Abstract
This paper derived the surface profile equations and the meshing equations of the spherical meshing elements from the homogeneous coordinate transformation matrix and the conjugate surface theory proved by the envelope theory. In the machining aspect, we demonstrated the position equation of cam profile using the coordinate transformation theory and obtained the perfected controlling position point of the tool path under the limitation of the chord errors. Finally, the design and the machining module was developed via Visual Basic that generated the cam profile points and the tool path points. The curves from UNIGRAPHICS to test and verify the cam profile equation. To verify the validation of the tool path, a cutting simulation software, VERICUT, is used to simulate the cutting geometry and kinematics of the roller gear cam, and demonstrate the practical application of the developed method.
