Roman Amphitheatres

For some reason, i am being drawn to the ancient Amphitheaters from the Roman empire. They were strong, elegant, pure, dramatic and purposeful. Could the stage set up for Lulik be somewhat influenced by these timeless icons?

String Art

the reason i am researching string art and the Bezier curve is because the form created by overlapping straight line elements can be very expressive and could be used as a canopy element for a structure...or the structure itself could become the canopy and have many possible outcomes of form, depending on the configuration.

The Mathematics of String Art:

A Tribute to Pierre Bezier (1910-1999)

Pierre Bezier at a confrence on Computer Aided Geometric Design, an obscure branch of mathematics that created most of the algorithms used in every drawing program from AutoCAD to 3D Studio Max, gave a lecture on how he came up with the Bezier Curve, the thing that made him famous among computer graphic junkies.

The story of the Bezier curve was an unusual one in the history of applied mathematics. Most of the time when you find a real world problem needing a mathematical answer, you just find the math you need and apply it. Such is the case with Einstein's General Relativity and Riemann's Non-Euclidean Geometry discovered a century earlier.

Bezier worked as an engineer for a french automaker. To satisfy the needs of manufacturing, they needed a way of describing a curve exactly at every point. In those days, engineers sitting at drafting tables would would mark a starting point and an ending point of the curve they wanted, then pulled out a french curve and drew an approximate best-fit curve.

At the machine shop level, these best fit approximations were not good enough. In order for pieces to fit together the parts could only vary within certain tolerances, many of these approximate curves were outside the tolerances. By 1960, hardware became available that allowed the machining of 3D shapes out of blocks of wood or steel, known today as CAM or Computer Aided Manufacturing. Computer graphics was still in its infancy at the time, so designing a method of describing any curve you wanted was of utmost importance.

Bezier had to come up with a method of describing a best fit curve that would be easy to use and exact enough to meet the demands of manufacturing. Unfortunately, no mathematics existed at the time to do the job adequately⁽¹⁾. After numerous schemes, he came up with a method of describing any 2nd degree curve using only four points.

The method is rather simple. He starts by describing a curve inside a cube (the figure below to the left) using a parametric equation equal to the graph of y = x². Then by transforming the cube into any kind of parallelepiped (below to the right), the curve will change as well. The four control points are the vertices of an imaginary parallelepiped. In the illustrations, points a and d represent the starting and ending points. Points b and c determine the curves depth and orientation. The slope of line ab is the starting slope of the curve, the slope of cd is the ending slope. Bezier's mathematical representation can be expanded to more than four control points to create curves of higher degrees, but for most uses four is enough.

For the real math junkies out there, the parametric function for Bezier Curve bⁿ(t), where point A is b₀, B is b₁, etc. and n is the number of points - 1 is:

2nd degree Bezier Curves can be lined up one after another to create all kinds of shapes in two dimensions. But, what was really important to auto manufacturing was describing a whole piece in 3 dimensions. Putting four curves together in a square shape creates a bezier surface with 12 vertices, and creating tiles of these surfacescan create any three dimensional shape you can imagine.

In today's computer aided world, the applications are numerous. Not just in obvious applications like computer graphics and animation (animation often uses bezier curves applied to the fourth dimension to describe smooth motion), but also in robot controlled manufacturing. The Bezier Curve changed the world.

The Bezier Curve Easily Simplified

For you non-math savvy people out there, let me explain the math of the Bezier curve as easily as possible. We will use the most simplified case: a curve from three coordinate points. Think about "String Art". Start with three arbitrary points, A, B, and C. Draw a line AB and divide it evenly into 10 (or so) parts. Draw another line from B to C and divide it into 10 parts as well. Draw a line from A to B. Draw another from the point next to A to the point next to B. Continue until you go from B to C. The curve created is a close approximation of a Bezier Curve using three points. You could say Bezier created a method of describing the mathematics of String Art. 1. At least two mathematicians solved the problem before Bezier: Airplane designer James Ferguson, and engineer Paul de Casteljau who worked for Citroen. The latter's work is mathematically equivalent to Bezier, in fact the formula listed above is De Casteljau's. Unfortunately, their discoveries were closely guarded industrial secrets and were not published until after Bezier. http://members.cox.net/mathmistakes/bezier.htm Some images of String Art.

Stage Study

This is a study on the circumnavigation of structural elements on a 500mm grid line up to 13m in radius.

