A4–3D Object Prototype

3D Printed King Chess Piece


Background Research

I’ve never 3D printed anything before, so this was a new experience for me. I was familiar with the basics of 3D printing, so I had that going for me, which is nice. The purpose of this project was to A) learn to render 3D objects in Rhino and B) experience 3D printing.

The assignment was largely open-ended, but the spec asked for something that would involve the extrusion, revolution, and boolean functions in Rhino. A class example was a rook chess piece, but I had decided to do a king instead. The specs gave the option of a chess piece other than a rook, so I decided to finish the king.

Staunton chess set (source: http://www.chessantiques.com/jaques/tn/pages/Cook44.htm, via Wikipedia)

I played a bit of chess, especially when I was younger. I was in chess club in elementary school, but I’ve never been particularly good. However, I have read a lot on chess designs. The history of chess is interesting and is rooted in several different traditions. Once the rules and configurations were largely standardized, it left the piece design. Sets could vary in shape and artwork, and this would have an adverse effect on the gameplay — players unfamiliar with a particular set would be at a disadvantage. Plus, some intricate pieces didn’t fit in the hand, or tipped easily. The Staunton design, first made in 1849, created a distinguishable yet and simple and elegant standard.

Summary:

  • Design in Rhino, then 3D print
  • Chess design — Staunton standard

Design

Screenshot of the king piece, first iteration

I quickly drew the profile of the king piece in Rhino. Being my first attempt at 3D printing, I wanted to start conservatively with my design. I inserted a picture of a Staunton king as a background bitmap in Rhino. Using mostly various curve options (parabola by focus, conic, handle, etc.), I created a profile view of the king. I then revolved the shape to make it three-dimensional.

To make the cross at the top, I created a set of boxes in a cross-shape. I then extruded the boxes to make them three-dimensional. After a bit of tweaking, I successfully created a 3D model that I was comfortable with to print.

Summary:

  • Quick design, used revolve and extrude

Printing

The first version printing

The next step was exporting the Rhino model to MakerBot. In the MakerBot software, I set the options, such as material and orientation. I decided to not use the option of supports. While there was overhang that may have warranted the need for supports, I thought it wasn’t that much and the supports would just add hassle. If there was a time to test, now was it.

Printed first iteration

After transferring to the SD card, I began my print. The print, in white PLA, took 1 hour 20 minutes. After that, I looked at my finished product.

It was actually quite good for a first run, but there were some issues:

  • The cross at the top was deformed, likely due to it being too small (1mm in thickness) and lack of supports.
  • The base was too wide — it was easily confused for the raft that the printer puts at the bottom. This made it look incomplete, and make the king too difficult to tip over during normal play (e.g. during a checkmate).
  • Some surface issues on the lower side of the middle disk
Screenshot of the king, second iteration

I quickly fixed these problems, by narrowing the base a bit and enlarging the cross. The cross’s vertical beam went further into the dome, to ensure that its larger size wasn’t more prone to breaking off. I also made the dome a bit more prominent by increasing the angle a bit, for aesthetic reasons.

However, there still was the issue of the boolean function, which I had not yet incorporated into my design.

Summary:

  • Successful first print
  • Some design issues, quickly fixed
  • Need to incorporate more Rhino operations

Boolean Operation

Not wanting to shoehorn a boolean operation into my chess piece, I needed inspiration. A boolean operation in Rhino takes two separate 3D objects and makes them interact — typically a join (combining them) or a difference (punching out material).

Crown sketches

My initial reaction was to create a crown surrounding the cross and to cut out the ridges to make a simple crown. This would create a combined cross and crown, which reminded me of the unique Imperial Crown of the HRE.

I made a new curve rotation on the top surface, creating a proto-crown shape. Then I created a punchout shape and began to arrange it around in a circle.

Aborted crown design on Rhino
Staunton queen crown detail

Unfortunately, I hit a couple problems with my new design idea. Arranging the punchout shapes (the objects creating the boolean difference from the chess piece) was quite difficult. Aligning the semi-circles in a pattern about the circumference of the crown was difficult, and owing to the wedge crown that I created, involved much more math than I anticipated. Furthermore, I felt that the crown shape that I devised was too close to the Staunton queen crown.

Letter punchout inspiration (source: http://www.luxchroma.com/chess-king-p-112.html)

I looked to the internet for new inspiration, and I came across a lighted sign of a king profile with the word “CHECKMATE” down its spine. I wanted to do the same but with the word “KING” — it would add a certain amount of visual flair, without detracting from the simple elegance of the Staunton desing.

