Meanwhile, back at the mini roundabout:
My simple lever is a very handy ratio conversion system for a trike but probably quite unsuitable for most bikes. There just isn't much room behind the seat tube/bottom bracket of a bike because of the rear wheel intervening. Though the lever could be placed elsewhere on a bike it has paint damaging and serious cosmetic problems which are probably best avoided.
I doubt a pulley would fit behind the chainwheel but it could be located forward of it with quite normal cable runs. In fact it can be placed anywhere on a normal, "bare" gear cable run. Even high on the downtube, top tube or seat tube if the cable runs that way. All it does is alter the gear lever's pull-per click to that needed for the rear derailleur and cassette. The only real stipulation is that it works on a bare [inner] cable. So it could be placed just below a cable stop on the downtube. Or even on the chainstay provided it doesn't get in the way. It just needs a decent clamp to avoid any movement. Where you want to fit the pulley and its size then become a cosmetic choice.
Making my original double pulley in the lathe left few options for the cable to rise from the smaller to the larger pulley. I had drilled the large pulley radially but it meant a very sharp change in cable direction and far too much friction to pull the cable through the resulting hole. Once committed to the bend there is no chance of further adjustment. The cable had already taken a right angle set and is jammed fast. It can only be pulled back out. Which is decidedly limiting. It was lucky I used a stump of old cable for the first cable threading trial.
Ideally the cable would leave the smaller pulley on a tangent, climb steadily [in radius] and then join the larger pulley again on a tangent. [No bends!] Small flats or "lands" between the three pulleys would provide harmless re-routing. The limited pulley rotation, from moving the changer from each end of the cassette, would avoid potential cable damage at the cable "detours."
On the trike, the cable would enter the pulley system horizontally and leave horizontally after taking almost, two full turns around the entire pulley system. Note how both entry and exit points are low on the pulleys to maintain normal cable runs. The lower image shows the actual cable run though it is limited to an arc of 36mm on the larger pulley rim and 26mm on the smaller pulley. In practice the cable can enter and leave the pulleys at any angle of the user's own choosing. I have digitally removed the unused portion of the middle "ramp" pulley for clarity. It is a normal pulley but offset from the axle of the other two which sandwich it.
The only way I can imagine how this pulley system might be achieved at home is to make three individual pulleys. Then fix them all together later. The pulley unit would be rotated to the correct phase on installation. This new, pull-ratio conversion pulley would be attached to a clamp on the bottom of the seat or down tube with the large pulley just clearing the bottom bracket shell.
The pulleys need not be quite as large as the ones I made to [literally] pivot around the bottom bracket but should not be made too small just for appearance. Otherwise the cable will quickly fray through bending stress and leading the stiff cable around the triple pulleys becomes much more difficult. Why bother making a better one when Jtek can provide a Shiftmate to fray your cables for you?
The hope is that the cable will experience so much friction on its journey twice around the pulleys that no clamping is necessary. A sharp-bottomed, narrow V-profile on the pulley rims, similar to that employed by V-belts, would increase the friction by means of a self-jamming effect. The cable must not slip on the pulleys or the ratio conversion is lost. Jamming would [hopefully] be further increased by the normal gear cable tension. The active radii for ratio conversion lies in the center of the cable when seated on the rims.
I am considering light alloy, rather than Tufnol, for the new pulleys. The ratio in diameter between the two outer pulleys would be as required by the lever/changer/cassette system. 1:1.38, in my case, but wide open to any variation to suit any bike gear system. The only major limitation is not being able to obtain any more gears than the indexing gear lever provides.