Build a Fibonacci Golden Section Gauge for 1

http://www.instructables.com/id/Build-a-Fibonacci-golden-section-gauge-for-1/

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Build a Fibonacci golden section gauge for $1by matthewtmead on April 15, 2012

Table of Contents

Build a Fibonacci golden section gauge for $1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Intro: Build a Fibonacci golden section gauge for $1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Step 1: Gather materials and tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Step 2: Prepare gauge template . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Step 3: Mark material using templates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Step 4: Cut gauge pieces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Step 5: Lightly torch plastic cutouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Step 6: Mark and drill holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Step 7: Again lightly torch plastic pieces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Step 8: Screw together gauge pieces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Step 9: Test gauge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

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Author:matthewtmead Matthew T. MeadI'm a maker and love building things using wood, metal, software, microcontrollers, fabric and other materials. I love to use creativity to build things withattention toward usability and asthetics.

Intro: Build a Fibonacci golden section gauge for $1Throughout the years I've read a lot about the golden ratio from a design perspective. The Greeks noticed there was a common ratio in nature that was pleasing to theeye. This ratio is 1:1.618 (i.e. 1 to 1.618) and is referred to as the golden section. Today, you will find this golden section reflected in design of buildings, logos, products,artwork, etc.

I wanted to create a durable measuring gauge that would allow me to refer to this ratio when designing things that I build with wood, metal, software and other materials.The gauge in this instructable allows you to measure drawings or on screen items and keep the scale and proportion of elements in a design. And, because the goldensection is about things that are visually appealing, I wanted the gauge to be visual appealing as well.

The gauge has 3 points, which always retains the ratio of 1 to 1.618, even as you expand and collapse the gauge. In the picture, the distance from the center and rightpoint is always 1.618 times the distance of the left to center points.

WOOD magazine has great video regarding the golden section with examples of the golden section in nature (your body), greek architecture and an example of how touse it to design furniture.

And you can read about it in Wikipedia as well.

I was able to build this instructable for $1 and your results should be similar.SIMPLIFICATION OPTION: If you don't want to hassle with cutting plastic on a bandsaw and torching it to get a nicer edge, there is an alternate approach (that I do notcurrently explain) that will reduce the effort and tools required for this instructable. I will create a followup instructable showing a simplified approach using wood.

Image Notes1. As it is widely know, the Parthenon in Greece follows the golden section. Thelower section with pillars is 1.6 times the height of the top section.

Image Notes1. As it is widely know, the Parthenon in Greece follows the golden section. Thetop section of the top is 1.6 times the height of the lower section of the top.


Image Notes1. This side of the gauge shows the "1" side of the 1:1.6 ratio.2. This side of the gauge shows the "1.6" side of the 1:1.6 ratio.

Step 1: Gather materials and toolsWood would be nice for the material to build this measuring device, but I decide that plastic would be more durable and last longer. I wanted to find plastic that would bethe desired thickness (1/8") to provide the right rigidity, but not be too bulky. So I walked around the local Dollar Store and wandered until I found what I thought was themost suitable plastic piece for reuse...a Betty Crocker cutting board. And at $1, the price was right.I also assumed I would use 1/4" aluminum rivets to hold the pieces together. However, as you will read later in this instructable, I found through experimentation, thatrivets did not provide the best mechanical joint and, possibly worse, looked horrible. For this device, that measures what is pleasing to the eye, it is a requirement that thedevice itself is pleasing to the eye. I decided using machine screws provided the best option to holding the tool together. But I'm getting ahead of myself...let's about theparts and tools you'll need.

Tools:- Band saw or some other saw to cut the plastic- Printed PDF of parts template (http://www.scrollsaws.com/images/Lathe/RicksGuage.pdf)- Phillips screwdriver- Propane torch or lighter- Straight edge- Tape- Scissors- Sharpie marker- Safety glasses- Wood or metal file- Center punch- Hammer- Drill- Drill bits (1/8", 9/64", 1/4" and 7/8")Materials:- Plastic for gauge pieces. I used a Betty Crocker cutting board I bought at the Dollar store for $1. I'd recommend material that is about 1/8" thick, although you could varydepending on the material you choose. For example, some people might use cardboard or wood rather than plastic. Bring your template (see step 2) with you to theDollar store to find the appropriate dimensional material. The cutting board (without the handle) is about 5.5" x 8" and just barely fits the template pieces.- 4 6/32 - 1/4" machine screws


Image Notes1. Propane torch. You could use a lighter instead.2. The template (pieces already cut out).3. Tape.4. Drill bits.5. Scissors.6. Small hammer.7. Safety goggles.8. Metal punch for marking holes for drilling.9. Sharpie permanent marker.10. Phillips screwdriver.11. Ruler.12. Metal file.

Image Notes1. 6/32 - 1/4" machine screws2. Plastic material from which to cut out parts. This is a $1 cutting board from aDollar store. The cutting board (without the handle) is about 5.5" x 8". This justbarely fit the template pieces.3. Ruler included to show size.

Image Notes1. Band saw.

Image Notes1. Drill press.


Step 2: Prepare gauge templateIn this step you download and print your template from the Internet.

First, download the template as a PDF. The template, that provides an outline of every part and location for holes to make joints, is NOT something that I created. Thereare many templates on the public Internet. I liked the shape of the following template: http://www.scrollsaws.com/images/Lathe/RicksGuage.pdf

Next, print the template to your printer. I printed to an 8.5 x 11 sheet of regular printer paper.

Finally, tape the pieces to the board or material from which you are going to cut the parts. Try to use only one piece of tape for each template piece as it will interfere withthe outlining in the next step.

As you position the templates, make sure you leave enough room for the kerf (width of your cut) for the blade on your saw. Don't, for example, tape the pieces so theytouch...you need to leave some room for the saw blade to pass between the pieces.

Image Notes1. Template pieces, sitting on board and being positioned. Not yet taped on board. Spread the template pieces apart so the are not touching.

Step 3: Mark material using templatesIn this step we outline each part onto our plastic cutting board material so we know where to cut in a future step.

Start by using a marker (I used a Sharpie) to mark the border of each piece. Note that you need to be careful to mark because the paper can easily be moved by yourmarker. I used one hand to hold down the paper (even though it is also taped) and marked the shape with the other hand.Specifically, I found it easiest to hold the template with one finger and flick the sharpie tip from the template off to the plastic. This resulted in a very jagged and sloppyoutside shape to each piece, but the inside of the outline was perfect (see pictures below). It is important to have a good edge to your markings so you can cut it neatly ina future step.

Keep the cut out templates pieces after marking the board because they are required in a later step.


Image Notes1. The board with all pieces marked. Note that I ended with my pieces pretty close, but was careful to make sure I could cut properly prior to marking.

Step 4: Cut gauge piecesIn this step we cut out the pieces using a band saw.

With your safety glasses on, start by slowly rough cutting all pieces from the large cutting board. This is to ensure you don't accidentally cut into an adjacent piece as youare every so carefully cutting another piece. Go slow.

Once all the pieces are rough cut, slowly keeping an eye on your line, cut each piece. The secret of the bandsaw is to cut close to the line, but not on or beyond the line.You can easily use sandpaper, a sander or file to clean up the pieces once they are cut. Because I was taking my time, I spent about 20 minutes making all my cuts.

Cut your pieces slowly. If necessary, you might not be able to make all turns with your blade, so you might have to make multiple cuts and end up having smaller piecesbeing cut out.

If you have any small pieces of plastic get stuck in the mouth of the saw table, turn off the saw, wait for it to stop, and remove it before continuing. As you are cutting yourpieces, you will notice that plastic is cut away and partially melted and is left hanging from the bottom of the cut piece. You should remove these pieces with a metal file.

Finally, using a file or sandpaper, make sure all pieces are smooth and that any irregular bumps are removed.


Image Notes1. I marked my pieces so the "inside" of the piece has a clean edge to my line.And the "outside" of the piece had a jagged line. As you can see, I'm cutting alongthe inside of the marking to make sure my pieces have straight sides.

Image Notes1. As you cut, small pieces of plastic might get jammed in the mouth of thesaw. Turn off saw and carefully remove.

Image Notes1. First piece was roughly cut out (not shown) and then cut carefully around thetemplate shape.2. Remaining pieces are not yet rough cut.

Image Notes1. Rough cutting the remaining two pieces.

Image Notes


1. See the fuzzy plastic that hangs from the bottom side after a cut. It is easilyremoved using a file.

Image Notes1. Use a file to remove any excess material after cutting with the bandsaw.

Step 5: Lightly torch plastic cutoutsIn this step we play with fire because it is fun. Actually, we use some sort of flame (I used a propane torch) to ever so slightly melt the areas that were cut to make themsmooth and melt any material left hanging on the edge. This step is purely cosmetic and if deadly plastic fumes make you nervous, you should skip this step!

NOTE: I'm sure the fumes from this step are very bad for you to breath, so do this step outside where there is plenty of ventilation. Do not breath the fumes!

Turn your torch to its lowest setting and practice on a piece of scrap material!

Wearing gloves and safety glasses, you want to bring your cut edge close to the flame and let it warm up so it quickly acquires a glossy finish. The material should NOTmelt to the point where your piece is malformed or anything drips from the heat. In fact, the flame should not touch your piece, just the heat from the flame. You can seein a picture below that the flame should be pointed parallel to the piece that is being heated.

When you heat your piece, any loose material should be burned away and any surface that is white from the saw blade should regain its original color (red for me) andalso get a gloss finish.

Image Notes Image Notes


1. This is a piece of scrap material that is being heated prior to treating the realpieces.2. It may not look like it, but this is the lowest setting for the flame.3. Notice that the flame is parallel to the piece that is being treated. Do NOTpoint the flame at the piece or your hand.

1. This is not yet heat treated, lots of white areas, also can see some loosepieces hanging off the left side.

Image Notes1. This piece has been heat treated.

Image Notes1. This area was not yet heat treated, see how it is white from where the sawblade cut the plastic?2. This side has been heat treated and has no white marks and is shiny.

Image Notes1. Here are the parts that have been cut and heat treated.

Image Notes1. A close up of the pieces after they are heat treated. You can see that all thesides are slightly melted and shiny.

Step 6: Mark and drill holesIn this step we will mark the hole location and drill them.

Keep in mind that your cut pieces will likely not be perfect like your printed template, but what is critical is that the points on each piece and the hole position ismaintained. The exact shape of the handles and ends away from the points do not matter as long as the distance from each hole matches the template.

Place the paper template on top of each cut out part so we can see where the holes need to be drilled.

Using a center punch or something with a sharp point, mark the center of each hole in the template. Once the center punch is poking into the paper template, using asmall hammer, put a dent in the plastic piece through the center of the hole in the paper template. Repeat marking all holes using the paper templates.

Before you drill, mark the holes for the appropriate bit (1/8", 9/64", 1/4" and 7/8") using the image below as your guide. The 9/64" hole allows the screws to fit without anyfriction whereas the screws are threaded into the 1/8" plastic hole. The 1/4" hole is simply a way to hang your gauge and the 7/8" hole is for your fingers while using thegauge.

Make sure you have wood underneath your plastic as you are drilling to control tear out and make sure the plastic does not crack. Drill slowly and take your time. Testeach drill bit on scrap plastic prior to drilling the actual gauge pieces.


Image Notes1. All holes are drilled.

Image Notes1. With the pieces all cut, sanded and torched, set the original templates backon top so we can mark the pivot points.

