First published in the Science and Engineering forum of the For Freedom Forums
Posted: Tuesday 25th December 2012 06:21 pm
|Tessellated I in Steel
View larger version of Tessellated I in Steel 1800 x 800
View colours of the spectrum version of Tessellated I
Representing a surface of "I"-shaped steel tiles or an embossed "I" tessellation pattern in a steel sheet. Produced using Paint.NET.
The "I" shape is of square proportions, the column of the I being one third of the width of the square and the top and the base one quarter of the height of the square.
The image has my own watermark added.
Tessellated I or H bricks and tiles for stronger, lighter assembled structures (YouTube)
This video shows a model by Peter Dow (of Aberdeen, Scotland) of the 3-dimensional shape of a simple structure composed of 6 bricks or tiles, each of which, when viewed from one-direction anyway, are a 2-dimensional "I"-shape (equally when rotated by 90 degrees "H"-shaped).
This model has been made from aluminium tubing and in order to distinguish one brick from another they have been coloured using marker pens - so there are two bricks coloured blue, two coloured green and two coloured red. This colouring was necessary for clarity because otherwise the permanent joints within bricks (which are only an artifact of the method to make a brick from square tubing) might be confused with the simple touching surface where two neighbouring bricks abut, abutting securely but without being in any way stuck by glue etc.
The 2-D "I" shape being modelled is supposed to be of square proportions, the column of the I being one third of the width of the square and the top and the base one quarter of the height of the square.
These 2-D I or H shapes can be mathematically said to be able to tessellate a plane, that is to say, one can fit many of these shapes together to cover a surface completely.
This 3-Dimensional model reveals a further design feature of the I or H brick and tile structures, which secures the bricks and tiles together in 2 further dimensions, some such feature being necessary because the 2-D I or H shape in of itself only secures the bricks together in 1 dimension.
This feature is revealed here to be nothing more complicated than dowels or fixing rods which run in the vertical direction of the Is (or the horizontal direction of the Hs) through shafts in the Is' bases and tops and which serve to lock the tops and bases of neighbouring Is together, preventing movement radially from the dowels.
These dowels may henceforth be referred to as "Mazurka Dowels" named after the username of a scientist in an internet science forum who first correctly anticipated this feature of my 3-D design and its function to hold the structure together in all 3-dimensions, in a reply post to my topic there describing in detail only the 2-D tessellation, suggesting somewhat vaguely that some such design element was required for a good 3-D design with a view to seeing who would suggest the solution I had thought of first.
As I explained in that topic I could hardly call those dowels the "Dow dowels" there being too many dows in that name and anyway, my name can be used to reference this particular shape of I or H tile and brick and structures composed of them, as per "Dow tile" "Dow brick" "Dow I-tile" "Dow H-brick" "Dow I-H-brick" "Dow I-H-brick structure" "Dow I-structure" etc.
Posted: Monday 14th January 2013 03:55 pm
HI-BRICKS & DOWELS demonstration video by Peter Dow (YouTube)
Transcript of the video
Hi everybody and welcome to my "H" / "I" Bricks or HI-BRICKS & DOWELS demonstration video.
This is Peter Dow from Aberdeen, Scotland.
There are two components to a HI-BRICKS & DOWELS construction -
The shape of the "H" or "I" bricks is designed so that they fit together to form a layer or a wall of bricks and importantly, the bricks, just by their very shape, immobilise each other from moving, in one dimension only.
Let's have a look at that.
Let's consider this green brick here as the fixed point.
We can see that it immobilises its neighbouring bricks in one dimension. They can't move with respect to the green brick in this dimension. So that's locked. Even though there is no bricks here or here, the very shape stops it moving in that dimension.
Now the shape doesn't stop the bricks moving with respect to each other in that direction, or in that direction but they are fixed in that one dimension.
Now if we want to make a rigid structure of bricks in all three dimensions but without using mortar or glue so that we can assemble and disassemble the structure whenever we like, what we need next are the DOWELS.
As you can see, the "I" or "H" bricks have shafts running through the corners so that you can run a dowel through the corners - two shafts, four holes per "I" or "H" brick.
And when you assemble the bricks you can slide the dowel in ... and this forms a structure which is rigid in all three dimensions, which is what we need to form structures.