Respected teacher, please give me an example where at a time rectilinear, circular and periodic motion is going on.

Sometimes an object can display combinations of different types of motion: For example A moving car which moves straight on the road displays rectilinear motion but at the same time the wheels of the car which are moving in circles display circular motion. So a moving car displays both rectilinear and circular motion. 

 Every body executing circular motion can be said to be executing periodic motion