Online since 2002. Over 3300 puzzles, 2600 worldwide members, and 270,000 messages.

TwistyPuzzles.com Forum

It is currently Wed Jul 23, 2014 4:49 pm

All times are UTC - 5 hours



Post new topic Reply to topic  [ 31 posts ] 
Author Message
 Post subject: Revolutionary mechanism designs (CAD inside)
PostPosted: Sat Mar 05, 2011 6:59 pm 
Offline
User avatar

Joined: Thu Nov 26, 2009 2:28 pm
Location: Ukraine, Kyiv
Recently Oskar Van Deventer set a new record in puzzle building with creating a 17x17x17 cube. Without doubt, that is a great achievement. The new puzzle also marked a major breaktrough as a proof that there are other approaches to puzzle mechanism design that are no less effective than that of V-Cubes. This shatters the view of the V-mechanism as being the one and only optimal for super high orders. And that is the most important accomplishment of Oskar's work.

Oskar published several ideas in two threads: "17X17X17!! BY: OSKAR VAN DEVENTER!!", "Linear versus Binary style for super high NxNxN"
Having picked up his ideas, I have refined and improved them. Now I am happy to present my results in this topic. The important part of this work is that I've got an opportunity to compare all advantages and disadvantages of different approaches to inner mechanism construction. Demonstration of various approaches is performed best on a cube of a large order. To honor Oskar's initial desire I am going to demonstrate all design approaches on a 17x17x17 cube. A cube of this size has enough number of layers to see the general trend of how the layers are split. Also, this makes for convenient arithmetic for binary design where 17 is precisely 4 levels plus a central layer (17 = 16 + 1 = 2^4 + 1).

Image

The discussed designs don't make up a complete group, nor they exaust all possible variants, I suppose. Moreover, they are not really classified. Considering that these designs can be combined in practice, we get a pretty impressive set of various approaches. I must note that approaches for mechanisms of an even order deserve a separate discussion. Those could use a central layer that is split in two, or hidden layers inside the mechanism. Another dilemma is whether the core should be a spider with voids inside, or a sphere on which the adjacent layers stand.

All presented designs are multipurpose in a sense that they can be applied not just to hexahedrons, but to any shape. That includes megaminxes (dodecahedrons), tetrahedrons, octahedrons, icosahedrons, etc. The constant here is the presence of a central element on each face with one or another design built around it, and corner elements as pieces that connect these faces.

I am not going to evaluate each of the following approaches in full. Even though I do have certain understanding of and experience in the issues I discuss here, I believe that you need to have a real prototype in your hands to actually understand all of the mechanism properties. I leave further discussion privilege to the readers. I hope that will reveal all nuances of the designs.

I hope that my beautiful rendered images will help you to get a complete grasp of each design approach. And even more, I offer to send the original CAD-files to those who are competent enough to make full use of them.

---
Here is the link to my original article: "Revolutionary mechanism designs" ("Революционные подходы ко внутреннему механизму головоломок").

---
In this thread
I`m very thanks to Oskar - for major initial ideas;
thanks to Drewseph - for beginning CAD-tutorials;
and Aleksey - for help of the article translation.

---
In case new designs or ideas will be invented - I can CAD them in such style to easy comparing, or beautiful presentation.

---
so there are:

Image Image Image Image
Image Image Image Image

---
See also sketches for cross-sections post below.

_________________
sorry for my quite bad ukrainian english :)


Last edited by Tesseract750 on Sun Mar 06, 2011 12:14 pm, edited 7 times in total.

Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sat Mar 05, 2011 7:00 pm 
Offline
User avatar

Joined: Thu Nov 26, 2009 2:28 pm
Location: Ukraine, Kyiv
1. Cylindrical Design

Image

This is the first internal structure of a puzzle mechanism. It was there from the beginning, and it is still used in classic Rubik's cubes. Here we take a look at the variation that is used in Eastsheen cubes, but extended to any number of layers. This approach is not perfect, and with addition of more and more layers it results in a puzzle that is highly unstable in the next to last layers. With this design it was always possible to create puzzles of higher order than 5x5x5, even before the invention of conical design.

