FYI in the Fusion360 version that you uploaded the ratio control cap, the rack and pinion parts that changes the pushrod stroke, and the shaft that connects the two are missing.
I think I've puzzled out how it works but I'm not 100% without seeing your implementation.
By the way, what you've devised is similar (in effect at least) to some car engine tech that's popping up right now. If instead you imagine the skinny ends of you mechanism being the engine's pistons, then the current input shaft becomes the output shaft. This means you've created a variable length compression system.
Car manufacturers have been after that technology basically forever, here's one that finally made it into production: https://www.youtube.com/watch?v=79LjflIo-5I