The present invention proposes an inverse kinematics modeling and solving principle for multi-axis systems based on axis invariant, including: the D-H and D-H parameter determination principle based on fixed axis invarian, “Ju-Gibbs” quaternion and class direction cosine matrix principle, the inverse solution principle of general 6R and 7R robotic arms based on axial invariant. These principles are versatile, convenient, and precise. They can be set up as circuits, code, directly or indirectly, partially or completely within a multi-axis robot system. In addition, the present invention also includes analysis verification system constructed on these principles for designing and verifying multi-axis robot systems.