Devious Pythagorean Cup

by jsteuben, published

Devious Pythagorean Cup by jsteuben Jul 25, 2013

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26728Views 2571Downloads Found in Engineering
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The Pythagorean cup is a drinking vessel designed to drain its contents via siphon action if it is overfilled. If the cup is partially filled, it holds liquid which can be drunk in the usual fashion. If it is overfilled it drains the entire contents of the cup into the drinker's lap. This object was classically used as a warning of the dangers of gluttony and over-consumption.

Unfortunately, Pythagorean cups feature a distinctive central stem to house the siphon tube which drains the cup - see for instance http://www.thingiverse.com/thing:27533. This gives away the surprise and spoils some of the fun! Fortunately, modern 3D printing allows us to build a more devious cup, with a hidden siphon.

This object is a Pythagorean cup with the siphon tube concealed in the drinking vessel walls. The siphon tube traverses more than 300 degrees of the circumference of the rim, so a moderately filled cup will not drain when it is tilted. This object has been printed and tested, and is 100% functional! It makes a great brainteaser or science demonstration for students.


This object was originally printed on a Makerbot Replicator 2:

Material: Makerbot True Yellow PLA
Layer Thickness: 0.2 mm
Shells: 3
Temp: 240 C
Infill Type: Hex
Infill Density: 20%
Raft: None
Supports: None

All other settings remained at the Makerware "standard" profile default values. The cup should be oriented in a standing fashion for printing.

For other printers and materials, the chief concern is producing a watertight or nearly watertight surface on the inside of the cup and siphon tube. If you have trouble achieving this, decrease the layer thickness to 0.1mm and bump up the number of shells. If this does not do the trick, tune your extruder for fatter extrusions.

The STL file produces a ~8 cm tall cup at native scale. The STL mesh is dense enough that it should scale up or down very nicely.

I have included the original Solidworks file used to produce the STL in case anyone would like to improve this design. If another file format is requested, please leave a comment.

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The problem with not having the central column is that if the drinker does not know how the cup is designed, they most certainly will spill all their drink. If the user brings the cup to the mouth with the internal pipe closest, the cup will empty. The reason for the central column is that when the cup is brought to the mouth the water level will not rise above the top of the internal pipe. The designer of the first cup probably had the tools to build the pipe in the walls of the cup but choose not to. I designed my own column-less cup not thinking about this and learnt this the hard way.

This is an awesome design! Printed great with 2 shells, 7% infill on a Replicator 2. I can confirm the siphon works.

I made this as is on a CUBE (setting it upright on its base) and it works fantastic! Great design.

At default size, the tube isn't quite big enough and water gets stuck. I had much better results scaling 1.5 times.

Why is the STL file on it's side?

This is because SolidWorks and Makerware do not use the same default orientation of the x-y-z axes. The part should be rotated into a standing orientation for printing.

LOL nice, I like this idea :P