Inverse kinematics solves the problem of how to control robot arm joints to achieve desired end effector positions, which is critical to any robot arm design and implementations of control algorithms. It is a common misunderstanding that closed-form inverse kinematics analysis is solved. Popular software and algorithms, such as gradient descent or any multi-variant equations solving algorithm, claims solving inverse kinematics but only on the numerical level. While the numerical inverse kinematics solutions are relatively straightforward to obtain, these methods often fail, even when the inverse kinematics solutions exist. Therefore, closed-form inverse kinematics analysis is superior, but there is no generalized automated algorithm. Up till now, the high-level logical reasoning involved in solving closed-form inverse kinematics made it hard to automate, so it's handled by human experts. We developed IKBT, a knowledge-based intelligent system that can mimic human experts' behaviors in solving closed-from inverse kinematics using Behavior Tree. Knowledge and rules used by engineers when solving closed-from inverse kinematics are encoded as actions in Behavior Tree. The order of applying these rules is governed by higher level composite nodes, which resembles the logical reasoning process of engineers. It is also the first time that the dependency of joint variables, an important issue in inverse kinematics analysis, is automatically tracked in graph form. Besides generating closed-form solutions, IKBT also explains its solving strategies in human (engineers) interpretable form. This is a proof-of-concept of using Behavior Trees to solve high-cognitive problems.