Whether or not it would work was a different question. I was unsure if it would print properly — how the piece was printed, meant that the weight of the upper portion of the piece would have to weigh onto the letter punchouts.

I decided to test this with a small piece. I made a box with dimensions of 1x1x3mm, and punched out the letters “KING” vertically about its shaft, using bold Arial font (cleaner lettering). If I printed this vertically, it would show if the letters could come out properly on the king.

Printed “KING” tests, without supports (L) and with (R)

I printed two versions, with and without supports. The supported version had better lettering, but the leftover shards of the supports meant I had to cut, trim, and sand quite a bit. With the small font size, I wasn’t able to cleanly remove the supports. With the unsupported version, the ‘G’ was misshapen without supports.

With neither option particularly desirable, I decided against using the word “KING” on the piece. This meant I had to go back to the drawing board.

Summary:

  • Tried a crown design, but it was too complex and confusing
  • Tried to use the word “KING”, but 3D printing prototypes showed it wouldn’t work

Iteration

I wondered if I could simply do a ‘K’, since it still represented the king, but the K turned out well enough. But the knight piece also starts with a ‘K’. I looked it up on Wikipedia and in algebraic notation, the manner for recording moves and actions in chess, the king is given “K” and the knight is given “N”. However, I noticed that each language has a different letter to represent each piece, reflecting the languages terms for each word. For example, in French, the knight is represented with a “C” (for cavalier — knight), but in Dutch it’s “P” (for paard — horse).

This localization perplexed me, and made my idea for using “K” for king not seem in the spirit of the international standard that Staunton brought.

Algebraic notation icon for king

While on the page of algebraic notation, I recalled the symbols for each piece. The symbols, unlike the algebraic notation, are internationally-recognized. The king symbol is simple enough — simply a crown in the style of the British Imperial State Crown.

As I did with the outline of the king piece earlier, I used the algebraic chess icon as a bitmap background image and trace over it with lines and curves. As with my original small cross, the cross on this bitmap was too small, so I excluded it.

Extruding it took a while, because the shape I made had various line segments and intersections that didn’t make it fully enclosed. But once I cleaned it up, it extruded as a solid object.

Rhino screenshot of my original boolean difference location

My initial idea was to do the boolean difference above the middle disk, but I kept getting an error saying that “Boolean Difference Failed”. From what I gathered from an hour of reading forums, readjusting, and trying, the section I was cutting from was too complex. Cutting from an area composed of two curve revolution areas created too many intersection points.

Final punchout location

I decided to move the cutout lower, to the main shaft. Boolean difference worked this time, since only one curve revolution object comprised the shaft. This seemed to work wonderfully — the universal king icon, on the universal Staunton design was a winning combination.

Summary:

  • Discovered using letter violated the international spirit of the Staunton design
  • Algebraic notation icon fit the spirit and would be printer-friendly
  • Placement of punchout on shaft, caused by Rhino boolean difference issues

Final Print

Printing the second time was as uneventful as before. This time I needed to use supports. Although I knew it would come out rougher, I needed it for the punchout and to prevent the issues with the middle disk’s underside.

Printed final design, with supports

With the supports, I needed to cut, file, and sand the piece, unlike the first round where I only had to rip the base raft off.

Final sanding of the final print

Thanks to my middle school woodshop classes, I knew how to polish it properly. I started by cutting off the supports with an Exact-O knife. I then took a metal file to file off the main shards. Finally, I worked my way up in sandpaper grit — I started with 100 for the rough edges, then 220 for minor smoothing, then finished with 400.

The larger cross and smaller base worked much better. With the supports, the issue of middle disk warping was fixed, too. The punchout was clean, and suffered none of the issues I saw with the “KING” lettering that I had seen.

King piece 3D prints: first iteration (L), second iteration (R)

Summary:

  • Easy second print
  • Supports led to more post-print polishing

Lessons Learned

The project went well, for the most part. Issues between my vision and Rhino’s capability caused issues, but my vision became clearer and more coherent, thanks to the extra time I needed to think it through.

  • Good design needs inspiration, ingenuity, and iteration
  • Having a wide-breadth of knowledge comes in handy when designing
  • 3D rendering and printing have come a long way, but they’re still not perfect, and this requires human ingenuity to make up for it (Rhino’s boolean difference failed, “KING” printing)
  • I’m really a European history nerd