Cams are designed to produce a prescribed motion of an output device called a follower. The follower rides on a surface that is machined to produce that desired output motion. The surface is what is called a cam. The cam-follower together are the mechanism,because one without the other is useless. So the question is how are they designed.
The basics of cam design has to start with the kinematics of the follower; i.e., we describe how we want the output and then design the shape of the cam to produce that output.
Like any design, the problem must be defined if it is to be solved. In the case of a cam-follower, we need to know what the output requirements are. That is what is the follower to do and when, A timing diagram is used for this purpose. The timing diagram can be drawn by hand, using a 2D CAD program, or Excel.
After the timing diagram has been completed, a decision needs to be made as to what kinematics profile is needed for the motions of the follower. The properties of each of the kinematic profiles is one way to decide which one(s) to use in each movement. See the video on Kinematic Bascis to understand each of these profiles.