Introduction: Cell Phone Gramophone

These are so cool looking. I've been wanting to make one for quite some time now. The mathematics involved in the creation of the bell has put the project on the back burner. Some will read this explanation and find it daunting. Others will at a glance, know what it all means and how to use it.

A compound angle is an algebraic sum of two or more angles. We employ trigonometric identities to connote compound angles through trigonometric functions. The sum and difference of functions in trigonometry can be solved using the compound angle formula or the addition formula. These types of formula are used when working out trigonometric ratios of compound angles.

sin (A + B) = sin A cos B + cos A sin B
sin (A – B) = sinA cosB – cosA sinB

cos (A + B) = cosA cosB – sinA cosB

cos (A – B) = cosA cosB + sinA cosB

tan (A + B) = [tanA + tanB] / [1 – tanA tanB]

tan (A – B) = [tan A – tan B] / [1 + tan A tan B]

sin(A + B) sin(A – B) = sin2 A – sin2 B = cos2 B – cos2 A.

cos(A + B) cos(A – B) = cos2 A – sin2 A – sin2 B = cos2 B – sin2 A.

After lots of googling and head scratching I've put together a calculator to do the math. The project is now off the back burner and in the oven.


Wood (I use a discarded palette)

Cast iron flange, elbow and threaded joint all ½" thread. (I use 3 of each)

Nuts and bolts for attaching the flange

#6x½" screws (I used 33 pcs)

Skill saw



Table saw

Fence for table saw

Miter gauge with a sacrificial wooden extension

Cutting sled for table saw

Box joint jig

Belt sander

A sheet of 120 grit sand paper

Assorted screw drivers

Wood stain


A few natural bristle brushes

Paper bag

Personal protective equipment

Step 1: A Splayed Miter Calculator

A calculator to determine some mathematical requirements for this project is a must. Knowledge of how to make the calculations is also required. The bell of the gramophone is the dilemma at hand. To create an octagon is easy enough 22.5° cuts and Bob's your uncle. But once you start to make the sides splay out from 90° you will find that things get difficult. I've created an Excel file that does the calculations for you. All you do is set the number of sides you want, and the offset angle to determine the miter, tilt and R/L or radius over length ratio. The R/L ratio is the number that you must multiply the chosen radius by to determine the length of each piece. This way you get the diameter you need on the open end.

Step 2: The Master Plan

Having a plan is always a good place to start. This is mine. As you can see I'm no draftsman but it'll do.

Step 3: Wood

OK now with a plan and a calculator were ready to go. Raw material for this project is a nice clean pallet from Brothers Brewing. They get lots of these. Empty bottles and cans come in on them. Grain is delivered on them as well. This one is just a soft wood, spruce or pine I suspect. After looking it over for stones and staples, the skill saw made short work of breaking it down.

Step 4: The Thickness Planer

The thickness planer does a nice job of taking the curve out and dirt off. I took the thickness down to just over 3/8" to allow for some sanding.

Step 5: The Jointer

The jointer cleans up the edge so my table saw can work its magic.

Step 6: Cut All the Pieces

With the one side of each piece planed true, I rip enough pieces for my sides, fronts and backs. I then use my table saw sled to make the cross cuts. The perimeter pieces and the bell pieces can be cut to length. The top and bottom pieces need to be a touch larger so the completed box can be sanded flush once assembled. Due to the size of my raw materials I`ll have to laminate the top and bottom pieces.

Step 7: Set Up the Miter Gauge

My miter gauge needs to be reworked for this project. I need to support both sides of my work. A sacrificial wooden fence must be added.

Step 8: Setting the Angle and Tilt

I used my trusty splayed miter calculator to calculate my settings. Unfortunately my table saws tilt angle setting is no match for the INCRA miter gauge. I`ll do my best to get it as close as I can. I`m not building an aircraft so close enough is good enough. I hope.

Step 9: Cut the Bell Pieces

Cut the first angle then flip the piece end for end. This makes the opposite angle on this cut. I made enough for three bells with three extra pieces in case I needed to replace any.This is close quarters. Be careful! That`s a lot of repetitive cutting. It can`t be stressed enough to know the location of all your fingers, all the time. They don`t grow back.

Step 10: Clean Them Up

With a bit of sand paper, you can clean these up nice. The exterior will be sanded after assembly but, this is your last chance to smooth out the inside.

Step 11: Fan and Tape

Now lets fan the 8 pieces out evenly. If they need any adjustments now is the time. With Frog Tape attach the pieces snugly. Only but them together though, no overlapping allowed. There should be one more strip of tape on the assembly than what is pictured. it will be used to close the bell once its glued up.

