A systematic development for the theory of envelopes with proof is presented. It offers a simple and general procedure to determine the planar and spatial cam profiles. Based on the theory, a planar or spatial cam profile is defined as the envelope of its follower surfaces represented in a parametric form in different relative positions of the cam and the follower. The procedure is illustrated by determining the 2D and 3D cam profiles with analytical formulations. To demonstrate its accuracy and effectiveness, the results are then compared to those obtained by an earlier approach using the screw theory.

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