This study proposes an approach that is based on the theory of envelopes in a parametric form, to derive the analytical expressions of profile surfaces and pressure angles of the cylindrical cams with translating and oscillating arbitrary-shaped followers. The profile curvature is also analysed for the consideration of undercutting. The obtained results are feasible for various types of follower contours, which can be represented by parametric or explicit expressions, and then they can be thought of as the general forms of the cylindrical cam—follower mechanisms. The generalization and practicability in application of the results are also demonstrated in the design and numerical examples.
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