This paper studies the surface geometry of roller gear cams with hyperboloid rollers as meshing elements. The surface equation of the hyperboloid roller is established. Coordinate systems and coordinate transformation matrices corresponding to the roller gear cam are defined. The mathematical expressions for the surface geometry of the roller gear cam, by applying the theory of conjugate surfaces, differential geometry, and coordinate transformation, are derived. Based on available surface geometry of the roller gear cam, the unit normal of the cam surface is obtained by differential geometry. The contact lines of the conjugate surfaces are defined according to the equation of meshing and the specified input-output relation. Once the contact line is transformed to the coordinate system which is rigidly connected to the globoidal cam, the surface profiles of the globoidal cam are obtained. Two design examples are given.
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