Friday, December 15, 2017

Figure Sculpture Fabricated in Paper

This week my son and I finished fabricating a digital figure sculpt I created three years ago. Well it was a long time coming. But I'm delighted it's done!

It was sculpted from two live models in an embracing pose.

I used ZBrush as I usually do and the result was a high resolution mesh. This was greatly reduced in complexity and unfolded. It was then plotted on paper and cut out. Then the parts were folded up and glued together. The full details of how that was done are shown below. 

Here's a video of the result: 

Fabrication Details

I wanted to make this out of folded paper. This means the higher resolution ZBrush sculpt needed to be decimated down to far fewer triangles. Here's the sculpt at 1000 polygons:

ZBrush decimates nicely. But the arrangement of the triangles is not necessarily aesthetically pleasing. To improve that, but not alter the form much, I used the simple mesh editing tools inside Rhino. The main tools were SwapMeshEdge and SplitMeshEdge.

This takes the form from as on the left to as on the right. The difference is subtle but the flow of the polygons is better at matching the flow of the human body.

Next I wanted to colorize the triangles. I did this using two simple Grasshopper definitions:

The upper one randomly assigns grayscale values to the triangles of the male figure. The lower one assigns a color gradient to the female figure. The lowest triangles get the start of the range and the top most in height get the end of the range.

By changing the gradients you can quickly alter the look and feel:

I settled on this scheme:

To fabricate the parts need to be unrolled and cut out, then reassembled. To unroll we used Pepakura Designer 4. The parts look like this when unfolded in Pepakura, then broken up into smaller sections, then imported into Rhino:

The black lines are cut lines with tabs. The blue are mountain folds (convex portions of the form) and the red are valley folds (concave).

Coloring the Laid Out Parts

Once they are laid out flat the color information is lost. In order to match the laid out parts up with the colored 3D model the area of the triangles are used. This is done with Grasshopper as well. There are two Python nodes to make the overall definition simpler. One converts a triangle mesh into a list of meshes, each which has a single face. These become colored surfaces. The other Python node finds the laid out triangle with the same area.

Triangular surfaces are build with the correct colors. This gets nested on a sheet so they can be plotted at Taubman College. There are cross-hair marks on the corners of the sheet. This allows the sheet to be oriented on the Zund  Knife Cutter bed to match the cutting file.

A simple test was done cutting with a utility knife and securing the tabs with Krazy Glue.

Okay... it works. Onward.

The Zund

The idea was to cut the parts from the sheet on the Zund Knife Cutter. This CNC machine holds a knife (think X-Acto blade) which it can rotate to align with the cut. It's very fast and is perfect for cutting out all the parts... in theory.

The plot is aligned on the Zund using a laser (you can see the small red dot in the image below). I had boxes draw in the corners of the sheet I could use for test cuts to make sure it was aligned well. I cut a few test on opposing corners. It was not perfectly dead on... but was very close. I thought it would come out well.

The result were... drum roll please... horrible! Zoom in and check out the terrible alignment issues:

In addition to alignment issue there were issues with the parts being pulled loose. At maximum vacuum they still came up enough to tear. I'd tape them back down and hope to get through more of the sheet. But all in all it was a disaster:

The corners lined up well. I dunno man, I dunno. I think it might work if I used sheets of plastic. It would be thicker, and have much greater resistance to tearing. That of course still doesn't fix the alignment issue.

Cut and Assembled by Hand

So, the parts were cut by hand: Robots - 0, Humans - 1. Here my son, Kirk, cuts and scores the parts. It took 32 hours to cut and assemble both figures!

This work is challenging and I'm glad he was helping me. 

Almost finished with the assembly:


Here are the figures fully folded and glued.


It's actually quite challenging assembling forms of this complexity. I think about 500 triangles per figure is about the limit of what's doable while maintaining sanity, or at least quality of life. As a first go I thought it turned out well. But both Kirk and I learned some things about how to break up the parts into pieces which are easier to fold. And also some methods of sequence of assembly which make the whole process go easier. Our next attempt will be better!

Thursday, November 30, 2017

Sheet Metal Overview

This post is a simple introduction to metals, with a particular focus on carbon steel sheet metal. It covers metal's place in the periodic table, and the common and mechanical properties of all metals. It also covers how iron is mined and processed. It covers how steel is produced from iron, and some common types of sheet metal used in fabrication.


