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I guys i'm also VERY,VERY INTERESTED IN THIS TOPIC . I designed a magnetic card last year .. i used a steper motor for the head (more like a floppy). And i would like to improved with a new servo design .. I would also appreciate any information on any IP !
I think you are talking about velocity profiles. Trapezoidal profile is used when you can reach your maximum intended speed. You accelerate in a linear fashion, move at constant speed and then deccelerate. Triangular is the same thing, but when you have a very high programmed speed or a very shot increment of position. In this case you have to begin decceleration before you reach max speed.
Other profiles are used. Second and 3rd order parabolic are the most usefull. Secon order is energy eficient and 3rd order can null acceleration discontinuities, wich is important if you need a very smooth movement.