Spring Based Robotic Arm Design

"If a picture paints a thousand words, then why cant I paint you"

Please provide figures so that its easy to analyze. Having your questions being understood easy is convenient for us readers and commentors. It's one way making this world efficient, don't you think?

Does this simple schematic make it clearer?

the cylinder is for perspective (and the body of the piece will likely be cylindrical)

the dashed line has just enough spring force to keep the load (circle) above a minimum height

the length of the two thin lines (wires) controls the motion of the load

the 2D motion of the load is simple trig, and that should map onto the the z axis (height).

I need to develop a rough tensor function at the load end and be able to spec a spring (or rod or whatever) for "off axis" loading. I would be very surprised if this was novel, "insanely" non-linear or a strictly FEA problem.

i know there are other similar and simpler solutions, but this is for the stage so the abstract qualities of the system as presented here are important.

Oh, your problem now becomes my problem. It is somewhat impossible somehow that the load will just move in circles in (say x, z) plane from the figure you provided.

This is quite not so easy problem but as far as I can recall, i think i encountered it before. What I can give you now is just this tool, however the link pdf is not complete, so i suggest you go look for a text book -> Advance Dynamics

I have experience with using quarter-elliptic springs as hinge points where the spring is also needed. I'm not sure why you want a spring instead of hinge and arm, but it should work OK. The only variation from regular cantilever beam calculations comes from the change in geometry due to large deflections. There are lots of ways to change the shapes or materials to get different degrees and directions of stiffness and to affect durability.

The dynamics on the plane between the two wires is simple trig...

Easyway- are you saying that I can successfully treat subdivisions of the deformed spring as cantilevers? That would be good news.

The trouble with subdividing the cantilever is getting the new starting angle for each section. That takes a lot more calculation. I'd just estimate the loss in length caused by the bending if it is significant. It does not sound as if you need precision for a display job. If you just choose a beam material that would spring back from twice as much deflection as you want, that will probably do. If you want a specific shape of curve, you can tinker with that by partly crushing a tube or planing off some wood where you want more bending.

Thanks for the advice.