Möbius Transformations and the Analytic--Geometric Reconstruction of the Induction--Machine Circle Diagram

The Heyland circle diagram is a classical graphical method for representing the steady–state behavior of induction machines using no–load and blocked–rotor test data. Despite its long pedagogical history, the traditional geometric construction has not been formalized within a closed analytic framework. This note develops a complete Euclidean reconstruction of the diagram using only the two measured phasors and elementary geometric operations, yielding a unique circle, a torque chord, a slip scale, and a maximum–torque point. We prove that this constructed circle coincides precisely with the analytic steady–state current locus obtained from the per–phase equivalent circuit. A Möbius transformation interpretation reveals the complex–analytic origin of the diagram’s circularity and offers a compact explanation of its geometric structure.