Third-order Motions (three circles composition)

Why thank you! I did not know about that first picture! I likey

I'm still catching up on this thread (been in Africa for the past month), but I'd be delighted to host these images. Zalty, can you email them to me? drex (at) drexfactor dot com

Okay guys the images are back !

Great explanations Jon !
Thanks to make me avoid writing a too excessive reply.




Okay first don't forget that i am french ... so what is written on the pictures is in this language.

"Trajet" means Path, "Centre" means Center, "Main" means Hand & "Extremité" means Extremity in English. "Inter" is for Intermediary as explained before.

So, "Trajet CentreInter" is the path described by the point I, "Trajet Main" is the path described by the point M & "Trajet Extrémité" is the path described by the point E in my model and from the audience poitn of view.

"Relatif" means Relative in English.

So, "Trajet Main Relatif" is the path described by the point M with the point of view of a fly putted on [OI] (as Jon explained before about the local frame reference).
And "Trajet Ext Relatif" is the path described by the point E with that same point of view.




I have to do an english version of my excel sheet ... so let me a few days to make it more understainable and i'll send it to Drex in order to make it freely downloadable.




Actually i consider the segments of my model as a linkage which means that the angles and numbers of turns are counted relatively to the previous one. Thus, only [OI] is counted according to the absolute (or audience) reference because it is the first segment.

That type of reference enable to make sense to the numbers as used in the notation as explained before (first post of the topic) because there is a direct correspondance between these ones and the numbers of foils inside the patterns.

It also enables to extract some basic rules of composition (serial & parallel) with simple maths operation (addition and substraction).


A word about Zan's Diamond :

According to the video posted by [ Unregistered ] & Jon, Zan's Diamond and the AAS spinned by Mel in his Video are definitely not the same patterns.

As Jon explained it is based on linear version of hand CAP.
In terms of elementary patterns used for this CAP we have and AKA 1 -4 ; 3/4 1/4 and 1 -2 ; 1/2 1/2 (they are in cycloid case because it is the closest to the polygonal representation).

Hand follows a 4p antispin flower while the poi does a 4petal antispin flower

The same pattern (Anti-AntiSpin(4,4) in Open-Open StartMode) in a graphical version :



If you want to see all the parameters, i have saved this pattern and Mel's pattern seen previously (Anti-AntiSpin(4,2) in Close-Close StartMode) as examples in the Trochoïd Engine(.xlsx) (or Trochoïd Engine (.xls))

WOW!!! I just find this topic!

Guys, I love you! I am so happy that I am not alone in this searchings!
Nice to see that you and me thinking in the same ways!

I want to know, you guys discover third-order motions same time with me? Or my video was first? (I just shocked, cause this topic looks like a copy of my notebook :D)

sorry for bad English! (

Hi Mel.

The first post is from 21/08/2010. I suspect it is one of those ideas that was found by a number of people all at once.

Well, I think you right!
Anyway I an happy that I am not alone in my searchings (I am not only one theoretical freak :D)!

Hello Mel. Nice to "meet" you !
Aston has right effectively i work on those 3rd order things for a few years now ... and i guess this is something "in the air" that more and more spinners are catching in their mind !
If you have anything to share on these subject please do not hesitate to use this topic as well.
I'll contact you on FB if ever we want to exchange on the notions later !

Heya, just a random question about this part specifically, and I'm sorry if this was covered already....

Shouldn't the first example be 1 5 ; 1 1 (4 petal inspin), and the second be 1 -5 ; 1 1 (6 petal antispin)?

Hello Mesh

Your description is also correct, however you are counting the turns of all the segments (arm & object) in the absolute referential (the earth let's say).

I have chosen to start with an absolute referential : In general it is the half straight line define by the starting position of the arm but let's say it is the one going from the center to the bottom for that case.

Then i count my arm turns relatively to it and i count the object turn relatively to the arm (each time they are aligned for example).

This system is efficient for me in term of notation because it gives meaning to the 2 first numbers.

Example : the description of the pentacle pattern is written 2 -5. 5 fits with the numbers of "petal" and 2 fits with the numbers of jump the object do to go from a petal to another.

I think these kind of keys facilitate a lot the visualization of the pattern once written on a piece of paper into a notation.

Does it make any sense to you ?

Ah, maybe I had misunderstood what the two numbers defined.

I was thinking the first number was number of arm rotations and the second was the number of poi rotations.

For example I was thinking an antispun pentacle would be "2 -3" as the arm makes two full rotations while the poi makes 3.

As i said the numbers does represent the number of rotations (respectively of the arm and of the object) !
The only thing that make a difference in your example is the way these rotations are counted.
If you count it all along the earth or audience referential, you get "2 -3" for the pentacle.
If you count each part of the chain relatively to the previous one (arm/ground ; object/arm), you get "2 -5" which is more meaningfull for visualizing the motion out of the numbers.

Damn, dude...only took me two years to catch up to you on this, Damien

Nice job for the vid & nice motion execution Drex !
It looks pretty the same than what my sim draw !
Keep practising & Cheers \°/

PS : For my own information, what do you call antibrids in the video ?

As it was originally described to me, an antibrid is any hybrid wherein one poi is orbiting around the head of the other poi. I think of it as creating a relationship between one hand and the poi attached to the other hand. If you just refer to them as hybrids, however, you're not wrong