About three-quarters of the period table is composed of elements which are metal. All those shown below in gray are metal.

Common Properties

Metal elements share several other common properties:
  • They are usually solid at room temperature (mercury is an exception)
  • They are usually shiny.
  • They have a high melting point.
  • They are a good conductor of heat.
  • The are a good conductor of electricity.
  • They are malleable (able to be hammered or pressed permanently out of shape without breaking or cracking). 
  • They are ductile (able to be deformed without losing toughness; pliable, not brittle).
  • They have a high density (exceptions are lithium, potassium, and sodium).
  • They corrode in air or salt-water.
  • They lose electrons in reactions.

Categories: Ferrous and Nonferrous 

There are two main categories of metals used in fabrication. 

Ferrous materials contain iron. Ferrous materials are those primarily found in iron, cast iron, steel and wrought-iron. Other examples are mild steel, medium carbon steel, high carbon steel, stainless steel and high speed steel.

Nonferrous materials do no contain iron, or only extremely small amounts of it. Some examples of nonferrous materials are aluminum, titanium, copper, zinc, and lead.

Ore and Iron 

Metal is mined from the surface of the earth! Iron is the 4th most abundant element on the earth's crust and aluminum is the most abundant metal on the earth's crust. Aluminum, or the ore named Bauxite, comprises 8.1% of the earth's crust. Iron is 5%.

The eight most common elements in earth’s crust, listed by mass, are:
  • 46.6% Oxygen (O)
  • 27.7% Silicon (Si)
  • 8.1% Aluminum (Al)
  • 5.0% Iron (Fe)
  • 3.6% Calcium (Ca)
  • 2.8% Sodium (Na)
  • 2.6% Potassium (K)
  • 2.1% Magnesium (Mg)

Ore is the rock which is mined from the ground from which the metal is extracted. Iron ores are rocks containing iron and other minerals. In certain areas the rocks will contain higher percentages of Iron Oxide - the more iron oxide in the rock the better. The name of the ore depends on the percent content of iron present.
  • Hematite - Fe2O3 - 65% Iron
  • Limonite - Fe2O3+H2O - 50%-65% Iron
  • Taconite - Fe3O3 - 25%-35% Iron
  • Magnetite - Fe3O4 - 22% Iron

Hematite - Image Source

Magnetite - Image Source

Making Iron from Ore

Sometimes the ore is refined by crushing it and concentrating the iron oxide by removing waste rock. This refined ore is made into marble size pellets which are then put into the blast furnace with limestone. The limestone is used as a flux, it melts and removes unwanted impurities in the iron.

The following video is a brief look at the process of extracting iron from ore: 

This next video is a longer (45 minute) and offers a more complete look at the production of iron from ore. It also looks at other uses for iron:

Carbon Steel

Pure, cast iron has a major problem. It's brittle - it breaks easily under impact. In 1856 British engineer Henry Bessemer found a way to make a stronger form of iron. He combined iron with carbon in a blast furnace to make steel. Steel is a a hard, strong, gray or bluish-gray alloy of iron with carbon and usually other elements, used extensively as a structural and fabricating material.

Carbon steel is a steel with carbon content up to 2.1% by weight. As the carbon percentage content rises, steel has the ability to become harder and stronger through heat treating; however, it becomes less ductile. Regardless of the heat treatment, a higher carbon content reduces weld-ability.

Mild or Low-Carbon Steel
Mild steel (steel containing a small percentage of carbon, strong and tough but not readily tempered), also known as plain-carbon steel and low-carbon steel, is now the most common form of steel because its price is relatively low while it provides material properties that are acceptable for many applications. Mild steel contains approximately 0.05–0.25% carbon making it malleable and ductile. Mild steel has a relatively low tensile strength, but it is cheap and easy to form.

Higher-Carbon Steel
Carbon steels which can successfully undergo heat-treatment have a carbon content in the range of 0.30–1.70% by weight. These are known as high-carbon steel.

The term "carbon steel" may also be used in reference to steel which is not stainless steel; in this use carbon steel may include alloy steels.

