# What is the reasoning for solving inverse kinematics problems?

I am a student, and I am studying robotic arm manipulators. I am focusing on the concept of inverse kinematics, I have understood is the process of finding, from the direct kinematics, the joint varibles.

For easy problems, such as a 2R manipulatoer, I am able to solve algebraically the inverse kinematics problem, but for more complex problems I really get in troubles, and almost every time I can't solve the preoblem.

For example, consider the following arm manipulator:

if I compute the direct (or forward) kinematics of it, I get:

I have tried computing analitically the inverse kinematics for it, but without success.

My problem is that I don't understand how to tackle the problem of the inverse kinematics and so I don't know how to move.

What is the reasoning for solving inverse kinematics problems (both easy and hard) ?