I guess I'm a little naive. If you want to build your own tapering machine, why do you need other people to tell you how? Tapering machines are not complex machines at all. There's any number of about 4700 options you could use for a slide. I find it utterly fascinating that guys want to build their own equipment, but want others to give them all of their ideas because they lack the knowledge or imagination. Buying a couple linear rails and bearings doesn't make a machine or a machine builder. The point is, if you're unable to look around on the internet to get ideas, look at other pool cue specific machines, and make a decision, machine design and construction isn't for you, building cues probably isn't either! Nobody is going to hold your hand, you need to have some imagination and get it done if you want it done.
You will be better served by educating yourself on a couple things.
1. Screw pitch and lead... This is twofold, you will need to set up a powered longitudinal feed, as well as a manual cross feed.. Understanding how a screw works will help a bunch!
2. For your cross slide and feed ideas, look through the 8020 catalog. Search tapering machine on here. Go to the Thompson Linear website and look at how they construct linear stages, no Pacific Bearings website has a wealth of info too.
Educating yourself will prove more useful than most questions you'll ask on here.