Sheet Metal

Sheet metal is metal formed by an industrial process into thin, flat pieces. Sheet metal is one of the fundamental forms used in metalworking. It can be cut and bent into a variety of shapes. A great many everyday objects are fabricated from sheet metal. Its thicknesses can vary significantly; extremely thin sheets are referred to as foil or leaf, and pieces thicker than 1/4" (6 mm) are considered plate.

There are many different metals that can be made into sheet metal, such as aluminium, brass, copper, steel, tin, nickel and titanium. For decorative uses, some important sheet metals include silver, gold, and platinum.


In most of the world, sheet metal thickness is consistently specified in millimeters. In the US, the thickness of sheet metal is commonly specified by a traditional, non-linear measure known as its gauge. The larger the gauge number, the thinner the metal. Commonly used steel sheet metal ranges from 30 gauge to about 7 gauge.

Gauge differs between ferrous metals and nonferrous metals such as aluminum or copper; copper thickness, for example is measured in ounces, which represents the weight of copper contained in an area of one square foot.

Cold Rolled Steel

Cold rolling happens at temperatures that are close to normal room temperature. This increases the strength of the finished product through the use of strain hardening by as much as 20 percent. This steel often has a gray finish that feels smooth to the touch.

The cold rolled process creates a finished product that is more precise dimensionally than a hot rolled steel. This is because it is already closer to the finished dimension since it has already gone through the cooling process.

Hot Rolled Sheet Metal

Hot rolled steel comes from a rolling process which happens at temperatures above 1000 degrees Fahrenheit. The steel actually re-configures itself during the cooling process, giving the finished product looser tolerances than the original material and when compared to cold rolled steel metal. Hot rolled steel is more malleable than cold rolled.

Pickling and Oiling

The surface of hot steel reacts with the oxygen and water vapor in the air, forming something similar to a very heavy rust. This is called scale. The scale needs to be removed, and pickling is the name given to the chemical removal of scale (using acid). Once the steel is cleaned it can be oiled to prevent future contamination.

Common Sheet Metals from Alro

Below is a link to the online Alro Metals site. You can use the link to price sheet metal. For water jet cutting in the FabLab we often use Carbon Steel > Sheet > A1008 CR. You can specify the dimensions and add to the shopping cart to get pricing information. 

Alro Online Store - Steel


This section provides a few links to general information about sheet metal and a list of terminology of its mechanical properties: 

Mechanical Properties of Metal

The mechanical properties of a material determine its usefulness for a particular application or product. The following terms help to classify material properties into categories which can be tested. 

Strength: The strength of a material is its ability to resist changing its size or shape when an external force is applied to it.
Malleability: Malleability is the property by which a metal can be rolled into thin sheets.
Ductility: Ductility is the property by which a metal can be drawn into thin wires.
Hardness: Hardness is the ability of material to resist permanent change of shape caused by an external force.
Brittleness: The tendency of material to fracture or fail upon the application of a relatively small amount of force or impact.
Elasticity: Elasticity is the tendency of a solid material to return to its original shape after being deformed.
Creep: When a metal is subjected to a constant force at a high temperature below its yield point, for a prolonged period of time, it undergoes a permanent deformation called creep.
Fatigue: Fatigue is the of material weakening or breakdown of equipment subjected to stress, especially a repeated series of stresses.
Plasticity: Plasticity is the property by which a metal retains its deformation permanently, when the external force applied is released.
Resilience: Resilience is the ability of metal to absorb energy and resist soft and impact load.
Stiffness: When an external force is applied on metal, it develops an internal resistance. The internal resistance developed per unit area is called stress. Stiffness is the ability of metal to resist deformation under stress.
Toughness: When a huge external force is applied on metal, the metal will experience a fracture. Toughness is the ability of metal to resist fracture.
Yield Strength: The ability of metal to bear gradual progressive force without permanent deformation.
Stress: The load per unit area. Types of stress include shear, tensile and compressive stress.
Strain: The unit deformation of a metal when stress is applied.


The following video discusses many aspects of welding:

Tuesday, October 17, 2017

More Ceramic Vessels Made with Robots

In an earlier post I discussed getting started making ceramic vases using a clay extruder and a robot. After those initial attempts I realized I needed to make a few improvements. This post documents the refinements I've made and shows some of the results.

