In honor of the Stella Artois star, the Star Harp is a self-playing harp inspired by orreries, old mechanical models of the motions of the planets around The Sun. It uses the stem of the chalice as a bridge and the bowl as a resonator.
The most finely-crafted orreries include the planetary moons. I started by looking at these mechanisms. The Harp form and other design decisions can all be traced back to these mechanical movements.
Modern Orrery ‘Overweight Archie’
The form of the harp comes mostly from necessity. Its sheath of harp strings must be circular, so the machine’s five mechanical arms can reach each string. And the strings must connect with the soundboard at an angle, so both their transverse and longitudinal vibrations will sing in the sound board, making that harp-like timbre. We end up with a handsome and classic hyperboloid of revolution, a curved surface made from straight lines.
Hyperboloid curves made from straight lines.
The First Paper Prototype
We start with a level zero prototype, a full-sized cardboard model. It’s a fast way to test proportions, design ideas and the spatial interaction of moving parts. It helps us identify and solve many problems before we start using the expensive materials later.
We start with paper or cardboard prototypes
- The harp’s sound board would need to be bigger, for a bigger voice.
- We should adjust the design for 15 gearwheel rings instead of 18, so each gearwheel can be wider and stronger.
- The software will have to be very smart to keep the arms from colliding with each other.
- This instrument was going to be a real looker.
The Hubristic Death First Wooden Prototype
Prototypes answer questions. Often question you hadn’t thought to ask.
How would this complex harp geometry sound and hold up with the tension of 60 strings? We built a stronger prototype with steel and inexpensive woods. The idea was to use 60 strings under the same tension, so they’d have similar timbres. Bridges would divide them into different lengths, following the harmonic curve found in the harp of a piano.
We started with the thinnest piano strings that could hold the tension without snapping. The first few sounded amazing. Why don’t we always use metal strings on harps? I did a quick calculation of the tension using the Taylor Formula. It reported that the fully-strung harp would have to withstand over 1000 lbs of tension. I loved the sound. It wasn’t clear how to calculate the strength of our carefully balanced design. I thought we might just get away with it.
With about one third of the strings on, the prototype warped and imploded! So … math is right. Sorry, no photo. It was a rough moment for Marina and me. We discovered we were still in the forest.
The First Gearwheel Prototype
The Star Harp’s 5 floating arms are mechanically driven by 15 concentric gearwheels. The gearwheels, the largest of which is 8 feet across, must be perfectly round and move with no noise or vibration.
This first prototype was pretty jittery. But it confirmed that the whole mechanism – drive gear, rollers, capstans – generally worked.
I later got it silent by replacing the rollers with slabs of a slippery plastic called Delrin. Now they all just gliiiiide.
The Final Harp Prototype
We applied the lessons we’d learned to what we hoped would be the final prototype. This final harp was made of high quality spruce tone wood, thick slabs of maple, stronger steel tubing, and a homemade layered composite of maple veneer and epoxy.
The harp resonator must be strong enough to hold the tension of the strings and light enough to vibrate freely. We tried to solve this with precise geometric structures. Here, Marina and Jenny are building the resonator:
Marina and Jenny create the delicate inner structure of the harp resonator.
The Second Arm Prototype
The arms of the Star Harp each have an elbow and wrist, which are driven by the turning of the gearwheels on with side of its mast. This report gives a peek into the prototyping process.
In the following prototype, I learned to mount the sprockets to the axles by first freezing/shrinking the axles and heating/expanding the sprockets with a torch. It produced a very clean-looking connection. But each time, there was only one chance to get it right!
In the end we made four generations of arms. The final arms copper counterweights, drive chains, and hand-crafted bearings.
Making The Gearwheels
Making the full set of gearwheels required cutting 90 precise wooden rings by hand. It took about 10 days and I was often ankle-deep in sawdust. As I was cutting, Marina was carefully assembling them in layers, which must have taken two or three weeks, as 75 layers had to be individually glued overnight like this:
Gluing the rings. Or a wooden particle accelerator.
Once assembled, they had to be made perfectly smooth and round. Marina invented a good technique for the largest gearwheels:
Marina put a lot of dust masks through their paces!
The Glass Picks
The stem of the Stell Artois chalice makes a beautiful glass pick with which to play the strings.
Like starry little fishes.
Putting it all Together
Here is the second-to-last prototype, just before adding the steel gears and arm hardware:
The second to last prototype
Aligning the Gearwheels
The gearwheels must be perfectly centered on the 8ft. table, precise to about 1/16th of an inch. We did it old-school style, like da Vinci might have, with just hands and eyes and geometry.
Here, Ranjit helps with some precise measurements:
The First Two Arms
It was a long road. But here are the first two arms moving. You can see the interaction of the big gearwheels with the pair of gears at the base of each arm’s mast.
This may be the most complex software I’ve ever written. It takes a musical score as input and composes a choreography for the mechanical arms, a pre-computed set of motions which pluck the score on the strings. All the software can see is the current time and rotary positions of the 15 motors under the table. Everything about the motion of the arms, including collision avoidance, must be inferred with polar geometry and lots of pre-measured calibration. I spend the first night counting the gear teeth and computing ratios. The biggest gear has over 2500 teeth!
Mechanical Arms Completed
First Working Version
This amazing documentation by Green Card Pictures features the final two prototypes.
I am forever grateful to these kind and ingenious people for all of their assistance:
Marina Litvinskaya – Artist and Master Fabricator
Jeremy Bloom – Gear Wheel Assembly and Alignment, Fabrication, Good Vibes
Ranjit Bhatnagar – Gear Wheel Assembly and Alignment
Nick Yulman – Gear Wheel Assembly and Alignment
Jenny Long – Harp Assembly and Musical Arrangement
Karl Biewald – Gear Wheel Assembly and Alignment