i think, really, your definition of perpetual motion is still wrong or at least too confusing.

This is a machine that will, with no friction or loss due to an imperfection of that sort, create energy. Every cycle or whatever, it will have more energy than it did last cycle.

Friction and things like that are NOT the reason these machines don't work. We can theoretically reduce friction to ~0. There are other more fundamental flaws (laws of thermodynamics) which we can never ever ever overcome.

For an example. We can spin a ~frictionless wheel, and it will spin forever. That is not exciting. However, if someone was to design a wheel that actually did spin forever, and it did this with significant friction, that wheel would be creating more energy than it started with every cycle, because it starts with x energy, loses y energy to friction, and then ends up with x energy again.