A Pressure Angle Function （PAF） was defined. A PAF- ba sed method for generating conjucate tooth profiles was developed. A conjugate in tegral equation was introduced. PAF must satisfy this equation to assure the con jugate action between two conjucate tooth profiles. PAF- based conditions for de termining the cusp of tooth profiles were presented. PAF- based conditions for i dentifying the conjugate limits of tooth profiles were also given. When a PAF is defined

the shape of generated tooth profiles and their geometric properties a re determined. Various types of tooth profiles can be generated systematically b y given different PAFs without rotational coordinates transformation

and the ge ometric properties of generated looth profiles can be also investigated mathemat ically and directly by a given PAF instead of the tooth profiles. Five types of conjucate tooth profiles are generated based on PAFs

and their geometric proper ties are also investigated. PAF may provide a logical and systematic method for gear design.