It is almost impossible to design a complex motion for a machine-cycle with one mathematical function only.

Therefore, you usually split, or divide, the motion into a series of motion-periods that you join end-to-end to give a complete machine cycle.

We use the term Segment for a motion-period. We use the term Blend-Point for the instances at the start and end of each Segment.

You can then use a different mathematical-function for each motion-period, or Segment.

We use the term Motion-Law or Cam-Law for the mathematical-function.

Not only do motion-designers need to control when and where to split the motion into different Segments, they must also select the mathematical function that can best satisfy the motion requirements at all points in the machine-cycle, not only at the Blend-Points.

The mathematical-functions, from which you can select, can meet the different requirements of most machine designs, each with different applications or advantages.