I try to avoid push-ups from the knees if at all possible, and prefer to have my clients perform them in an incline position. The mechanics of a push-up on the knees compared to those while in a fully extended position are very different, primarily in terms of core stabilization and involvement. Push-ups from the knees also have much less of a carry over to a full push-up than one done from an incline.
I agree with Karin. I do have clients who can’t perform a perfect push-up and I make them use the knee option. I also like to have clients try to do a push-up in an incline position by placing their hands either on a bench or a smith machine bar or a step (sometimes from the 2nd, 3rd or 4th step). This way they can still keep their body in a straight line and do a good push up (this option is also great for clients who have hard time getting on the ground). Once they get stronger then I lower the bar or have them perform the push up from a lower step.
I am not quite sure what you are asking.
A push-up which is executed from the knees is a perfectly valid exercise and is great for those who do not have the upper body strength and shoulder girdle stability to handle the load that a full push-up presents. Personally, I’d rather have people to a properly executed push-up from the knees than watch them fudge with a full push-up.