Step 12: Glue and Close

Don`t overdo the glue. Use just enough to stick the pieces together. You don`t want it squishing out into the bell. If some does, leave it alone until it dries completely. Then try to remove it without scratching the wood. Pick up the assembly and roll it closed. Squeeze the bell together tightly, then rub the last connecting piece of tape to hold the bell closed. Leave it alone for 24 hrs then remove the tape. The Frog tape is amazing its not cheap but it doesn't bleed through.

Step 13: Laminate

Laminate the top and bottom pieces.

Step 14: Finger Joint

Now cut the finger joints for the boxes. I used an INCRA Ibox tool for this.

Step 15: Glue Them Up

Glue the joints and clamp them up for 24 hrs.

Step 16: Sand

Sand all the pieces. In the first pic the orientation of the piece is wrong. I turned the piece so I sanded with the grain.

The finger joints get sanded flush then the top and bottom edges are cleaned up as well.

Step 17: Drilling

Measure and drill the center hole for the flange. Once that hole is drilled set the flange over it. Now mark and drill the mounting holes. Measuring these all out would be a waste of time. As I said before this isn't an aircraft so close enough is good enough for this step.

Step 18: More Drilling

Now these measurements need to be more precise. Drilling a #6 countersunk hole this close to the edge needs to be measured and drilled carefully.On my first bottom piece I drilled a hole where the opening for the phone will be located. Don't do that!

Step 19: Even More Measuring and Drilling

Now that the tops and bottoms are drilled, marking the sides is pretty simple. Hold each piece in place and mark the locations of the pilot holes. Drilling pilot holes is essential in such a thin piece. If you don't the wall will split during assembly. From this point keep these pieces in sets to assure their holes match up.

Step 20: Assemble and Sand

Now screw everything together and sand the perimeter nice and flush. Also lightly sand the top and bottom to remove any bits around the newly drilled holes. Then very carefully sand all the 90° edges. Just a touch to knock the edge off. This will give the box a nice feel when finished.

Step 21: The Opening

I used a sled on the table saw to make the opening where the cell phone will slide in. Remove the bottom of the box, mark the location of the outer edges of the opening and set the height of the blade. Make each outer edge cut, then lower the blade to about 1/4". Slide back and forth between the outer cuts. Only take small amounts off at a time. Slide the sled forward just slightly for each pass. Once you have all the material removed at this height, slide the sled back and raise the blade a bit higher and continue. use this procedure until you reach the desired height . This will create a nice straight edge to the opening. Be careful. The blade will exit the back of the sled as you advance it forward. You need to be conscious of your thumbs location at all times! They won't grow back!

Step 22: Drill the Bell

The bell needs to be drilled to accommodate the ½" threaded pipe. There isn't much material to remove here, but if you skip this step, you could split the bell opening. Use a ½" forstner bit and go slowly.

Step 23: I Can't Wait

This step isn't required, but it's impossible to wait until assembly time to see how it looks.

Step 24: Staining

Staining is an amazing process. A raw piece of wood comes to life when you add the color to it. Every woodworker has a favorite stain. I like the Minwax product line. For the bell I'm using dark walnut and for the resonator box I've chosen golden oak. The golden oak makes the finger joins on the box look amazing.

Step 25: The Finishing Coat

For the finish I'm using a Minwax product as well. Its a clear semi gloss polyurethane. I applied a coat, wrapped my brush and went thrift store shopping with the wife. Three hours later I wiped all the pieces down gently with a piece of a paper bag to smooth them. Then I coated the outside of the bells and retired for the day.

Step 26: Buff

Its been 24 hrs since I put the polyurethane on. With it now dry I can rub vigorously with the paper. The pieces shined up nice. I'm happy with the finish, so I'll move ahead with the assembly.

Step 27: Add Felt

I played some music with and without the felt pad. Its louder without, but the tone is more harsh. I've opted to add felt but not to glue it in. This way it can be removed if the owner values volume over warmth of sound.

Step 28: The Hardware

I've noticed a decline in the quality of my local hardware stores. I bought the iron pieces at Home Depot after an extensive tour of the hardware stores in my area. I forgot to buy the nuts and bolts. I wanted beveled bolts and nuts with nylon in the threads to keep them from loosening. I went to the two closest stores and found both were out of stock on those items. Home Depot is half an hour drive away. So this is what I purchased. They look pretty nice though.

Step 29: Thredding the 45°

I threaded the 45° into the bell as if I was tapping the hole. Turn a bit then back up then turn a bit and back up over and over. This is a pipe thread fitting so it gets larger as you go. Only go far enough to be stable, you don't want to split the bell. The install into the flange is easy enough, just don't use the bell for leverage. When it starts to tighten up use pliers or a small pipe wrench if you have one.

Step 30: Set Them Up and Smile

These look pretty cool. It looks like I'm at the GRAMMYs

Made with Math Contest

Second Prize in the
Made with Math Contest