The improvements I wanted to make were:
  • Extrude in a continuous helix rather than individual contours to remove the seam on the side of the vase. 
  • Get the air out of the clay. Air bubbles wreak havoc with the walls of the pot. 
  • Automatically generate the bottom of the vessel so I don't have to manually attach a base. 

Helix Extrusions

Previously I was taking horizontal sections through the 3D form and moving vertically between them. That robot motion creates an ugly seam as shown on the early test pot pictured below:

My new method generates the robot path in a single continuous motion. The process works like this... (in these diagrams the vertical distance of the helix is expanded greatly and the number of points along the helix is reduced greatly to make them more readable)

From the centerline of the vessel horizontal lines are generated starting at the bottom of the vase projecting outward. The intersection of lines and the vase surface are computed (shown as green Xs below). These are connected together in sequence (shown as a green helix).

That forms the path of the robot motion. However this example is far too course a spiral.

This shows an accurate representation of the helix. The vertical spacing is about 3mm per rotation. There are usually about 150 points along each rotation.

Air Bubble Free, Soften Clay

It was clear that a consistently softened and air free tube of clay was critical to getting acceptable results.

The clay has to be softened to work with the extruder. To get more moisture into the clay I cut it into quads, vertically.

The I put towels into the joints. Then add 15 ounces of water to the 25# bag. I let this soak in for at least two days, rotating the bag a few times so all the clay gets exposed. When done the clay is much softer and appropriate for the extruder.

Getting the Clay into the Tube via a Pugmill

A pugmill is used to unify the moisture content in clay and remove air from it. It uses a powerful motor to push the clay through a set of grates which divide the clay into thin rods. These are then pushed through a vacuum chamber. This pulls all the air bubbles out of the thinned clay tubes. The clay is then unified back into a solid mass which is extruded through the end of the mill.

Here's a view of the pugmill disassembled so you can see the auger which pushes, mixes, and compacts the clay, and the grates the clay is pushed through.

Milling the Fixture

I cut the fixture which holds the tube to the pug mill on my router. The fixture was designed by Taubman College FabLab Manager Asa Peller - thanks, Asa.

It goes together with glue and screws. It holds the tubes tightly. And the circular inlet to the tube tapers from the 3" output of the pugmill to the 2-7/8" inside of the tubes.

You can see the finished fixture in the video below.

Milling the Tubes

3D Potter sells the tubes ready to use for $56 each. I wanted 9 so that's $504. That's not acceptable. So I bought  (3) 6' clear PETG plastic tubes, 3" O.D., 2.75" I.D. Those were $188 from McMaster-Carr. I just needed to cut them to length and mill the holes.

I cut plywood supports to hold the tube at each end. There's a dowel through the middle to align them precisely. They are cut 0.01" smaller than the tube diameter.

It's a simple process to cut them on my 4-axis setup. There are 8 holes at each end of the tube, 45 degrees apart. So I helix bore in a few times at increasing depth to get a hole at one end. Move to the other end and do the same. Then rotate the tube 45 degrees. Rinse, repeat - 7 more times.

Using the Pugmill

My research assistants Yixen Xiao and Issam Bourai helped with the pugmill use. Here's a video of it doing a great job loading up air-free clay!

It took 2 hours to load 10 tubes of clay. That was actually fun:

It then took me 4 hours to completely clean the pugmill. Painful! I should have extruded 50 tubes!! Well, I'll enjoy it while I have all this clay ready to go.

The Results

After all the preparation it was time to extrude some new, improved vases! Here's a look at the motion of the robot. As you can see the extruder is fixed in space. The robot draws the helix beneath it.

Here are some pots having just finished extruding and waiting to dry out:

More Refinement Needed

Extrusion of the base layers is messed up! This is easy to clean up manually but can easily be improved. The basic problem is how evenly the extruder runs at startup. That wavy pattern you see in some pots is uneven initial clay output. I can start at the center of the pot and work outward. That'll put the uneven flow on the inside. There are two floor layers so the second one will cover up the first.

It may be time to mount the extruder on the robot and see how that can improve things. This has some potential for better adhesion from layer to layer when cantilevering.