Image Image Image Image

Image Image Image Image

Image Image Image Image

Image Image Image Image

_________________
sorry for my quite bad ukrainian english :)


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sat Mar 05, 2011 7:01 pm 
Offline
User avatar

Joined: Thu Nov 26, 2009 2:28 pm
Location: Ukraine, Kyiv
2. Conical Design

Image

Invented by Panagiotis Verdes, this design made a furor and gave a huge push to puzzle building. Extremely easy to comprehend, the design makes it very simple to add more layers or approximate it to any shape variants. Extremely stable when properly used. Has the lowest friction between the layers, despite the large contact area in the next to last layers. The "V" in the name of the design is most probably derived from the conical form of cross-sections which permeate the entire construction concentrically.

Image Image Image Image

Image Image Image Image

Image Image Image Image

Image Image Image Image

_________________
sorry for my quite bad ukrainian english :)


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sat Mar 05, 2011 7:02 pm 
Offline
User avatar

Joined: Thu Nov 26, 2009 2:28 pm
Location: Ukraine, Kyiv
3. Mirrored Design

Image

To avoid overspending of the useful footprint and materials, conical approach can be somewhat modified. Because the size of the elements closer to the outer layer increases proportionally, they can be "reversed". That way we get sort of a mirror reflection of the middle layers. This approach is slightly less reliable that the conical design as the mirrored layers are not attached to the puzzle's frame.

Image Image Image Image

Image Image Image Image

Image Image Image Image

Image Image Image Image

_________________
sorry for my quite bad ukrainian english :)


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sat Mar 05, 2011 7:03 pm 
Offline
User avatar

Joined: Thu Nov 26, 2009 2:28 pm
Location: Ukraine, Kyiv
4. Binary Design

Image

Extension of the mirrored design in conjunction with the idea of fractals. This is the most mathematical structure. However, in the essence it is even less practical than all previous approaches. It has all the shortcomings of the mirrored design, and adds the need to narrow the cross-section in certain places of each subsequent self-similar shape, which reduces strength. Also, there's a huge size differential between various parts.

Image Image Image Image

Image Image Image Image

Image Image Image Image

Image Image Image Image

_________________
sorry for my quite bad ukrainian english :)


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sat Mar 05, 2011 7:04 pm 
Offline
User avatar

Joined: Thu Nov 26, 2009 2:28 pm
Location: Ukraine, Kyiv
5. Pagoda Design

Image

Really beautiful structure! The reinforced alternative to binary approach. Portion of the load is transferred onto the main elements of the puzzle frame. This is the most solid design that provides the most grip between pieces. At the same time that leads to huge friction between the layers which is a disadvantage. The name of the design comes from the specific shape of certain parts of the puzzle's frame.

Image Image Image Image

Image Image Image Image

Image Image Image Image

Image Image Image Image

_________________
sorry for my quite bad ukrainian english :)


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sat Mar 05, 2011 7:05 pm 
Offline
User avatar

Joined: Thu Nov 26, 2009 2:28 pm
Location: Ukraine, Kyiv
6. Cascaded Design

Image

An attempt to hide entire mechanism inside. This leads to a huge increase of the number of constituents. Very inefficient and impractical structure that leads to a loose mechanism. But it has the right to exist.

Image Image Image Image

Image Image Image Image

Image Image Image Image

Image Image Image Image

_________________
sorry for my quite bad ukrainian english :)


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sat Mar 05, 2011 7:06 pm 
Offline
User avatar

Joined: Thu Nov 26, 2009 2:28 pm
Location: Ukraine, Kyiv
7. Flat Design

Image

If we cut all inner layers from the cascaded design and leave just the outer visible pieces, we get the flat design. In this case we see lots of elements that are very much alike. The small size differential can be considered a good thing. In practice, however, the pieces will get stuck during rotation. Actually, flat design is very funny - you can see how the corner pieces looks like to hedgehog.

Image Image Image Image

Image Image Image Image

Image Image Image Image

Image Image Image Image

_________________
sorry for my quite bad ukrainian english :)


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sat Mar 05, 2011 7:07 pm 
Offline
User avatar

Joined: Thu Nov 26, 2009 2:28 pm
Location: Ukraine, Kyiv
8. Floating Anchors Design

Image

If we elongate each element of the flat design further deep down, we get some sort of an anchor that will not allow these elements to turn in place as freely. That way the elements will not get stuck during rotation as in flat design. What's interesting, the current approach is the closest to the perfect case where each piece of the mechanism seeks the shortest path that leads to the center. I'm very curious how this "fan" structure would behave in practice. Most probably the tension will need to be very high.

Image Image Image Image

Image Image Image Image

Image Image Image Image

Image Image Image Image

_________________
sorry for my quite bad ukrainian english :)


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sat Mar 05, 2011 7:23 pm 
Offline

Joined: Sun Mar 27, 2005 7:37 pm
I am not sure if this is the appropriate response but I just want to say beautiful!