The green zone is the area possible for the stage structure to sit without hindering the movement of the back line structures that have the ability to be moved in their individual arcs around the stage area to create everything from a wide open avenue to the stage or could enclose to create an intimate space for very small performances or speeches.

The Stage in Open Mode

The Stage in Intimate Mode

The Stage in Pack-Away Mode

The stage with it's Radii

Graphical Analysis of East Timor

The Following are percentage breakdowns of the population, population density, area and how many households are in each of the 13 districts of East Timor.

Series 1 = Population Density

Series 2 = Population

Series 3 = Households

Series 4 = Area

Fast Footings

A major part of pre-fabrication construction is versatility and deconstructability - the ability to be able to erect a structure and dis-assemble it for re-use on another location in a possible reconfigured state.

Here is a footing system that is extremely versatile and would enable such dis-assembly with ease, leaving very little evidence behind that it once existed in that space.

There is no concrete, no site preparation, no excavation, no holes, no mess and no heavy machinery involved.

MEGA ANCHOR Foundation Systems are an Australian Product and has full supply and installation capabilities across Australia and could be implemented as a new system abroad in East Timor with a little training and technical guidance.

How it's done.

First step is to complete 90∞ set-out at the site, install “hurdles”, specify building lines and provide datum for finished floor height.

The second step is to string the building area to determine the location of posts specified on the foundation plan;

Position Mega Anchor mainframes in the correct locations;

and For each foundation location:

Select appropriate orientation of mainframe for best appearance (may dig in on outside rows) and clearance for sub-floor plinths;

Use Installation Guide to align mainframe horizontally and vertically; Drive piles of (at least) specified length – 3 for each mainframe – into the ground using an electric jackhammer with special driver head. Maintain vertical and horizontal alignment and ensure required frictional resistance achieved (note: installation into rock requires specialised equipment);

and, Remove installation guide and drive mainframe down to screw mainframe and lock with piles. Fix mainframe to piles with self-drilling Tec screws to form an integrated foundation unit.

The next step is for the installation of the risers and saddles.

Interpret plans to determine height/s of saddles relative to specified finished floor height/s;

Select diameter/s of riser appropriate for height/s;

Set up level; and,

For each post:

Use level to determine length of riser;

Cut riser to length, attach saddle, install to height with laser level accuracy and align with bearer run; and

Fix saddle to riser and riser to mainframe with specified number of Tec screws. Note: Variations on the standard system can be made available to suit non-standard posts.

The final stage is to add bracing.

Interpret plans to determine extent of bracing required (as required for height and loading);

Measure and cut each brace to length;

Prepare each brace for fixing; and,

Fix bracing to riser/riser cap/bearer in accordance with bracing plan with Tec screws.

Now the building platform is ready for further construction of walls and the roof structure.

MEGA ANCHOR can be supplied and installed by:

CV-Substructures in Queensland

http://cvsubstructures.com.au/about.htm

Explorations in cardboard

Using band sawed slices of hardened cardboard from packaging and deliveries to form rigid structures as an exploration in scale and form.

The outcome plays with repetition and versatility to experiment with passageways.

These explorations were done fast so as to harness a spontaneous form.

Flat packing it

Flatpacking it

Posted by BILLERWELL DAYE at Saturday, 5 September 2009 03:34:59 PM EST
Last Edited: Saturday, 5 September 2009 05:52:44 PM EST

FlatPacking it...a how to and how not to guide

During my virgin excursion into Flatpack i discovered that time and complexity of construction are two of the biggest challenges one faces when designing a structure that is to be flatpacked, shipped and assembled, in this case, in a foreign country by relatively unskilled people...But simplicity is your greatest friend.

Let us go on a journey.

a journey into

FLATPACK MODEL MAKING

1. I decided i would use my new skills obtained in the workshop and create a piece of Flatpack (to get the ball rolling) by using the shelter that myself, Kirsty, Dan and Maria had developed and designed for Project 1a. in week 1. I figured it would take me approximately 1 week to disassemble the 3D modelled shelter, add some simple keys and teeth to join it back together in assembly, laser cut it out using the laser cutters in the workshop from 3mm mdf board and then assemble it without the use of glues or nails.

2.First insight - the shelter was not 'designed' with flatpack in mind and therefore took quite considerably longer to disassemble it and an incredible amount of mental mapping and assembly to work out how it was to be joined in construction.

