Thank you @jan_priban!
I'm already very pleased with you because you have been the only one so far who has understood the essence of this issue and has tried to find this difficult answer.
I believe I understood everything you wrote.
What you've been writing is the same answer that all those experienced in Inventor, in their own way, respond, is the same as I observed before starting this thread:
"A CONSTRAINT CLOSING A LOOP CAUSES OVER-CONSTRAINT THAT LOCKS MOVEMENTS".
1D and 2D ConstraintThe novelty you brought was that this occurs in 1D and 2D with was expected, showing that this behavior is intentional, not a BUG and is the working philosophy of Inventor.
You explained what an over-constraint is, but you did not explain why an over-constrain should cause problems in the Inventor environment.
Let's clarify and organize the objectives.
There are two distinct environments: The Inventor environments and the Real-World environments that the Inventor environments tries to simulate.
Your objective has been to show the workings of the Inventor environments and mine is to show that the Inventor environments is different from the Real-World environments because in the Real-World an over-constraint does not cause problems:
Lines supporting weightFor example: YES, a line is enough to hang a weight, but in the Real-World we can have in parallel how many lines we want and I can define the length of any one, if we vary the lengths of these N lines, the weight will move and the position of the weight is defined by the shorter lines of the same length, if I cut (delete) a shorter, the next shorter ones take up the weight dynamically. I can vary/control/distribute the stresses on the lines by varying their lengths.
In the Inventor environment this is not possible with constraints.
In the Real-World the same occurs with four looped gears (as in the initial image of this thread), the angular position of each gear is defined by its two adjacent gears, each gear receives movement by two distinct paths that divide the forces of movement, this is an over-constraint in the Real-World and this does not cause problems and the movements are free, we continue with the same DOFs. If one gear is removed the other three still continue to rotate because it still has the other adjacent to transfer movement to it.
In the Inventor environment this is not possible with constraints.
I think my post 36 explanation is the truer one so far, that would imply that Autodesk should make corrections to the "Solver" Philosophy/Algorithms/Codes to get closer to being able to simulate the Real-World.
Please think more and see with your colleagues in Autodesk if there is any light, otherwise there are errors in Inventor algorithms that distances it from the Real-World.
Regards