_________________
Image


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sat Mar 05, 2011 7:35 pm 
Offline
User avatar

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
The images are astonishing. I don't know much about the pros and cons of the internal structures. But these illustrations are truly artistic.

_________________
Check out some virtual puzzles I created at http://nan.ma


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sat Mar 05, 2011 7:53 pm 
Offline

Joined: Sun Jan 02, 2011 6:48 pm
Location: Canada
Its just crazy how many design you can make for the same cube. Its very cool.

_________________
katsmom wrote:
My grapes are making noises right now. They keep saying drink me, drink me.


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sat Mar 05, 2011 8:15 pm 
Offline
User avatar

Joined: Tue Mar 10, 2009 7:06 pm
Location: Nowhere in particular.
Very, very cool images. The mechanisms each seem to have their pros and cons, and each must have some sort of applications which are beyond us all. :P

Fantastic advancements!

_________________
~Kapusta

PB: At home (In Competition)
2x2 1.xx (2.88)
3x3 11.xx (15.81)
4x4 1:18.26 (1:24.63)
5x5 (3:00.02)
6x6 4:26.05 (6:34.68)
7x7 6:38.74 (9:48.81)
OH (35.63)

Current Goals:
7x7 sub 6:30
4x4 sub 1:10


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sat Mar 05, 2011 8:57 pm 
Offline
User avatar

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
I'll take one of each, thanks. Where's the checkout?

Seriously though, I can see 2 things:
1, all the Chinese manufacturers running for their note pads, and
2, Verdes pulling his finger out and warming up his machinery to get his product out there before all the Chinese manufacturers use `any one` of the other designs.. hopefully.

Burgo.

_________________
1st 3x3 solve Oct 2010 (Even though I lived through the 80s).
PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
1st 3x3 Earth (nemesis) solve Jan 2011 My You Tube (Now has ALLCrazy 3X3 Planets with Reduction)


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sat Mar 05, 2011 9:22 pm 
Offline
User avatar

Joined: Mon Mar 30, 2009 5:13 pm
Just WOW, nothing much else I can say. I would love to know what Erno Rubik would think of these beautiful designs and images...

_________________
If you want something you’ve never had, you’ve got to do something you’ve never done - Thomas Jefferson


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sat Mar 05, 2011 9:30 pm 
Offline
User avatar

Joined: Wed Oct 01, 2008 2:39 pm
Location: Marquette, MI, USA
Very very impressive. It looks as though a lot of thought and work went in to all of these designs, and I must say they are all very impressive and very beautiful.

If I may put some of my own input in I personally think that the binary and mirrored designs still have great potential, not only for higher order puzzles, but for all different designs. My personal favorite is of course the conical design as its simplicity is what makes it so easy to work with a wide range of puzzles. (and I believe it is called V-cube not because of the shape, but because of the inverters name.)

The Floating anchors design surprised me when it worked so well with Oskar's 17x17. I must say I did not believe in the mechanism when I first saw it. Surprisingly much like V-Cubes simple Conical design, the simplicity is what makes it work so well.

I personally think that the cascade and pagoda designs over complicate things for higher order puzzles, but might work for something a little smaller. Otherwise I think there is just too much going on, however this is only opinion, I really do not know.

I think the Mirrored design has the most probability of being viable. It takes V-cube conical design and when mirrored I believe it makes for a very stable looking design. Not only are the pieces being held in by the centers, but also by the corners. I am not sure if it would cause more friction and take away from the design however.

I will try to implement these designs on some dodecahedral puzzles just to see how the look, I am very interested.

Sadly I don't think we will see any of these designs come to a massed produced stage.

Tesseract750, do you care to show some variations with some of these other shapes? Your renderings are so nice.


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sat Mar 05, 2011 9:39 pm 
Offline
User avatar

Joined: Mon Oct 18, 2010 10:48 am
Very impressive designs! I wonder if any of them are viable (if money didn't exist :roll: ) for mass production? As in, turning quality.

_________________
++Noah (NType3 here, Emrakul elsewhere)

Moderator for Puzzling Stack Exchange - a new site for specific puzzling questions!


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sat Mar 05, 2011 9:41 pm 
Offline
User avatar

Joined: Wed Apr 21, 2010 3:45 pm
Beautiful renders, beautiful designs, this is just plain awesome.

I wish I could design like you.

_________________
Image
Sig made by me.

Dragonball is amazing.


