By ground with no platform, I presume you mean the bottom edge of the world window which has a y-coordinate value of one less than the height of the world -- 'getWorld().getWidth()-1'. To keep your actor 'on' the edge (without half of the image of the actor 'below' that edge) you must account for the height of the image of your actor. The y-coordinate of your actor is half way between the top and bottom edge of its image. Therefore, if we ensure that the y-coordinate of your actor does not exceed 'getWorld().getHeight()-1-getImage().getHeight()/2', then you are home free. In short, if the y-coordinate of your actor exceed that value, set it to that value.

I've already did it and also i've got another thread on how to apply the healthbar to my shooting game please help I'm new in greenfoot and my prof didn't teach us anything about this