Abstract: In the mechanism study of scroll profile, for the continuity of its derivatives is at least up to the second order for a regular curve, the scroll profile is expressed in terms of its instantaneous center of curvature, radius of curvature and polar angle. The engagement theory of scroll profiles is established under this situation. Aiming at existed problems of general profile designed for scrolls, it carries through deep study and analysis on scroll profile en-gagement theory, conjugate profile pitch line theory, general control equation and general equation. And the geometry equa-tion of stroke volume, inner volume ratio, length of profile and radius of curvature etc. are also studied. Summarization on general scroll profile, conjugate profile pitch line and its control equation are given. The shortage of general scroll profile in exis-tence and the theoretic one sidedness of control equation are ana-lyzed. A new methodology based on functional theory to study scroll profile that widening method for general profile design of scroll compressor is developed. Using functional analysis theory, general functional equation that can represent random geometry and integrate all mathematical models of scroll profile in exiting is established.Then using variation method and functional ex-treme condition, the analytic character of gliding property, first variation, second variation and high order variation, etc. can be studied. It offers an opportunity for studying scroll profile theory adopting functional theory and analyzing scroll profile in differ-ent ranks metric space.

Key words: General profiles, Mathematic models, Scroll compressor, Scrolls