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sat Mar 05, 2011 11:12 pm 
Offline
User avatar

Joined: Wed Oct 01, 2008 2:39 pm
Location: Marquette, MI, USA
I made this real quick. It is a higher order Megaminx using the mirror design. Unfortunately with the high number of parts my computer glitched a bit, so I added in a few cuts with paint. I hope at least it proves this can be applied to other puzzles. Takes a little practice to get it right.


Attachments:
1.png
1.png [ 52.75 KiB | Viewed 12779 times ]
2.png
2.png [ 49.08 KiB | Viewed 12779 times ]
3.png
3.png [ 37.78 KiB | Viewed 12779 times ]
4.png
4.png [ 50.67 KiB | Viewed 12779 times ]
5.png
5.png [ 52.94 KiB | Viewed 12779 times ]
6.png
6.png [ 30.29 KiB | Viewed 12779 times ]
Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sun Mar 06, 2011 6:01 am 
Offline
User avatar

Joined: Thu Nov 26, 2009 2:28 pm
Location: Ukraine, Kyiv
Thanks for replies on my thread! I`m wonder to see so many responses during one night. Yes, there were a lot of work, so to see the applauses "beautiful" - very glad to me. And yes, I can apply a couple of designs on other shapes if it`s really needed, on dodecahedral for instance. Muffet`s example is good enough for preview.

Keep going your comments about different approaches to detect disadvantages, and discover benefits. By the way, I have already one mistake: on cascaded design there we can`t use inner layers fluently in such way represented - because of getting stuck after first rotation. I suppose they have to be connected to outer visible pieces, or any else.

---
Personally I would like to hear there Oskar`s opinion about all these :wink:

_________________
sorry for my quite bad ukrainian english :)


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sun Mar 06, 2011 7:49 am 
Offline

Joined: Sat Jan 15, 2011 10:22 am
Sorry I'm not Oskar :( Your designs impressed me a lot!

But aren't there thousands of ways to make a big cube work (and to make it stabile)?
What I mean is, what if you just put small...hmm...rails to all these wings of one piece(an edge or so), so it pulled the pieces around it to itself? That's, I suppose, all you need to give it a good stability. As long as all the pieces are connected to the pices around them very well, a cube can't be fragrile.


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sun Mar 06, 2011 7:59 am 
Offline
User avatar

Joined: Sat Jan 16, 2010 11:48 am
Location: In Front Of My Teraminx (saying WTF?)
Can I know how much dozen hours you passed on those puzzles?? :shock: This is amazing!!

- Greg :D

_________________
My Shapeways Shop!
My Designs
My Official Results
My Website on Twisty Puzzles with Gears

Grégoire Pfennig


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sun Mar 06, 2011 8:53 am 
Offline
User avatar

Joined: Mon Nov 30, 2009 1:03 pm
Tesseract750 wrote:
Personally I would like to hear there Oskar`s opinion about all these.
This is a wonderful enumeration of design ideas for large-order puzzles. I hope someone will test them in practice some time. Could you publish the cross-section design, like this one, as they help understand which pieces hold which.

Oskar

_________________
Oskar's home page, YouTube, Shapeways Shop, Puzzlemaster, and fan club
Image.


Last edited by Oskar on Sun Mar 06, 2011 10:47 am, edited 1 time in total.

Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sun Mar 06, 2011 10:35 am 
Offline
User avatar

Joined: Sun May 17, 2009 1:33 pm
Location: USA, North America, Planet Earth, Solar system, Milky Way galaxy, Universe
Art.
No other way to describe it.

Seriously, though, I'd like to see these methods implanted to 7x7x7 and 9x9x9, because those are of a lot more reasonable size and price to prototype, and there is always the V-mech 7x7x7 to compare to. (By the way, I bet that the 'floating anchors' will be able to support a miniature 7x7x7 with minimal popping.)

_________________
-sj

NEW VIDEOS-
3x3x3 stop-motion solve
Meffert's new Pyraminx Crystal solve
QJ 4x4x4 solve


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sun Mar 06, 2011 11:44 am 
Offline
User avatar

Joined: Sat Feb 03, 2007 10:03 pm
Location: Mississippi
Yes - beautiful! Is there any type of "open-source license" that can prevent anyone from getting a patent on these designs? :)

_________________
Space for rent


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sun Mar 06, 2011 11:50 am 
Offline
User avatar

Joined: Fri Feb 08, 2008 1:47 am
Location: near Utrecht, Netherlands
jabeck wrote:
Is there any type of "open-source license" that can prevent anyone from getting a patent on these designs?
Having public disclosure on the internet is enough for that.

