Gear Ratio Corkscrew Help

HI, I'm a new member and a student doing Design Engineering at uni. Im in the middle of creating a corkscrew requiring less force to be used. And also the screw translates vertically, but it is the bottle that rotates not the screw.

The bottle is secured and roatated by a ratchet gear. Meaning it only rotates as the screw is coming down and not going up. The problem I'm having, being a design engineer, is making the maths work for the prototype. I know that one roation of the bottle has to equal the vertical translation of one turn on the screw; and the torque required to free a cork from a bottle is 1.64nm or 14.5 inch pounds. The length of one roatation on the corkscrew is 3mm.

The layout of the screw is a crank, which is turned by the user, which in turn rotates the gear under the bottle, then two more gears as a train (allowing for speed changes) before a pinion gear provides the vertical movement of the corkscrew.
Any help would me greatly appreciated as I've been struggling with this for weeks.

I'm not necessarily asking for the answers... could someone please just show me how to split it up and what equations i need to be looking at as I'm lost!

Many thanks in advance,
Allan

Allan,
Include whatever drawings or sketches you have so far. You'll get much better response.

Also, learn to think in small increments. The first step in analyzing a mechanism is to realize that none of the components involved "know anything at all" about any other components or about the job to be done. They are all blind. You are hearding blind cats. All they "know" is the forces to which they are subjected. That includes both applied forces and supports or restraints. That means that your analysis must focus on each piece individually all the way through the chain of power transmission, while temporarily ignoring all the rest. Often times the best place to start is at the end. Define exactly what the last piece in the chain (either the bottle or the corkscrew) must do. Then, what forces (both applied and restraints) will be required to make motion that happen. Then define how will that piece interact with the components that touch it. Then move to those components. Look closely at them and ask yourself how to get them to move in the manner you require, and how to apply the force you require. And so on down the chain until complete.