RigTigWhat is needed is a way to stop the wobble caused by acceleration of the effector, and possibly the drag of the extrusion material. Two sides of a parallelogram stay parallel even if the angle with the other two sides changes. So, how about we use two strings from each support so the parallelogram is in the vertical plane? Well, that means three attachment points higher and three lower to the effector. Strings can get shorter by folding up a bit, but are (relatively) inextensible. So the parallelograms should be stable enough. Mmm...ok at the effector, but what about the motors?
Well, each motor now needs to wind in and out two strings at the same rate. One motor can handle that easily. Each spare string needs to be kept clear of the other, and still have an accumulator, and that seems to be a simple piece of engineering, too.
There is no change to the kinematics needed, so software is unaffected.
This whole idea was the result of just thinking further about a question asked by @Florian Festi in a reply to one of my comments on Someone please build a parallel cable robot over in https://hackaday.io/project/11583-odrive-high-performance-motor-control. Now, Florian might be disappointed that I have not reverted to kinematics more like a delta printer, but Florian should be pleased that I have been inspired to think further about stability of this printer. Thanks Florian, for making me think about delta printers.
Oh, yeah, and if this idea doesn't work, it is nothing to do with Florian.
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After reading about SkyDelta linked in one of the project comments I am even more convinced that having the cables horizontally is better. The issue with two points with 3 cables each above each other is that this creates a singularity, It is undetermined which point carries how much of the weight. This may lead to instabilities and loose cables and though wobble.
The delta layout is better as it distributes the weight evenly - and predictively - between all cables.
I understand the attraction of the above each other solution: Just bolt the older version below the newest ones and run them in parallel. Even the print head can be fixed by using a chop stick. While this is a good setup to check whether a solution with more strings attached is really worth it, it is likely not as good as the delta layout.
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In the end it does not matter whether you have the strings horizontally side by side or above of each other from a kinematics POV. Side by side requires a triangular platform but it is easier to get the centre of gravity between the attachment points which reduces tilting moments on acceleration.
As you need two points to attach your cables for the above each other configuration you will probably use a stick on top of the extruder to attach the cables to which leaves the weight dangling underneath. This was good for your previous solution as gravity stabilized things but now you stabilize with cables. So I'd guess having the cables parallel might be better (but more redesign work on the extruder).
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