3. The Explosion - this process involved drawing linework over each individual panel in an elevation or section, in order to then copy and paste it onto a sheet in a 2D format.

4. once all the elements had been copied into a 2D format, it was then arranged to fit as tightly into the allowable 400mm x 800mm dimensions that the laser cutter could physically cut in one sheet.

5. Now the hard part begins...and this was where the majority of time was used working out the joining system to complete the process before the template could be sent to the laser cutter. At first thought i assumed a 120mm x 60mm (1:20scale) squared sawtooth joint would be suffice for the whole job, and i would simply just draw this stitch into all edges of the panels and it would lock in together where needed.

6. Second Insight - nothing is as simple as you first think it is. If the design of the sctructure was universal in length and size of panels and all was designed to a grid, then perhaps the simple squared sawtooth joint could work as a universal connection. Alas, the shelter was not (refer insight 1) and so this joining system would have to be individually applied and designed for every 2 planes (x and y axis) that need to come together at an edge.

include a third edge in the 'z' axis and the connection becomes even more complex.

so, after over a week of development the flat pack is ready for cutting.

7. The beauty of laser cutting is, if you make a slight error, you can redesign the incorrect element and then laser cut it again, but it is best to still maintain as minimal wastage as possible in the process, so if there is multiple re-cuts, they should be cut in one session, as was the case with this.

Due to the experimental nature of this exercise and the fact we had initially designed the shelter with a wall thickness of 50mm, and the scaled flatpack equalled 60mm, there were a few overlooked calculations and these elements had to be recut.

8. Third insight - even laser's have a thickness when cutting. Working with timber using traditional tools like a saw for example, the blade of the saw has a thickness and therefore cuts a larger area than the guide line. This thickness is acounted for in carpentry when creating joints that fit tightly. And so, the laser cut must also be assumed a thickness if a joint is to lock in tightly when assembled. For the generic squared sawtooth joint used, this tiny, miniscule thickness was enough to not allow for a tight snap when assempling the model, and so a pva glue was used to fix the joints.

9. Joints that used a female/male key were the most effective in the process of being able to 'snap' into place without any extra fixing.

10. The finished product finally took shape 3 weeks after starting the process.

11. Final insights - this process would have been better executed had a simple system of fixing been developed along side the initial design for the shelter. By designing the mothods of construction and materiality concurrently with the form and design of the structure a true simple and usable product can eventuate and even successfully be realised from design, to manufacture, to packing and shipping, to unpacking, to assembly and construction, to use, and to disassembly and re-use.

Nail-less join prototype

Nail-less join prototype

Posted by BILLERWELL DAYE at Saturday, 5 September 2009 06:35:07 PM EST
Last Edited: Saturday, 5 September 2009 06:37:19 PM EST

From my experimentation with creating the Shelter model by laser cutting and assembly, it made me question how we design. Not only for a designs usability, but how it is constructed and the systems that can be implimented to make that construction as simple and affective as possible. I guess it could be labelled

"Design and construction for dummies".

The complexity i faced when trying to fit 3 planes together was immense. my brain hurt for days on end, computing the dimensions of keys and locks and nodes in order to fit an 'x' panel into a 'y' panel and then add a 'z' panel into the connection. from there i asked whether a universal join could be created to allow such a fixing to perform without nails or glues, regardless of scale.

From here i asked if it was indeed possible, as for this to happen, all three planes must be able to physically be assembled and also lock together. So how do you do this?

Timber can't pass through timber or stretch and squeeze into tight spaces, therefore it has to be able to insert and fit naturally.

What i came up with was a locking system using 4 components. 3 being fixed onto the beams or columns and a 4th locking key. I call it the 'I C U Joint' or Inter-Connected Universal joint

Elements 1, 2, 3 & 4.

Element 1 - is the base element that must be inserted or placed first, which would sit on a foundation.

Element 2 - would then slot into element 1 from above, thus forming both the 'x' and 'y' beams.

Element 3 - or the column would then slide down into the joined 1 & 2 elements.

Element 4 - the locking piece would then be inserted into the centre space with a key, which would then be removed (the key) and the join becomes rigid, not allowing any of the componants to be seperated whilst element 4 is in place. this also makes for ease of disassembly as the key would be inserted into element 4 again, enabling element 4 to be removed and each elemant seperated in the reverse order to construction and packed away or transperted to another site for re-use.