Please see

Technical Report Inverse Kinematics: a review of existing techniques and intr...

Thanks Dr. Chiad for your suggestion, but this method is a kind of numerical and iterative method and what I am looking for is a kind of closed-form (analytical) solution for IK. But appreciate your answer.

Maybe this article can help you.

https://reader.elsevier.com/reader/sd/pii/S2090447917300965?token=2D5263F93A8978B416282B400B05ABF6BE5A4808B7DB6EA1647406057B4099D3974F17FC7FAF3353CBAF9FD5EA5A2E27

Thanks a lot Dear Neider Romero for your suggestion! Actually working with ANN is one of my favorites too and as I skim the article that you suggested to me, it makes me eager to do something in similar way in future too. But as I read the subject the "Soft computing Method" prepare you finally a black box that however you can use it on your real model and just with some easy calculation and so fast reach the desired target, but unfortunately it prepares a black or at the best try a gray-box of the model, and as my supervisor's purpose is on a totally white-box model, on my current project, this ANN is not working.

I already found a solution for my case and now I am in reporting phase and if somebody are interested in, I will ask my supervisor to publish my initial reports here too.

Best regards.

Shakib Sharifian I will be attentive to your results, since the closed solutions that until now I know are for very particular cases.