Algodoo

Not working as it should
Failed after few moves near edge.

Yes. I noticed that. Thanks for the feedback. I'm not sure how or where to set the limits of operation without severely limiting the range of motion.

Another way to fix this would be to change the equations of motion to be explicit as opposed to being implicit and iterative. Feel free to post a response with improved equations.

Through trial and error, I was able to locate the limits of both axes where the motion stays linear at the edges. Now, whether or not those limits would severely limit the desired range of motion would be dependent on the real world application. For some applications, a very limited range may be all that's necessary.

When I worked in the real world with real X/Y and multi-axis industrial machinery, we used very precise X/Y tables that used precision ball-screws and linear slides for the needed motions. Of course the limits (hard and soft) were tied to the table base, which made setting the limits very easy.

I took the easy way out and reduced the range of motion. I think that the cause of failure outside the range is due to the iterations diverging at indeterminate points (singularities) of motion. One point is when the four links that can change angle are all parallel to each other. Another point is when the horizontal spring becomes vertical.

It's now linear on all four edges of motion.

I noticed a slight instability at the bottom-left corner (-1.5,-1.5) but that can be smoothed out by increasing the spring damping.

Nice work!