i've been searching for some indications of how to apply my calculations of an endless screw to a drawing in solid works , please help me.
My vision of an endless screw is also called a worm gear. It can rotate endlessly, and the gear which follows it will also rotate forever.
In the image shown, it looks like the screw will cease motion once the transport contacts the base.
A thread, or screw can be made in SolidWorks. Newer releases have a "thread wizard", but older releases will utilize a helical path with a swept feature that describes the thread profile.
It sounds like you've invented a new thread with calculus. I'd just suggest practicing with some existing thread standards first to perfect the technique, then you should be ready to model the new thread.