_________________
Tom's Shapeways Puzzle Shop - your order from my shop includes free stickers!
Tom's Puzzle Website


Buy my mass produced puzzles at Mefferts:
- 4x4x6 Cuboid for just $38
- Curvy Copter for just $18
- 3x4x5 Cuboid for just $34


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sun Mar 06, 2011 12:07 pm 
Offline
User avatar

Joined: Thu Nov 26, 2009 2:28 pm
Location: Ukraine, Kyiv
Oskar wrote:
Could you publish the cross-section design, as they help understand which pieces hold which.

I thought every "##_Design_view-1.jpg" image helps to imagine cross-sections... Well, ok.
Here they are:

Image Image Image Image

Image Image Image Image

_________________
sorry for my quite bad ukrainian english :)


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sun Mar 06, 2011 12:13 pm 
Offline
User avatar

Joined: Thu Sep 24, 2009 12:21 pm
Location: Chichester, England
Are there any Eastsheen like designs where the corners and central edges are very close to the outside of the puzzle where as the center parts go right into the puzzle? It would probably be extremely impractical, but it would be a nice addition to this series of mechanisms.

_________________
3x3x3 single: 5.73 seconds.
3x3x3 average of five: 8.92 seconds.
3x3x3 average of twelve: 9.77 seconds.

Buy the Curvy Copter Skewb, NovaMinx, and more here!


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Sun Mar 06, 2011 12:13 pm 
Offline
User avatar

Joined: Mon Nov 30, 2009 1:03 pm
Tesseract750 wrote:
I thought every "##_Design_view-1.jpg" image helps to imagine cross-sections... Well, ok. Here they are:
Brilliant! I am quite curious how well the Cascade and Flat style work out. Someone should try these. Perhaps starting at a "lower-order" high-order cube.

Why are there free-floating pieces in the "Cascade" design?

Oskar

_________________
Oskar's home page, YouTube, Shapeways Shop, Puzzlemaster, and fan club
Image.


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Tue Mar 08, 2011 10:23 am 
Offline
User avatar

Joined: Sun Mar 15, 2009 12:00 am
Location: Jarrow, England
You've put a lot of work into this. Very impressive. But why did you not do this on a 33x33x33 cube :lol:

Slightly off topic, but which 3D program did you use, and what sort of super computer did you do the renderings on?

_________________
My Shapeways Shop: http://www.shapeways.com/shops/gus_shop

Image


Top
 Profile  
 
 Post subject: Re: Revolutionary mechanism designs (CAD inside)
PostPosted: Wed Mar 09, 2011 11:43 am 
Offline
User avatar

Joined: Thu Nov 26, 2009 2:28 pm
Location: Ukraine, Kyiv
Oskar wrote:
Why are there free-floating pieces in the "Cascade" design?
I`ve got it! Know about this mistake. As I`d wrote before we can`t use inner layers freely - because we`ll get stuck after the first rotation. Solution can be found by clicking (as v-cube 6 for instance), or by pairing every inner piece with upper outer visible piece. The second one is more reliable, but in this case cascaded design will be too close to pagoda design.

Gus wrote:
Slightly off topic, but which 3D program did you use, and what sort of super computer did you do the renderings on?
The reason is not in software. Anyway for rendering I used another program as for engineering. I`m sure my computer is less power as your`s, 1Gb of operation memory and non-modern kernel. However I know several tricks for avoid computer glitching. I use puzzle`s parts as instances instead of using as copies - it helps to save memory. Another artifice is: do not render elements, which aren`t seen on the screen. So my models are almost empty inside. Anyway observer will never guess about, right?!...

RubixFreakGreg wrote:
Can I know how much dozen hours you passed on those puzzles?? :shock: This is amazing!!
Many thanks! I really was in terrible about amount of work, at the beginning. Later I had systematized my process generation. Actually I had start my work about 1.5 months ago, before Oskar publish working Over The Top 17x17x17 prototype. So it was independently. The most of working hours were at night, when my wife and child were asleep, I think you understand :)
Now I`m in another big project. If it will be success - we all get a huge push in puzzlebuilding. Hush! )))

_________________
sorry for my quite bad ukrainian english :)


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 31 posts ] 

All times are UTC - 5 hours


Who is online

Users browsing this forum: Yahoo [Bot] and 4 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  

Forum powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group