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I've moved onto that part of the mechanism that I have been trying not to look at - hoping it would somehow resolve itself and let me go on my merry way. The main concern is part of the image in the diagram - a hinge point and linkage that is rather vague and has left me scratching my head. Rather than larking about trying to build a series of model armatures that may or may not work and really amount to devouring precious time, I went about mapping out some of the possible itterations.
To do this, I drew out orbits full scale and the location of a certain point during its rotation based upon gear ratios. I then applied different linkage scenarios and completed the drawing according to artoblevski's schematics. Displaying each armature during different positions and rotations demonstrated that none of my current itterations will produce the desired egg shape - they all produce objects that move on three vectors - generating oddly triangular spirograph shapes. This suggest that the linkage serves to reduce the three vectors down to two and producing the egg shape.
Either way, I found the mapping exercises extrememly helpfull, even if they proved fruitless. The end results are quite attractive and intresting to read.
With the intention of creating a more rugged and usefull mechanism, I went about drafting one up out of card-stock. The goal was to create a gear housing that contained the major orbital mechanisms to one plate that could then provide a clean, interference free surface on which to mount the armatures, all while transmiting any rotation to the neccesary peices. Also, as there are a few other mechanisms developed in the studio that require an exciter ring, I sought to make the mechanism modular so people could swap thier parts onto it [maybe I can rent it out, offset the cost of all this coffee....].
Keeping the weight down and the surfaces clean was a particular goal, so there is countersinking of axles, and significant material removed, while still keeping enough material to be durable. I also opened a small "window" into the gears - they're kind of neat and worth showing I believe. It gives an indication of the mechanism that concealed to keep the interference down.
Here are some pictures of the gear housing - its a good foundation on which to experiment with the next step - the armatures...
I 
immediately looked to solve the issue with the orbits, 
as the other two issues would resolve themselves as the design becomes more refined. To do this, I looked to a spirograph, a precedent that has very obvious links to artoblevski's work. We have been joking / comment on this from the start of the project, so it really wasn't a dramatic leap. The triangular series of arcs contained within the larger orbit suggests that it is transcribed from a point on the smaller circle as it rotates inside the larger one - again, something any seasoned spirograph vetran would spot.
To construct the gears accurately, I utilized the spur gear formulas discovered by carl [see his del.ici.ous site for the links] however, this proved to be ineffective as the gearing it produced wasnt quite right. At the same time, I tried to explore the notion of folding that Patrick has stressed throughout this project - essentially getting the 2D a little more active within the third dimension. Aesthetically, I think it has quite a nice effect, but functionally it compunds some of the issues associated with the gears. I have stepped away from the folding interactions for the time being, with the intentions of resolving a working mechanism before I advance into that stage - however, I havent forgotten about the intent here - I am mindful of the current means of construction and how it can eventually mesh with a more advanced prototype.
Use Dedale
link on right-hand side to see project descriptions.
Refer to Fig. 334 of Generation of Curves, Algerbraic and Transcendental.
How to Draw an Egg, the hard way.
The transformation from schematic to a operating mechanism is proving far more difficult than originally anticipated. The simple act of exploding the digram into its component parts introduces a whole new series of variables and issues. The most significant of these is the interference between the different parts - what "planes" each object is functioning on and how each peice may block or react to eachother. Closely tied to this is the issue of joinery, particulairy the dynamic joints such as sliders and points of rotation. My initial attempt was to simply build it as closely following the schematic as possible - almost a literal interpretation. This allowed me to investigate interference zones, and experiment with preliminary joint connections. It failed to work, and subsequent attempts and "tweaking" led to some creative applications of various four letter words. In addition to puncture wounds sustained from thumbtacks, three main issues emerged from this first iteration:
1. Interference points [obviously]
2. The critical nature of the 90 degree slider joint
3. Actuating both orbits at the same time was difficult and required another approach.
