This paper derives equations for the surface geometry of roller gear cams with cylindrical rollers based on coordinate transformation, differential geometry, and theory of conjugate surfaces. Mathematical expressions for the principal curvatures and directions and the pressure angles are also presented. A five-axis machining center is adopted for obtaining the coordinates and directions of the cutter for the final cutting. The conditions of undercutting is discussed for avoiding singular points occurs on the globoidal cam surface during machining process. A roller gear cam in an automatic tool changer for exchanging two parallel cutters is used as an example for illustration.
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