Part Description and Specifications for
"Basic Trefoil Modules"

These parts will serve as demonstration and proof of concept for the modularization of some of the Scherk-Collins toroidal structures with the ultimate goal of casting them in bronze or creating an injection mold. They will be used in classes on geometrical modeling and on the math of minimal surfaces, and they serve as small scale models for artists, e.g., Brent Collins, who is creating similar sculptures in wood.

This is part of a research program sponsored by NSF to streamline the process of rapid prototyping of free form parts, by defining a clean separation and interface between designers and fabricators.

All these parts were generated with a recently enhanced version of Carlo Séquin's sculpture generator

The three pieces below are all parts of a Minimal Saddle Trefoil with the following specifications:

branches = 2
storeys = 3
height = 1.50
flange = 1.30
thickness = 0.08
rim_bulge = 1.00
warp = 360.00
twist = -270.00
azimuth = -45.00
textr_tiles = 8
detail = 12
Initial, generated bounding box in arbitrary generator units:
xmax= 2.81, ymax= 1.38, zmax= 2.44,
xmin= -2.31, ymin= -1.38, zmin= -1.88

Module_2

This is one 6th of the Minimal Saddle Trefoil.

FILE ==> trefmod2.stl.gz
The same part in stereo from the other side.

Module_1

This half of the part above, i.e. it is one 12th of the Minimal Saddle Trefoil.

FILE ==> trefmod1.stl.gz

Module_0

This is the other half of the first part on this page; i.e., it is a different 12th of the Minimal Saddle Trefoil.

FILE ==> trefmod0.stl.gz

Fabrication Hints

Basically, the coordinates are given in inches. The scale or strength of these models is not critical; they can be scaled so as to fit optimally a particular process or fabrication machine. However, all three pieces on this page must be scaled by the same amount so that they can fit together.

To make a complete trefoil, three copies of each one of the three modules are needed.

In these .STL files, vertices have not been merged (yet); so they require software that does not get upset when shared vertices appear separated by one unit in the last digit due to rounding errors.

Part Description Files:

Compressed ASCII .STL file: FILE.stl.gz

The compressed file can be downloaded from our anonymous FTP site with:
ftp ftp.cs.berkeley.edu {login as "anonymous"; use your full e-mail address as password.}
Then change directory: cd ucb/projects/unigrafix/STL
Fetch desired files: get FILE.stl.gz
The FILE.stl.gz file can be uncompressed with gunzip.

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