.

Hello Jack

You are correct. I wish to implement/create a formula for this system of spinning circles. Being circles, the use of sine, cosine, and angles would yield the simplest solution.

For you, it is as simple as 1, 2, 3, 4. For me, having been out of school 35 years, it is next to impossible to undertake. It would be like asking a Neanderthal to invent a computer. :^D

Care to read my updated question and help this Neanderthal?

Thank you in advance.
Nean Derthal

I have updated my question nv3 and look forward to your input.

Thank you for your time.

Milan K.

Hello SAKryukov

Вы говорите по-русски?

I have updated my question and hope it is intelligible now. Please let me know what you think.

I look forward to your reply.

With regards,
Milan K.

Right you are again TRK3

I believe it is a form of hypocycloid plane curve I seek. Please see my updated question which includes few links to animated cycloids which should substantially clarify my question (I hope :^D ). Jack Dingler's approach is good but I am unable to do anything with it. Calculating the formula is beyond me and implementing it in a software for visual representation is doubly impossible for me.

Please see my updated question so that you may better comprehend the question.

Cheers.

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Danke/Thank you for your input Stefan.

I've been to that link previously yet it does not address my problem.

It is true that both circles can, and in this application MUST, rotate on their own axis. (See vane pumps). In vane pumps, there is motion of the inner circle relative to the outer circle, the stator/body/cylinder, without translation, which, unfortunately, produces friction yet these mechanisms are in wide use.

Please see my updated question.

Thank you again, Stefan.

Thank for your reply, TRK3.

You are correct about my sounding like a novice to programing and a dunce in my communication but please see my updated question which, hopefully, clarifies my previous miscommunication. (working 16/7 induces me to be brief. I apologize for my undue brevity and imprecision. To boot, English is my 3rd language, originally Czech born. Still learning its mastery.)

To clarify, you are correct when you say "...Also, what is it that describes the curve? Not the point of contact." As is true for any plot of plane curves that are produced by rotating/orbiting circles, it is the relative motion of the original points of contact that describe/trace/plot these new curves.

Thank you again for your input.