Creating miters in folded plates

Hey folks,

I`m an architecture student and as a beginner in grasshopper I have some problems with my structure. My intention ist to create a structure with folded plates, which shall be in the end made of wood, using a 5-axis milling machine. Each surface is triangular mainly to maintain the surface planar.

For that I will need miters that will be the connections for my plates. Therefore I am struggling to create the joints between my surfaces. My main problem is to get the right angle between my surfaces, because i want to have each angle between two connected surfaces in order to get the right angle (half of the angle between the surfaces) in which the plates connect with each other.

My second problem is to create the volume in a proper way. I tried to extrude the surfaces, but that doesn`t work as intended. I need to create equally plates in terms of thickness. If I use the extrude tool I only get the extrusion in one vector-direction, so it isn`t the same thickness for each plate. I also tried to offset them, but that doens`t work either, because all of them have another direction and offset in other directions. Second problem with the offsetting is that the edges get lost in some way, because they would have to be bigger then the original surfaces in order to maintain the right volume (might be a bit confusing, but thats the point with the connectoin-angle in which the sides of each plate are cutted in half the angle of the angle between the surfaces)

I hope it`s some kind of clear what I am trying to do and I would be really thankful if anyone could help me with this.

I will add some pictures of the 3d model and the grasshopper data, as well as the documents. The whole grasshopper model is based on a curve. each curve will work, but the best results are curves which are approx. 20 units in lentgh (or you change the variables of the data).

The surfaces themselves are made up with the points resulting in dividing my main curve.

Attachments:

Screenshot (5).png, 126 KB
Screenshot (6).png, 413 KB
Grasshopper_Endmodell_Triangular_7.gh, 55 KB

Replies to This Discussion

Permalink Reply by Daniel on June 1, 2016 at 9:36am

the connection should be like the pictures above, if anyone is wondering

Permalink Reply by taz on June 1, 2016 at 9:48am

You want a corner joint with a miter and dovetail connection? That a rather complex combination, even for a 5-axis mill.

Permalink Reply by Daniel on June 1, 2016 at 9:50am

that would be the best option, but if thats too complex, dovetail connections would be enough

Permalink Reply by taz on June 1, 2016 at 9:57am

You may want to look at finger joints, more like this project, but of course you will need to also know your joint angle (assuming it's not 90 degrees).

http://www.archdaily.com/520897/landesgartenschau-exhibition-hall-i...

Permalink Reply by Daniel on June 1, 2016 at 10:23am

Thought of that project as well, but there is a little difference between my intention and this project. The construction was made with more layers, in the inside there is one layer of wood plates and on the outside is one as well, between them there are layers to prevent water coming through the walls. My construction shall be made of one layer of wood. It is a bike canopy and therefor it can`t have all these edges of the finger joints coming out of edges of the plates. But that isn`t that importing in the firstplace, if could show me how to create the finger joints i could manage to solve the problems with the edges by hand.

But it isn`t impossible to create the dovetail/miter connection. There is a youtube video of the procedure https://www.youtube.com/watch?v=-kr7P9LuBuw

unfortunately they didn`t share the gh-data.

Permalink Reply by Daniel on June 1, 2016 at 10:36am

https://www.youtube.com/watch?v=-kr7P9LuBuw

unfortunately they don`t share the grasshopper data

Permalink Reply by taz on June 1, 2016 at 2:26pm

The engineering thesis from the video is interesting.

https://infoscience.epfl.ch/record/205759/files/EPFL_TH6564.pdf

The most recent application of integral finger joints has been presented by the Landesgarteschau Exhibition Hall in Schwäbisch Gmünd, Germany in 2014. (Figure 2.8) This doublycurved, segmented plate shell has been assembled from 243 planar, polygonal components. The parts were fabricated from 50mm thick structural beechwood panels, which form the single, load-bearing layer of this shell structure. Fabrication was carried out in two steps: First, 3-axis rough cuts were performed with a Hundegger SPM CNC Router, then the joints were fabricated, using a robot router setup with an external turntable, similar to the 2011 prototype.

Permalink Reply by taz on June 1, 2016 at 1:59pm

The interior Stuttgart wooden cladding is the same joint type as the video which is not the same as the sketch you posted.

What you showed is (apparently) called a "secret dovetail joint" (see wikipedia):

https://en.wikipedia.org/wiki/Dovetail_joint

Permalink Reply by Daniel on June 8, 2016 at 7:48am

Hi everybody,

I worked a bit on the project and stumbled upon some problems I can`t solve myself.

I need the angle between two connecting plates. It`s easy to measure it for two plates in rhino, but not for every plate in my construction, unless I measure every connection themself and that would be way too much effort.

Is there any option to get the angles between the plates or any way to code it? (I`m definitely not into coding, but maybe someone is and can solve it for me).

Permalink Reply by Daniel on June 8, 2016 at 7:49am

Here is the grasshopper-data, if needed

Attachments: