Fibonacci Spiral Clock

Clocks have been part of human lives since ancient times. People used to measure time using sundials and hourglass. The modern analog clock which we see today came into existence in the 15th century. Since then most of our analog clocks have had straight needles for their hands. In this Instructable we are going to build a clock with the Fibonacci spiral hour hand.

Pencil
Ruler
Paper
Compass
Protractor
Cd marker/ permanent marker
A4 size paper
Sheet metal 400*90*1 mm
Tin cutter
Drill machine
Vise
Empty spray can
Mallet

Old analog clock machine

Before understanding the Fibonacci spiral we need to understand the Fibonacci number and Fibonacci sequence.
Fibonacci numbers form a sequence such that each number is the sum of the two preceding ones, starting from 0 and 1.
So, 0+1=1, 1+1=2, 2+1=3, 3+2=5, 5+3=8, 8+5=13...
We get this sequence:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...
The Fibonacci spiral is a spiral that is built by constructing arcs that connect the points of these squares based on the Fibonacci sequence that is assembled in a spiral pattern.
A Fibonacci spiral gets wider or gets further away from the center for every quarter turn it makes.

So far we have talked about the Fibonacci sequence and Fibonacci spiral but what/who is Fibonacci?
Leonardo of Pisa, called Fibonacci, was a medieval mathematician  (1170 – c. 1240).

Fibonacci is famous for two major contributions to the mathematical world.
Fibonacci popularized the Hindu–Arabic numeral system in the Western world primarily through his book Liber Abaci (Book of Calculation).
The send one was an answer to a popular number riddle: If a pair of rabbits, male and female, can mate and every month their offspring produce a pair of male and female rabbits. How many rabbits will there be in one year?
The answer to this riddle gave birth to the Fibonacci sequence.
Can you solve this riddle?
Fibonacci spiral is extensively used in art and photography.

For this step you need an analog clock quartz machine, I have repurposed it from an old broken clock.

Make sure the machine is working properly.

To remove the clock machine from the clock remove the top pin using a nose plier. The top pin is attached to the second needle/ make sure you do not damage the needle although we are going to use only 1 needle in this Instructables the rest could be useful for other Instructables. Now remove other needles which are press-fitted to the machine shaft. Notice that the holes of the needle which are attached to the shaft are different. Unscrew the nut and remove the machine.

Measure all the shaft dimensions and take a note of them.
Mine are as follows.
Minute shaft= 3 mm
Hour shaft= 5mm
Threaded shaft= 8mm

Start with a square of 10cm.

Divide the top and bottom edge into half i.e. 5cm then follow the video to draw the spiral.

The Fibonacci spiral we have drawn is in one dimension but to make a needle we need to have a surface area hence we will offset the curve inwards by 3mm.

Use a compass to outline an offset with the same centers as seen in the video on the previous steps.

The Fibonacci curve is an infinite curve i.e. it will never meet the center but get closer and closer. Draw a circle of 2 cm radius from the center of the curve. This will provide strength and support for the spiral needle.

The spiral needle needs to be lightweight as well as stiff. This is the step that took a lot of time since I had to search for different materials. The solution that came to be was to use a 1mm plexiglass sheet but cutting the sheet into a spiral was a big hurdle. I came across an empty spraying can and experimented on it and was pretty much successful, so let's get started.

First, wrap the Fibonacci curve drawn on paper on the empty spraying can to check if it fits properly.
I am using a standard 400ml spraying can and there is plenty of free space after wrapping the paper on the can.
Make sure the can is empty by pressing the nozzle cap.
Cut open the bottom of the can using a normal can opener. The top of the can can not be opened using a can opener since the can opener cannot fit properly. Use a hacksaw blade to cut the top of the can.
Remove the mixing components in the can such as marbles and let the can dry.
Using a metal scissor cut the can along the seam of the can.
Flatten the can using a mallet or hammer.

Once the can sheet is flattened stick the Fibonacci spiral paper on the metal can sheet using paper glue. Let the glue dry.
Once the glue is dry drill a hole on the center of the spiral of 5 mm( this corresponds to the hour shaft diameter as measured in the earlier step). Now start cutting the outer curve of the spiral using a tin cutter. Make sure your safety gloves are on, the metal burrs are razor sharp and can injure you. Take the help of an experienced person if you think you cannot handle it.
Similarly cut the inner curve of the spiral.
Once the spiral is cut it might have deformed depending on the skill to cut the sheet metal, don't worry flatten the spiral using a mallet.
Small deformations can be cured using a kitchen rolling pin.
Tape the center circle on a flat surface and roll the rolling pin along the curve of the spiral.
Once the spiral is flat sand the edges of the spiral to remove burrs if any.
Once the spiral is perfect paint it black using spray paint.

(P.s. you might have noticed I have drilled the hole after cutting the spiral but drilling the hole before cutting the spiral provides a base for clamping and can avoid any accidents hence I have written drilling first in this step.)

For the base, I am going to use a 1 mm thick GI metal sheet. Stainless steel is preferable. The sheet needs to be stiff. Draw a center line dividing the shortest length of the sheet.

Measure 150 mm from the top of the sheet metal and mark a point on the centerline. Draw a line perpendicular to the centerline on this point using a compass draw a circle of 70mm diameter on this point and divide the circle into 12 equal parts resembling a clock numbering base. We know a circle has 360 degrees and we want to divide it into 12 equal parts so the math works as
360/12 = 30
Place the protractor on the point and mark the points on the circle with 30-degree increments. This will be helpful when marking the numbers in the step ahead.

Drill an 8 mm hole using this point as this center ( this corresponds to the threaded shaft of the clock machine ).

Now, measure 300 mm and mark a point on the centerline from the top edge(short edge ) of the sheet metal. Draw a perpendicular line from this point. Use this line as a base for bending the sheet.

Place the metal sheet in the vise jaws and use a mallet to bend the metal. Make sure the perpendicular line drawn coincides with the jaws of the vice. Make a bend of 85 degrees. Please refer pictures for proper understanding.

Before assembling we need to modify the minute hand. We are going to reuse our old clocks minute hand. In my case, I need to shorten the clock hand. Or you can make your minute hand with the leftover can sheet which we used for making spiral needle.
Now assemble the machine, spiral, and the needle as shown in the picture. Make sure the needles are aligned as shown in the picture.

Without Numbers and markings this can not be called a clock (maybe a kinetic art piece, not a bad idea)

Let's start marking our numbers

We know for 1 full rotation of the minute hand, hour hand rotates 1 unit of the clock i.e. 30 degrees.

Fix the minute and hour hand( Fibonacci spiral) as shown in the picture. This will be the base position that is both the hands are pointing towards 12. Mark this point by tracing the inner as well as the outer curve of the Fibonacci spiral on the metal sheet using a pencil/marker.

Now rotate the knob on the backside of the clock machine such that the minute hand completes 1 full rotation. Make sure the clock hands are rotating clockwise. The minute hand would be pointing at 12 but the hour hand would be pointing at 1. Mark this point by tracing the inner as well as the outer curve of the Fibonacci spiral on the metal sheet using pencil/marker.

Repeat this step 10 more times to complete the marking.

To mark the numbers I am using a drawing stencil with number cutouts.

To darken the marked points I have made use of cd marker.

Alternative

To ease the work a pdf file is provided. Print the file in A4 and cut the center hole as well as the curved markings and wrap the paper onto the metal sheet. If you have followed this instructables properly and made everything properly the paper sheet should snugly fit on the sheet. Make sure the centerline of the paper sheet aligns with the centerline of the metal sheet.

Insert the batteries, set the time and you are good to go.

Use power tool if it eases your job, here I have used basic tools so that it will be easier for any one to replicate this instructables.

If you are still struggling with keeping the spiral stiff here's a tip. Punch the spiral using a flat head screwdriver along the center of the spiral curve, Don't punch too hard we only need to make small indents. This will help stiffen the spiral a bit.

What else could I have used for spiral , please comment down, constructive feedback would be appreciated.

Update:

I had to squint my eyes to measure the time since the color of Fibonacci spiral and minute hand were same.I painted the minute hand white.

I have also provided a PDF of Fibonacci spiral, You no longer have to draw the spiral just print and cut the spiral.

I wish I had a 3d printer, 3d printed or laser cut Fibonacci spiral would have been perfect but not everyone possess one so here I am providing .dxf files for fibonacci spiral and clock base, if you wish you can cut with a laser cutter and skip the hassle to build from scratch.