Accuracy of 3 strings is as accurate as the motors allow. The little steppers I am using move 399 micrometers per step using a 65mm diameter drive. The maths of 3 intersecting spheres says there are two unique points of intersection, and strings don't hang up in gravity. (This means RB3DP won't work on the ISS!!) So, three lengths (radii of three spheres) is sufficient to define a single point in cartesian space. Now, using ODrives means we can have whatever accuracy we want (well, within the arithmetic limits of the driver and feedback). Using ODrives avoids the problems of missed steps (not uncommon with small, cheap steppers) and certainly provides a valuable contribution to overall reliability, too.

I have done a bit of experimenting with a spinning wheel in the horizontal plane and it certainly stabilises the swinging around. However, precession crept in and I just didn't have the skills and time to work out how to brake the spinning by the right amount and at the right time to offset the precessing. I am sure it has already been done, but I couldn't nail it. That's part of the reason for just building a really slow printer, and it'll just have to have a wide stroke to get anything worthwhile done in a practical time.

Ah yes, what I meant by accurate movements is movements that don't wobble around when you accelerate.

I think with gyrosensor feedback you can get pretty far. Still very difficult though.

I wonder what happens if the centre of gravity of the effector is at the effective support point. It does mean that acceleration produces no moment, but it is also an inherently unstable arrangement. Maybe there's a compromise in there somewhere. Engineering and physics challenges abound. Oooh, who wants to have a go before I get to it?

I am wondering why you don't use double strings to also determine the angles of the extruder. That way you'd have a similar kinematics to normal delta printers with a level print platform.

I started several years ago, and just chose to use as simple a physical arrangement as | could think of. I got the idea based on 2D printers hanging on walls with the effector hanging from just two strings. I simply added the third dimension both physically and in the code. It worked on a scale of about a metre. There are no angles needed in either the forward kinematics nor the inverse kinematics. Simple, easy, and works. So, I haven't fixed anything because it wasn't broken.

The RB3DP project (https://hackaday.io/project/13420-rigtigs-big-3d-printer) could be adapted to use ODrives, but RB3DP is still a work-in-progress and not quite ready for forking (but close, I hope). For RB3DP, the motors can be up to 20 or 30 metres apart, so requires 3 ODrive boards. I reckon acceleration is then going to be an issue, since the effector just hangs down, so then need to look at stabilisation of the effector (say like in a quadcopter). Ah! I am getting ahead of myself, but someone might like to try that path before I can get around to it.

The key characteristics of ODrive relevant to RB3DP are the repeatability (precision) and the recovery from movement errors such as lost communications (reliability).

And, yes, I am also inspired by the Hangprinter (https://github.com/tobbelobb/hangprinter).

The RB3DP looks cool, and yeah it could use ODrives. Like you say, it needs a bit of work to avoid it penduluming around with high accelerations. Maybe a gyro sensor and active stabilization? Sounds difficult to have accurate movements though. Maybe consider a 4th string, as in the hangprinter?

Cheers.