L9mp

Inspired and intrigued to the "flexion tension" system of the ITKE Pavillon 2010, I wanted to use this "active bending" construction system to build a lamp.
Using Rhino+Grasshopper I design my lamp as a parametric model, in order to be able to make easy changes during the development and adapt the lamps in function of the material, the space and desires...

Steps 1 to 6 explain roughly how I design my lamp

Steps 7 and 8 explain how to build it using the milling file .dxf

Thanks to Georgi Kazlachev and Djordje Stanojevic for the inspiration that they give me during the Woven Wood Workshop, thanks to Tiziano from Open Dot for the help using the laser cut of OpenDotand thanks to Jean de la Tour for some pictures

Step 1: Link Between Mechanical Behavior and Geometry

The structure is composed of an even number of strips. They are quite similar, but slightly different to create the flexion-tension principle.

For one wave, we can see a bending behavior for the 1st strip and a tension behavior for the 2nd. For the next wave the 1st strip is bended and the 2nd in tension.

Putting together only two strips we create a geometry due to the mechanical behavior. This geometry must be closed to the one defined, in order to be able to get the whole structure without troubles during the assembly procedure.

Step 2: Parameters of the Problem

On Rhino I worked only in 2D with a section of the lamp. I defined the axis and the position of the nodes (crossing of strips.

Knowing the position of the nodes the values of angles "a" and lengths "L2" are known. The difficult task is to find "L1" precisely, to create the right angle "a" needed.And this L1 is not governed by geometry but by the mechanical behavior of the strip...

Step 3: Relation Lengths - Angle

The relation between lengths and angle is far from simple. Because we cannot use the small displacement hypothesis and the inertia of the strip is not constant. By the way, as far as I understand, this relation does not depend on the material so I did some tests using paper to get an experimental relation. I used only "one wave" to carry out those testing because in the real structure, due to the zero curvature for both strips around nodes, there are no bending moment transiting from one wave to the other (this "non bending moment around nodes" is also a very useful fact to don't put stress in this region weaken by notch, so to reduce breaks probability)

Theoretically, this relation exist for constant inertia beam. So I added a parameter (beta) to take this effect into account, and I choose the value in order to fit experimental data obtained with the paper model.

In the design on Rhino, I had in reality two angle "a1" and "a2", so I managed to have all of those angle closed and I computed the mean of "a1" and "a2" to use the relation length-angle

I did several paper model using only two strips to understand the limits and the validity of this relation for my problem, and to check the drawing given by the Grasshopper program.

Step 4: Grasshopper Program

I built the grasshopper file starting from:

the axis and the list of nodes position defined in Rhino.
the list of numerical parameters
the shape for the width
the joint length evolution along the strip length

Using all of those inputs, I mathematically constructed the shape "ready to be cut" of strip 1 and strip 2. And I added a display tools (2D and 3D) to help design choices during the design process of the finale lamp.

Important steps of the program:

Computation to find the width of strips (For each nodes we find the width dividing the perimeter (2*pi*Ri) by the number of strips)
Computation of angles a from the nodes position
Computation of lengths "L1" using angles "a" and the previous relation
Computation of the notches orientation for each strips (using the fact that the intersection of two plans is given by the cross product of the normals of those two plans. anyway, this is one of the most cumbersome part of the program)
Drawing of the strips putting together all of the previous data computed before.
Building of 2D and 3D display tools

Step 5: Grasshopper Program - Video

Step 6: Interest of Parametric Design

Using a parametric design technique, it takes more time to develop a design but, as shown in this video, it's easy to make some changes of input, and to directly get the new display and the new drawing of strips "ready to be cut"

Step 7: Laser Cutting

Using the drawing of strips given by the grasshopper program it is easy to cut the strips with a laser cut machine.

The material is birch plywood of 0.6mm bought in model-making shop.( around 30€ for the whole lamp)

Step 8: Assembly

In order to have more flexibility, and to avoid breaks, I put strips into water for around 1 hour before starting the assembly process.

Steps:

I put together the two 1st strips starting from the bottom
I added the strips one by one alternating side, until to get a structure of 27 strips
I put together the 3 last strips
I added those 3 in the structure of 27 to make easier the final part of the assembly.
I added some brass wires in some nodes to tighten the whole structure.
I fixed the light bulb using a plywood washer blocked between the thread and the nut of the cap. and I linked the washer to the structure using a cord.

Note: If you want to try the assembly process is quite difficult, it requires time and patience....but it's possible.

Please let me know if you try to build it, and if you get some new understanding regarding this type of structure, because I'm still working on it...