Your question looks very strange; so I feel a bit confused. My first reaction of the question on robot kinematics was: it's not even "analytical", it's elementary school geometry! And this would be true if you consider simple industrial robots I worked with: 2-3 joints in one plain plus one more... As I could see, this is a majority. However, I do understand, there can be complex system; and I know about the use of neural networks, but that's for really complex systems and ill-posed problems that actually exist.
What I don't understand, is why are you asking about neural network approach while saying "I have already implemented it using analytical way". It you already did it and did correctly, this is an indicator of simplicity of your problem. How can you even think of applicability of neural network approach in this case? Moreover, how can you hope for any definitive answer if you conduct no idea of your robot problem and the complexity of your robot? I have an unpleasant feeling that you poorly understand this matter yourself. I would be very happy if you prove me wrong. To me, it looks like the presence of analytical solutions makes everything else an absurd. What for? Just to be "fashionable"?
I also cannot understand using brackets in "Neural network (fuzzy logic)". Are you talking about so called "neuro-fuzzy" approach. Normally, neural network and fuzzy logic (fuzzy sets and all that) are different branches of mathematics; I'm poorly familiar with neural networks, but fuzzy sets and logic is relatively easy stuff to learn. Again, I'm confused with your question. If there is a potential of using such advanced formalism in your problem, you would learn this stuff anyway, but if your were familiar with the backgrounds, your questions would be different. Do you really understand what are you asking about. Again, I have a feeling your problem is not a technical one but a whole methodical approach to knowledge and its application. And again, I would be very happy if you prove me wrong.
Best specialist I know in neural network, genetic and perhaps fuzzy methods in robotics is Anrew Kirillov, author of AForge.NET Framework: AForge.NET open source framework
]. He is a CodeProject author, you may want to contact him directly through CodeProject.
I saw other more or less relevant works on CodeProject, but you need to perform your search yourself.