Image Notes1. Using a center punch, carefully mark the center of each hole. It is critical thatthese holes are in the right location relative to the point of the piece in order tomaintain the 1:1.6 ratio.

Image Notes1. See the hole in the template and the mark in the plastic piece.2. See the hole in the template and the mark in the plastic piece.

Image Notes1. All the holes are marked in the plastic pieces. Now we are ready to drill the

Image Notes1. This is a practice hole in a scrap piece of plastic to make sure each bit works


actual holes. as expected. When drilling, go slow!

Image Notes1. Drilling a hole with wood underneath to provide support and prevent crackingthat would occur if the plastic was not supported.

Step 7: Again lightly torch plastic piecesIn this step we use a flame (I used a propane torch) to ever so slightly melt the areas where we just drilled holes to make them smooth and melt any material left hangingon the edge. This step is purely cosmetic and if deadly plastic fumes make you nervous, you should skip this step!

(See step 5 for additional details)


Image Notes1. This is a piece of scrap material that is being heated prior to treating the real pieces.2. It may not look like it, but this is the lowest setting for the flame.3. Notice that the flame is parallel to the piece that is being treated. Do NOT point the flame at the piece or your hand.

Step 8: Screw together gauge piecesIn this step, you will screw together your plastic pieces.

For this instructable, I assumed I would use rivets, but through experimentation using scrap pieces of the plastic material, I found it difficult to rivet the pieces and allowthe pieces to still rotate easily. I tried experimenting with various objects temporarily jammed between the plastic boards to create a temporary gap while inserting therivets. Eventually, I was able to get the rivets to pop and allow the joints to rotate, but ultimately, what drove me to find another option was that the rivet backs looks awful,even after I used a grinder to "knock them down". (See the pictures for details on this experimentation.)So, through experimentation, I decided to use screws that would thread directly into the plastic.

Screw your pieces together as specified in the template PDF. Remember to start your screw through a 9/64" hole and then fasten the screw into a 1/8" hole. See theincremental process of putting the pieces together in the pictures.

Image Notes1. Backside of screw. I decided this looks nice.2. I marked this scrap piece as requiring a 9/64" hole so I didn't forget.3. I marked this scrap piece as requiring a 1/8" hole into which the machinescrew is threaded.4. Scrap pieces I used for experimentation to determine how I was going toattach the pieces at their pivot points.


Image Notes1. Through experimentation and trial and error, I decided a machine screw wasthe cleanest way to connect the pieces.2. Scrap pieces where I experimented with various fasteners.

Image Notes1. I experimented with blind pop rivets and thought the front/top of the rivet looksnice and clean.2. The backside of the rivet does not look very nice. Although it looks nicer if it isground down with a grinder. But ultimately I decided I did not like the way therivet looked.

Image Notes1. Close up of rivet.

Image Notes1. Screwing through a 9/64" hole and threading it into the bottom 1/8" hole.


Image Notes1. First screw holding the two large pieces.


Image Notes1. Second screw holding shorts piece.

Image Notes1. Third screw holding center point piece into place.


Image Notes1. Fourth, and final, screw in place.

Image Notes1. Top 1/4" hole used for hanging gauge.2. The completed tool.

Step 9: Test gaugeIn this step we measure the opening of the gauge to make sure it maintains the 1:1.6 ratio. And we verify the gauge against known golden section architectures.

As you can see in the picture below, I've opened the gauge to a somewhat arbitrary width of 2" and measure the width on the other side of the gauge. The other side isabout 3.2", which is what we expect (2" * 1.6 = 3.2").Additionally, from the picture of the Parthenon in Greece, it is clear that the gauge accurately measures two aspects that follow the golden section.

Image Notes1. 2" on this side.2. 3.2" on this side. (that is the 2" * 1.6)


Image Notes1. As it is widely know, the Parthenon in Greece follows the golden section. Thelower section with pillars is 1.6 times the height of the top section.

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Build a Fibonacci Golden Section Gauge for 1

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